How much citric acid you should weight to get a specific pH

So you don’t like the smell of ACV or you just don’t have it on hand and want to replace it with citric acid instead? Or maybe ascorbic acid? This post is meant to help you to calculate the correct amount of the acid you’ll need to use in order to get the same pH you would get with ACV.

Note: If you’re already familiar with basic chemistry concepts, you can skip right away to the “STEPS” part of this post.

Before you read this post, I encourage to you to read first about pH here.

As I mentioned in the post about pH, acids and bases alter the amount of HYDROGEN or PROTONS (H+) and Hydroxide (OH-) ions in the solution. In this post we’ll focus on ACIDS.

Basically, an acid is a molecule, which upon contact with water will release protons (H+) to the water. Chemically this is written as:
1. HA → H+ + A-

Where HA – is an acid, and A- – is its CONJUGATE BASE (or the salt of the acid).

There are STRONG acids, which will FULLY dissociate in water to form H+ and A-, leaving no HA molecules. There are WEAK acids, which will PARTIALLY dissociate to form H+ and A-, leaving some original HA molecules. When you put the weak acid in water, an EQUILLIBRIUM will be formed between the three types of species. Which means that all three (the acid, HA, its salt, A-, and the protons, H+) will present together in the solution.

Now, if you live in America, you’re probably familiar with the “Bragg Organic Raw Apple Cider Vinegar”.

According to the label, it is diluted to 5% acidity. Which means it has 5% Acetic acid.

Chemical note: Acetic acid has a chemical formula of CH3CO2H (also is abbreviated as AcOH).

Acetic acid is a WEAK acid, which means that it does not fully dissociate in water. This means that once you add pure acetic acid to water, some of it will dissociate to form protons (H+) and acetate ions (its conjugate base), which is abbreviated as AcO-, and some will remain in its acid form. Chemically this is written as:
AcOH → AcO- + H+

One can calculate the acid dissociation constant, Ka, which is a measure of the strength of an acid in solution, or in other words, how much of the acid has dissociated. The formula for Ka is:
2. Ka=[A-][H+]/[HA]
and for the acetic acid:
Ka=[AcO-][H+]/[AcOH]

Which means – take the concentration of the acetate ion, multiply it by the concentration of protons, and divide it by the concentration of acetic acid. For many practical purposes it is more convenient to discuss the logarithmic constant, pKa, which is define as:
3. pKa=-log [Ka]

There are many already existing tables containing the Kas and pKas of different acids. Take this one for example.

Looking at the table you’ll find that Acetic has a pKa of 4.75.

To calculate the pH of the acetic acid in water we use the following formula:
4. pH=-1/2×logC+1/2×pKa

Where C is the initial concentration of acetic acid, used here in units of mol/L

5% Acetic acid means that in a 1kg solution, you can find 0.05 * 1000g = 50g acetic acid.
In order to find out the concentration you’ll have to know the MOLAR MASS (Mw) of your acid. This can be easily found out on the internet.

With the molar mass of your acid in your hands, you can now calculate its concentration using the following formula:
5. C=m/(Mw*V)

Where m – is the mass of the acid, Mw – its molar mass, V – the volume of water.

Water (in its liquid form) has a density of 1 g/cm³. Which means that 1L of water weighs 1kg. Because acetic acid takes 50gr of our 1kg of solution, this leaves as with a volume of 0.95L water. So our acetic acid concentration is then:
C=50g/(60.05g/mol×0.95L)=0.876mol/L

Now we can calculate the pH of 50g acetic acid in 1L water using eq. #4:
pH=-1/2×log(0.876)+1/2×4.75=2.4

Note: The actual pH of the “Bragg Apple Cider Vinegar” is 3.075. This is because the calculation we’ve made doesn’t take into account all the different factors that influence the final pH of ACV. I’ve added a note on the subject at the end of this post.

Now let’s say we don’t have ACV and we want to use citric acid instead. Here are the steps to calculate the amount of citric acid you’ll need:

*—STEPS—*
1. Decide which pH you need – In our case, pH=3.075.
2. Go find pKa of your acid – In our case, the pKa of citric acid is 3.08.
3. Use the following formula to calculate the needed concentration:
C=10^[(1/2×pKa-pH)]

In our case this turns out to be –
C=10^[(1/2×3.08-3.075]=0.0292mol/L

4. Find out the molar mass of your acid – In our case, this is 192.124 g/mol
5. Find the mass of the acid you’ll need for your volume using the following formula:
m=C×Mw×V

In our case, we want to substitute 24g of ACV with 24g of water with citric acid. Water has a density of 1 g/cm³, so 24g is 24mL or 0.024L. Therefore:
m=0.0292 mol/L×192.124 g/mol×0.024L=0.13g

So here you go. In order to substitute 24g of ACV with citric acid solution having the same pH, you’ll need to use 0.13g of citric in 24 g of water.

For the fun of it, let’s say that you have only ascorbic acid (also known as Vitamin C) and you’ve decided to use it instead of ACV. The pKa of ascorbic acid is 4.10. This means that you’ll need a concentration of 0.0944mol/L. With molar mass of 176.12 g/mol, this means you’ll need to weigh 0.40g of Vitamin C to get the same pH. I hope this gives you an idea how to choose your acid.

Few notes:
1. If you go and search for citric acid in a typical pKa table, you will find out several values: Citric (1) – pKa=3.08, Citric (2) – pKa=4.74, Citric (3) – pKa=5.40. This is because citric acid is a POLYPROTIC acid, meaning it can lose more than a single proton per molecule. Protons are lost through several stages (one at each stage), with the first proton being the fastest and most easily lost. We can make a calculation of the pH taking all the pKa values of citric acid into account, but that is a LOT more work, and ends up giving a negligibly different answer.
2. As you have seen, you can use different acids to form a solution with the same pH value. This DOES NOT mean that the solutions will also have the same chemical properties. While acetic, citric and ascorbic acids are generally considered safe, many other acids are usually not safe. So please do your research properly before you embark on a journey of using others acids.

Note regarding the true pH of ACV:
The important thing to point out is that the pH calculation made in this post is valid when you have pure acetic acid in water. In the case of ACV you have a much more complicated and in that, a much more interesting product. The ACV is made essentially in a two-step fermentation process:
1. Alcoholic fermentation, which converts natural sugars in an apple juice into alcohol using yeast.
2. Acid fermentation in which acetobacter, microorganisms present in the air we breathe, converts the alcohol into acid.

Therefore the final apple cider vinegar is a complex matrix of sugars, fats, vitamins, salts, enzymes and good bacteria. Each of these components influence the amount of protons in the solution, affecting the final pH of product (i.e. part of the acid is neutralized, which rises its pH).

If you’re interested in knowing more about ACV, I would suggest watching these series by CoralTree company based in New Zealand: