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2.2.2: Color Mixtures


Lesson

Let's see what color-mixing has to do with ratios.

Exercise (PageIndex{1}): Number Talk: Adjusting a Factor

Find the value of each product mentally.

(6cdot 15)

(12cdot 15)

(6cdot 45)

(13cdot 45)

Exercise (PageIndex{2}): Turning Green

  1. In the left cylinder, mix 5 ml of blue and 15 ml of yellow. This is a single batch of green.
  2. Suppose you have one batch of green but want to make more. Which of the following would produce the same shade of green?
    If you're unsure, try creating the mixture in the right cylinder. Start with the amounts in a single batch (5 ml of blue and 15 ml of yellow) and . .
    1. add 20 ml of blue and 20 ml of yellow
    2. double the amount of blue and the amount of yellow
    3. triple the amount of blue and the amount of yellow
    4. mix a single batch with a double batch
    5. double the amount of blue and triple the amount of yellow
  3. For one of the mixtures that produces the same shade, write down the number of ml of blue and yellow used in the mixture.
  4. For the same mixture that produces the same shade, draw a diagram of the mixture. Make sure your diagram shows the number of milliliters of blue, yellow, and the number of batches.
  5. Someone was trying to make the same shade as the original single batch, but started by adding 20 ml of blue and 20 ml of yellow. How can they add more but still create the same shade of green?
  6. Invent a recipe for a bluer shade of green. Write down the amounts of yellow and blue that you used, and draw a diagram. Explain how you know it will be bluer than the original single batch of green before testing it out.

Are you ready for more?

Someone has made a shade of green by using 17 ml of blue and 13 ml of yellow. They are sure it cannot be turned into the original shade of green by adding more blue or yellow. Either explain how more can be added to create the original green shade, or explain why this is impossible.

Exercise (PageIndex{3}): Perfect Purple Water

The recipe for Perfect Purple Water says, “Mix 8 ml of blue water with 3 ml of red water.”

Jada mixes 24 ml of blue water with 9 ml of red water. Andre mixes 16 ml of blue water with 9 ml of red water.

  1. Which person will get a color mixture that is the same shade as Perfect Purple Water? Explain or show your reasoning.
  2. Find another combination of blue water and red water that will also result in the same shade as Perfect Purple Water. Explain or show your reasoning.

Summary

When mixing colors, doubling or tripling the amount of each color will create the same shade of the mixed color. In fact, you can always multiply the amount of each color by the same number to create a different amount of the same mixed color.

For example, a batch of dark orange paint uses 4 ml of red paint and 2 ml of yellow paint.

  • To make two batches of dark orange paint, we can mix 8 ml of red paint with 4 ml of yellow paint.
  • To make three batches of dark orange paint, we can mix 12 ml of red paint with 6 ml of yellow paint.

Here is a diagram that represents 1, 2, and 3 batches of this recipe.

We say that the ratios (4:2), (8:4), and (12:6) are equivalent because they describe the same color mixture in different numbers of batches, and they make the same shade of orange.

Practice

Exercise (PageIndex{4})

Here is a diagram showing a mixture of red paint and green paint needed for 1 batch of a particular shade of brown.

Add to the diagram so that it shows 3 batches of the same shade of brown paint.

Exercise (PageIndex{5})

Diego makes green paint by mixing 10 tablespoons of yellow paint and 2 tablespoons of blue paint. Which of these mixtures produce the same shade of green paint as Diego’s mixture? Select all that apply.

  1. For every 5 tablespoons of blue paint, mix in 1 tablespoon of yellow paint.
  2. Mix tablespoons of blue paint and yellow paint in the ratio (1:5).
  3. Mix tablespoons of yellow paint and blue paint in the ratio 15 to 3.
  4. Mix 11 tablespoons of yellow paint and 3 tablespoons of blue paint.
  5. For every tablespoon of blue paint, mix in 5 tablespoons of yellow paint.

Exercise (PageIndex{6})

To make 1 batch of sky blue paint, Clare mixes 2 cups of blue paint with 1 gallon of white paint.

  1. Explain how Clare can make 2 batches of sky blue paint.
  2. Explain how to make a mixture that is a darker shade of blue than the sky blue.
  3. Explain how to make a mixture that is a lighter shade of blue than the sky blue.

Exercise (PageIndex{7})

A smoothie recipe calls for 3 cups of milk, 2 frozen bananas and 1 tablespoon of chocolate syrup.

  1. Create a diagram to represent the quantities of each ingredient in the recipe.
  2. Write 3 different sentences that use a ratio to describe the recipe.

(From Unit 2.1.2)

Exercise (PageIndex{8})

Write the missing number under each tick mark on the number line.

(From Unit 2.1.1)

Exercise (PageIndex{9})

Find the area of the parallelogram. Show your reasoning.

(From Unit 1.2.1)

Exercise (PageIndex{10})

Complete each equation with a number that makes it true.

  1. (11cdotfrac{1}{4}=underline{qquad})
  2. (7cdotfrac{1}{4}=underline{qquad})
  3. (13cdotfrac{1}{27}=underline{qquad})
  1. (13cdotfrac{1}{99}=underline{qquad})
  2. (xcdotfrac{1}{y}=underline{qquad})

(As long as (y) does not equal 0.)

(From Unit 2.1.1)


2.2.2: Color Mixtures

Let's now look in detail at the process of additive mixing on a computer monitor (Fig. 4.2.1).

Figure 4.2.1. Interactive demonstration of additive mixing of RGB screen colours. Sliders control the brightnesses of the R (top), G(middle) and B (bottom) screen phosphors on a perceptual (nonlinear) scale, like the RGB values seen in Photoshop. Copyright David Briggs and Ray Kristanto, 2007.

With all three lights at maximum intensity the result is white light. This means that in terms of our opponent processing, the redness vs greenness (r/g) and yellowness vs blueness (y/b) opponent signals are both zero. Additionally, in terms of our lightness perception, the screen is seen as having a greyscale value of absolute white, because based on the complete array of colours seen, we judge the brightness of the result to be the maximum possible. With all three RGB lights at 50% on their (perceptual) brightness scales, the light coming from the screen is still white, but the screen is seen as middle grey.

Whenever the RGB primaries are unequal in brightness, however, the r/g and/or y/b signals are unbalanced, and the screen appears coloured. The most saturated coloured mixtures are obtained by combining the red (R), green (G) and blue (B) primaries two at a time, and having the third primary at zero. When R and G are both at their full intensity with B on zero, we see the result as bright yellow. Reducing one or other component shifts the yellow towards red and green respectively. The mixing of red and green light is surprising visually because it involves generation of a strong yellow signal (strongly positive y/b) only subtly evident in the components, and cancellation of their conspicuous r and g signals. (It is additionally unexpected to anyone used to the results of mixing paints). Less surprisingly, mixing the B and G lights in various proportions creates a continuous range of visually intermediate hues with generally negative y/b and negative r/g, passing through a blue-green colour called cyan, while R and B in various proportions generate a range of hues of negative y/b and positive r/g, passing through the red-violet colour we call magenta. Together these pair-wise combinations of primaries span the entire hue circle (Fig. 4.2.2). "Monitor" yellow, magenta and cyan are all lighter than the primaries forming them, for the obvious reason that they are additive mixtures of both of those primaries.

Figure 4.2.2. Additive mixing of RGB colours.

Less saturated (more whitish) colours are produced by adding the third primary. You will see that the position of the slider for the third primary in effect controls the proportion of white light (left from the slider) to coloured light (right from the slider) in the mixture. The parameter of saturation (S) in HSB space is a measure of the coloured component of an RGB colour, and increases as the smallest of the three RGB components decreases.

Keeping the ratio of R/G/B constant while varying the absolute brightnesses generates a series of mixtures of uniform hue and saturation. The maximum brightness of this series is reached when one of the RGB components reaches 100%, because no greater brightness is possible without changing the R/G/B ratio. The position of the slider for the highest primary in effect determines the proportion of black (right from the slider) in the colour. The parameter of brightness (B) in HSB space a measure of the brightness of an RGB colour relative to the maximum possible at that hue and saturation, and increases as the largest RGB component increases.

Mixing of projected light beams (Fig. 4.2.3) is another example of additive mixing, and produces the same results as we saw with on-screen additive mixing, with one important exception: the mixtures are seen as light rather than object colours, and so the less bright mixtures are seen as dimmer light instead of greyed object colours. (You will however see greyed colours if you look at Figure 4.2.3 as a 2D image instead of a 3D scene, and concentrate on the image colours present).


Modelling Mixtures: the Dirichlet distribution¶

You are given a set (mathcal) (here taken as finite) and a probability density (p(x), (p(x)geq 0, sum p(x)=1)) . Also given is a set (A) in (mathcal) . The problem is to compute or approximate (p(A)) . We consider the Birthday Problem from a Bayesian standpoint.

In order to go further we need to extend what we did before for the binomial and its Conjugate Prior to the multinomial and the the Dirichlet Prior. This is a probability distribution on the (n) simplex

It is a (n) -dimensional version of the beta density. Wilks (1962) is a standard reference for Dirichlet c omputations.

With respect to Lebesgue measure on (Delta_n) normalised to have total mass 1 the Dirichlet has density:

The uniform distribution on (Delta_n) results from choosing all (a_i=1) . The multinomial distribution corresponding to (k) balls dropped into (n) boxes with fixed probability ((p_1,cdots,p_n)) (with the ith box containing (k_i) balls) is

From a more practical point of view there are two simple procedures worth recalling here:

To pick ( ilde

) from a Dirichlet prior just pick (X_1, X_2, ldots ,X_n) independant from gamma densities

To generate sequential samples from the marginal distribution use Polya’s Urn: Consider an urn containing (a_i) balls of color (i) (actually fractions are allowed).

Each time, choose a color (i) with probability proportional to the number of balls of that color in the urn. If (i) is drawn, replace it along with another ball of the same color.

The Dirichlet is a convenient prior because the posterior for ( ilde

) having observed ((k_1,cdots,k_n)) is Dirichlet with probability ((a_1+k_1,cdots,a_n+k_n)) . Zabell (1982) gives a nice account of W.E. Johnson’s characterization of the Dirichlet: it is the only prior that predicts outcomes linearly in the past. One special case is the symmetric Dirichlet when all (a_i=c >0) . We denote this prior as (D_c) .

(The Birthday Problem) ¶

In its simplest version the birthday problem involves (k) balls dropped uniformly at random into (n) boxes. We declare a (match) if two or more balls drop into the same box. Elementary considerations Feller (1968, page 33) show that:

Proposition: If (n) and (k) are large in such a way that : (frac<<choose<2>>> longrightarrow lambda) then in the classical birthday problem :

Expand the (log) using (log (1-x)=-x+O(x^2)) to see that the exponent is

Setting the right side equal to (frac<1><2>) and solving for (k) shows that if (kdoteq 1.2 sqrt) , (P(match) doteq frac<1><2>) . When (n=365) , (k=1.2sqrtdoteq 22.9) . This gives the usual statement : it is about even odds that there are two people with the same birthday in a group of 23.

In contrast with the clean formulation above, consider an introductory probability class with 25

students. When considering ‘doing’ the birthday problem, several things come to mind :

  • It is slightly better than a 50-50 chance of success with 25 students.
  • If it fails it’s quite a disaster, 10 minutes of class time with a big build-up, devoted to a failure.
  • If it succeeds, the students are usually captivated and they are interested in learning how computations can dissipate the ‘intuitive fog’ surrounding probability.
  • The students are practically all from the same year, it is quite well known that birthdays within a year are not uniformly distributed far more births occur on weekdays than on weekends (Doctors don’t like to work on weekends, and the induced births and c-sections are never scheduled for weekends). There are also seasonal trends (more births in the summer) and lunar trends.

Taking these things into consideration, you realize that you have no idea what the ‘true underlying probabilities’ are! The considerations above make a match more likely. It seems sensible to carry through a Bayesian version of the birthday problem.

The problem becomes : drop (k) balls into (n) boxes where the chance of a ball falling in box (i) is (p_i) . Here ( ilde

=(p_1,p_2,ldots,p_n)) has some prior distribution on the (n) -simplex (Delta_n) . We will work with a Dirichlet prior (D_< ilde>) , with ( ilde=(a_1,a_2,ldots,a_n)) . This has density proportional to (x_1^ x_2^ cdots x_n^) .

For (a_i=1) we get the classical uniform prior on the simplex.

For (a_iequiv c) we get the symmetric Dirichlet prior.

The Dirichlet prior is the n-dimensional version of the 2-dimensional beta prior we have already studied.

This interpolates between the uniform prior(c=1) and the classical case (p_i=frac<1><365>) ( (clongrightarrow infty) ). For more general choices of (a_i) we get a flexible family of priors.

Let us we carry out necessary computations in the following cases in each we give (k) required for a (50-50) chance of a match when n=365:

Uniform Prior, c=1 (kdoteq .83 sqrt) , for (n=365) , (kdoteq 16)

In coin tossing the standard prior is the uniform on ([0,1]) . The standard prior on the (n-) dimensional simplex (Delta_n) is the uniform distribution (U) where all vectors ( ilde

) have same probability.

The probability of a match, averaged over ((p_1,p_2,ldots,p_n)) , represents the chance of success to a Bayesian statistician who has chosen the uniform prior. As is well known, (Bayes (17. ), Good (1979), Diaconis and Efron (1987)) such a uniform mixture of multinomials results in Bose-Einstein allocation of balls in boxes, each configuration, or composition ((k_1,k_2,ldots,k_n)) being equally likely with chance (displaystyle< frac<1><<choose >>>) . For this simple prior, it is again possible to do an exact calculation:

Under a uniform prior on (Delta_n)

(fraclongrightarrow lambda) , then

Represent the uniform mixture of multinomials using Polya’s urn as described in the introduction. The chance that the first (k) balls fall in different boxes is

approximations detailed in the proof of Proposition [prop1].

Thus in order to obtain a 50-50 chance of a match under a uniform prior (k) must be (.83sqrt) . When (n=365) , this becomes (k=16) , and for (k=23) , (P_u(match)doteq .75) .

The uniform prior allows some mass far from ((frac<1>,frac<1>, ldots, frac<1>)) and such “lumpy” configurations make a match quite likely.

The uniform prior studied above is a special case of a symmetric Dirichlet prior (D_c) on (Delta_n) , with (c=1) . We next extend the calculations above to a general (c) . For (c) increasing to infinity, the prior converges to point mass (delta_<(frac<1>,frac<1>,ldots frac<1>)>) and thus gives the classical answer. When (c) converges to (0) , (D_c) becomes an improper prior giving infinite mass to the corners of the simplex, thus for small (c) , the following proposition shows that matches are judged likely when (k=2) .

Under a symmetric Dirichlet prior (D_c) on (Delta_n) ,

For a proof see the paper here

In order for the probability of a match to be about (frac<1><2>) (k_cdoteq 1.2sqrt>) is needed. The following table shows how (k_c) depends on (c) when (n=365) :

Honest Priors Construct a (2) “hyper”parameter family of Dirichlet priors writing (a_i= A pi_i) , with (pi_1+pi_2cdots+ pi_n=1) . Assign weekdays parameter (pi_i=a) , weekends (pi_i=gamma a) , with (260 a +104 gamma a=1) . Here (gamma) is the parameter ‘ratio of weekends to weekdays’, (roughly we said (gamma doteq .7) ) and (A) measures the strength of prior conviction. The table below shows how (k) varies as a function of (A) and (gamma) . We have assumed the year has (7 imes 52=364) days.


Examples of Mixtures

  1. Air is a homogeneous mixture. However, the Earth's atmosphere as a whole is a heterogeneous mixture. See the clouds? That's evidence the composition is not uniform.
  2. Alloys are made when two or more metals are mixed together. They usually are homogeneous mixtures. Examples include brass, bronze, steel, and sterling silver. Sometimes multiple phases exist in alloys. In these cases, they are heterogeneous mixtures. The two types of mixtures are distinguished by the size of the crystals that are present.
  3. Mixing together two solids, without melting them together, typically results in a heterogeneous mixture. Examples include sand and sugar, salt and gravel, a basket of produce, and a toy box filled with toys.
  4. Mixtures in two or more phases are heterogeneous mixtures. Examples include ice cubes in a drink, sand and water, and salt and oil.
  5. The liquid that is immiscible form heterogeneous mixtures. A good example is a mixture of oil and water.
  6. Chemical solutions are usually homogeneous mixtures. The exception would be solutions that contain another phase of matter. For example, you can make a homogeneous solution of sugar and water, but if there are crystals in the solution, it becomes a heterogeneous mixture.
  7. Many common chemicals are homogeneous mixtures. Examples include vodka, vinegar, and dishwashing liquid.
  8. Many familiar items are heterogeneous mixtures. Examples include orange juice with pulp and chicken noodle soup.
  9. Some mixtures that appear homogeneous at first glance are heterogeneous upon closer inspection. Examples include blood, soil, and sand.
  10. A homogeneous mixture can be a component of a heterogeneous mixture. For example, bitumen (a homogeneous mixture) is a component of asphalt (a heterogeneous mixture).

Contents

Mixtures can be characterized by being separable by mechanical means e.g. heat, filtration, gravitational sorting, centrifugation etc. [8] Mixtures can be either homogeneous or heterogeneous': a mixture in which constituents are distributed uniformly is called homogeneous, such as salt in water, otherwise it is called heterogeneous, such as sand in water.

One example of a mixture is air. Air is a homogeneous mixture of the gaseous substances nitrogen, oxygen, and smaller amounts of other substances. Salt, sugar, and many other substances dissolve in water to form homogeneous mixtures. A homogeneous mixture in which there is both a solute and solvent present is also a solution. Mixtures can have any amounts of ingredients.

Mixtures are unlike chemical compounds, because:

  • The substances in a mixture can be separated using physical methods such as filtration, freezing, and distillation.
  • There is little or no energy change when a mixture forms (see Enthalpy of mixing).
  • Mixtures have variable compositions, while compounds have a fixed, definite formula.
  • When mixed, individual substances keep their properties in a mixture, while if they form a compound their properties can change. [9]

The following table shows the main properties of the three families of mixtures and examples of the three types of mixture.

Mixtures Table
Dispersion medium (mixture phase) Dissolved or dispersed phase Solution Colloid Suspension (coarse dispersion)
Gas Gas Gas mixture: air (oxygen and other gases in nitrogen) None None
Liquid None Liquid aerosol: [10]
fog, mist, vapor, hair sprays
Spray
Solid None Solid aerosol: [10]
smoke, ice cloud, air particulates
Dust
Liquid Gas Solution:
oxygen in water
Liquid foam:
whipped cream, shaving cream
Sea foam, beer head
Liquid Solution:
alcoholic beverages
Emulsion:
milk, mayonnaise, hand cream
Vinaigrette
Solid Solution:
sugar in water
Liquid sol:
pigmented ink, blood
Suspension:
mud (soil, clay or silt particles are suspended in water), chalk powder suspended in water
Solid Gas Solution:
hydrogen in metals
Solid foam:
aerogel, styrofoam, pumice
Foam:
dry sponge
Liquid Solution:
amalgam (mercury in gold), hexane in paraffin wax
Gel:
agar, gelatin, silicagel, opal
Wet sponge
Solid Solution:
alloys, plasticizers in plastics
Solid sol:
cranberry glass
Clay, silt, sand, gravel, granite

In chemistry, if the volume of a homogeneous suspension is divided in half, the same amount of material is suspended in both halves of the substance. An example of a homogeneous mixture is air.

In physical chemistry and materials science this refers to substances and mixtures which are in a single phase. This is in contrast to a substance that is heterogeneous. [11]

Solution Edit

A solution is a special type of homogeneous mixture where the ratio of solute to solvent remains the same throughout the solution and the particles are not visible with the naked eye, even if homogenized with multiple sources. In solutions, solutes will not settle out after any period of time and they can't be removed by physical methods, such as a filter or centrifuge. [12] As a homogeneous mixture, a solution has one phase (solid, liquid, or gas), although the phase of the solute and solvent may initially have been different (e.g., salt water).

Gases Edit

Air can be more specifically described as a gaseous solution (oxygen and other gases dissolved in the major component, nitrogen). Since interactions between molecules play almost no role, dilute gases form trivial solutions. In part of the literature, they are not even classified as solutions. In gas, intermolecular space is the greatest—and intermolecular force of attraction is least. Some examples can be oxygen, hydrogen, or nitrogen.air can be more specifically described as a gases

Making a distinction between homogeneous and heterogeneous mixtures is a matter of the scale of sampling. On a coarse enough scale, any mixture can be said to be homogeneous, if the entire article is allowed to count as a "sample" of it. On a fine enough scale, any mixture can be said to be heterogeneous, because a sample could be as small as a single molecule. In practical terms, if the property of interest of the mixture is the same regardless of which sample of it is taken for the examination used, the mixture is homogeneous.

Gy's sampling theory quantitavely defines the heterogeneity of a particle as: [13]

During sampling of heterogeneous mixtures of particles, the variance of the sampling error is generally non-zero.

Pierre Gy derived, from the Poisson sampling model, the following formula for the variance of the sampling error in the mass concentration in a sample:

in which V is the variance of the sampling error, N is the number of particles in the population (before the sample was taken), q i is the probability of including the ith particle of the population in the sample (i.e. the first-order inclusion probability of the ith particle), m i is the mass of the ith particle of the population and a i is the mass concentration of the property of interest in the ith particle of the population.

The above equation for the variance of the sampling error is an approximation based on a linearization of the mass concentration in a sample.

In the theory of Gy, correct sampling is defined as a sampling scenario in which all particles have the same probability of being included in the sample. This implies that q i no longer depends on i, and can therefore be replaced by the symbol q. Gy's equation for the variance of the sampling error becomes:

where abatch is that concentration of the property of interest in the population from which the sample is to be drawn and Mbatch is the mass of the population from which the sample is to be drawn.


Mercury 115 2+2 How smooth should this idle?

I have a 2005 115hp 2+2 Merc, probably one of the last one's made, just my luck.

This motor runs great, but starts & idles poorly.
Last year my wife and I put on over 800 miles averaging about 3.5mpg per the GPS on several of the Southern waterways. Above idle, this motor runs great, never a miss, sputter, etc.


Its cantankerous when starting, sometimes at the touch of the key, other times it may take several attempts, never predictable, warm, cold, unpredictable starts. Sometimes it idles good, sometimes(usually) it doesn't. Seems like it runs rich at idle, some noticeable blue smoke.

The question I have is how smooth should this engine idle? What are the experiences of other owners of these 2+2? Did Mercury make a motor that idled so poorly, or is it just mine?

Things I've tried: (note this was before the 800 mile run last summer)
Removed and disassembled all 4 carbs( I know, only 2 have idle adjust) blew air through every visible passage way, adjusted the floats, put all back together.
Adjusted the idle screws many times, seems like 1 1/8 to 1 1/4 works about the best.
Motor runs well, just doesn't idle smooth, and starts hard.

The one other observation is that the type of gas seems to make a difference. I'll generally fill up before going to lake/river while boat is still on trailer and its likely that it's gas with the ethanol mix. Later that day while on the water I'll fill up at a marina and I believe the gas doesn't include ethanol, and/or may be a premium (sure costs more). Idle often needs adjusting after a fill, other times no difference.

I noticed in the shop manual that there is a oil injection pump adjustment but it doesn't seem to be clear to me. Anyone have suggestions on if oil pump needs adjusting and how? Again, there seems to be blue smoke at idle at times, but not all times?


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Abstract

A color image encryption scheme is proposed based on Yang-Gu mixture amplitude-phase retrieval algorithm and two-coupled logistic map in gyrator transform domain. First, the color plaintext image is decomposed into red, green and blue components, which are scrambled individually by three random sequences generated by using the two-dimensional Sine logistic modulation map. Second, each scrambled component is encrypted into a real-valued function with stationary white noise distribution in the iterative amplitude-phase retrieval process in the gyrator transform domain, and then three obtained functions are considered as red, green and blue channels to form the color ciphertext image. Obviously, the ciphertext image is real-valued function and more convenient for storing and transmitting. In the encryption and decryption processes, the chaotic random phase mask generated based on logistic map is employed as the phase key, which means that only the initial values are used as private key and the cryptosystem has high convenience on key management. Meanwhile, the security of the cryptosystem is enhanced greatly because of high sensitivity of the private keys. Simulation results are presented to prove the security and robustness of the proposed scheme.


CFR - Code of Federal Regulations Title 21

The information on this page is current as of April 1 2020.

For the most up-to-date version of CFR Title 21, go to the Electronic Code of Federal Regulations (eCFR).

Subpart A - Foods

Sec. 73.1 Diluents in color additive mixtures for food use exempt from certification.

The following substances may be safely used as diluents in color additive mixtures for food use exempt from certification, subject to the condition that each straight color in the mixture has been exempted from certification or, if not so exempted, is from a batch that has previously been certified and has not changed in composition since certification. If a specification for a particular diluent is not set forth in this part 73, the material shall be of a purity consistent with its intended use.

(a) General use. (1) Substances that are generally recognized as safe under the conditions set forth in section 201(s) of the act.

(2) Substances meeting the definitions and specifications set forth under subchapter B of this chapter, and which are used only as prescribed by such regulations.

Substances Definitions and specifications Restrictions
Calcium disodium EDTA (calcium disodium ethyl- enediamine- tetraacetate)Contains calcium disodium ethyl- enediamine- tetraacetate dihydrate (CAS Reg. No. 6766-87-6) as set forth in the Food Chemicals Codex, 3d ed., p. 50, 1981May be used in aqueous solutions and aqueous dispersions as a preservative and sequestrant in color additive mixtures intended only for ingested use the color additive mixture (solution or dispersion) may contain not more than 1 percent by weight of the diluent (calculated as anhydrous calcium disodium ethyl-enediamine-tetraacetate).
Castor oilAs set forth in U.S.P. XVINot more than 500 p.p.m. in the finished food. Labeling of color additive mixtures containing castor oil shall bear adequate directions for use that will result in a food meeting this restriction.
Dioctylsodium sulfosuccinateAs set forth in sec. 172.810 of this chapterNot more than 9 p.p.m. in the finished food. Labeling of color additive mixtures containing dioctylsodium sulfosuccinate shall bear adequate directions for use that will result in a food meeting this restriction.
Disodium EDTA (disodium ethyl- enediamine- tetraacetate)Contains disodium ethyl- enediamine- tetraacetate dihydrate (CAS Reg. No. 6381-92-6) as set forth in the Food Chemicals Codex, 3d ed., p. 104, 1981May be used in aqueous solutions and aqueous dispersions as a preservative and sequestrant in color additive mixtures intended only for ingested use the color additive mixture (solution or dispersion) may contain not more than 1 percent by weight of the diluent (calculated as anhydrous disodium ethyl- enediamine- tetraacetate).

(b) Special use - (1) Diluents in color additive mixtures for marking food - (i) Inks for marking food supplements in tablet form, gum, and confectionery. Items listed in paragraph (a) of this section and the following:

Substances Definitions and specifications Restrictions
Alcohol, SDA-3AAs set forth in 26 CFR pt. 212No residue.
n-Butyl alcohol Do.
Cetyl alcoholAs set forth in N.F. XI Do.
Cyclohexane Do.
Ethyl celluloseAs set forth in sec. 172.868 of this chapter
Ethylene glycol monoethyl ether Do.
Isobutyl alcohol Do.
Isopropyl alcohol Do.
Polyoxyethylene sorbitan monooleate (polysorbate 80)As set forth in sec. 172.840 of this chapter
Polyvinyl acetateMolecular weight, minimum 2,000
PolyvinylpyrrolidoneAs set forth in sec. 173.55 of this chapter
Rosin and rosin derivativesAs set forth in sec. 172.615 of this chapter
Shellac, purifiedFood grade

(ii) Inks for marking fruit and vegetables. Items listed in paragraph (a) of this section and the following:

Substances Definitions and specifications Restrictions
AcetoneAs set forth in N.F. XINo residue.
Alcohol, SDA-3AAs set forth in 26 CFR pt. 212 Do.
BenzoinAs set forth in U.S.P. XVI
Copal, Manila
Ethyl acetateAs set forth in N.F. XI Do.
Ethyl celluloseAs set forth in sec. 172.868 of this chapter
Methylene chloride Do.
PolyvinylpyrrolidoneAs set forth in sec. 173.55 of this chapter
Rosin and rosin derivativesAs set forth in sec. 172.615 of this chapter
Silicon dioxideAs set forth in sec. 172.480 of this chapterNot more than 2 pct of the ink solids.
Terpene resins, naturalAs set forth in sec. 172.615 of this chapter
Terpene resins, syntheticPolymers of [alpha]- and [beta]-pinene

(2) Diluents in color additive mixtures for coloring shell eggs. Items listed in paragraph (a) of this section and the following, subject to the condition that there is no penetration of the color additive mixture or any of its components through the eggshell into the egg:

Alcohol, denatured, formula 23A (26 CFR part 212), Internal Revenue Service.

Diethylene glycol distearate.

Dioctyl sodium sulfosuccinate.

Ethyl cellulose (as identified in § 172.868 of this chapter).

Ethylene glycol distearate.

Pentaerythritol ester of fumaric acid-rosin adduct.

Polyethylene glycol 6000 (as identified in § 172.820 of this chapter).

Rosin and rosin derivatives (as identified in § 172.615 of this chapter).

(3) Miscellaneous special uses. Items listed in paragraph (a) of this section and the following:


Preparation of two novel monobrominated 2-(2′,4′-dihydroxybenzoyl)-3,4,5,6-tetrachlorobenzoic acids and their separation from crude synthetic mixtures using vortex counter-current chromatography

The present work describes the preparation of two compounds considered to be likely precursors of an impurity present in samples of the color additives D&C Red No. 27 (Color Index 45410:1) and D&C Red No. 28 (Color Index 45410, phloxine B) submitted to the U.S. Food and Drug Administration for batch certification. The two compounds, 2-(2′,4′-dihydroxy-3′-bromobenzoyl)-3,4,5,6-tetrachlorobenzoic acid (3BrHBBA) and its 5′-brominated positional isomer (5BrHBBA), both not reported previously, were separated from synthetic mixtures by vortex counter-current chromatography (VCCC). 3BrHBBA was prepared by chemoselective ortho-bromination of the dihydroxybenzoyl moiety. Two portions of the obtained synthetic mixture, 200 mg and 210 mg, respectively, were separated by VCCC using two two-phase solvent systems that consisted of hexane–ethyl acetate–methanol–aqueous 0.2% trifluoroacetic acid (TFA) in the volume ratios of 8:2:5:5 and 7:3:5:5, respectively. These separations produced 35 mg and 78 mg of 3BrHBBA, respectively, each product of over 98% purity by HPLC at 254 nm. 5BrHBBA was prepared by monobromination of the dihydroxybenzoyl moiety in the presence of glacial acetic acid. To separate the obtained synthetic mixture, VCCC was performed in the pH-zone-refining mode with a solvent system consisting of hexane–ethyl acetate–methanol–water (6:4:5:5, v/v) and with TFA used as the retainer acid and aqueous ammonia as the eluent base. Separation of a 1-g mixture under these conditions resulted in 142 mg of 5BrHBBA of ∼99% purity by HPLC at 254 nm. The isolated compounds were characterized by high-resolution mass spectrometry and proton nuclear magnetic resonance spectroscopy.

Highlights

► First practical application of vortex counter-current chromatography (VCCC). ► Synthesis of two novel monobrominated benzoylbenzoic acids. ► Conventional and pH-zone-refining VCCC for separation of synthetic mixtures.


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