# Acid Number to FFA Conversions

By *Rick Da Tech*

Free Fatty Acids (FFA) are the result of the breakdown of oil or biodiesel. FFA% is usually used to describe the FFA content of oils, while Acid Number (AN) is commonly used to describe the FFA content of finished biodiesel. With a little math, we can use the same titration procedure we use to titrate WVO to determine FFA% and AN.

### FFA%

FFA% is the weight to weight ratio of FFA found in an oil sample. The weight of an oil sample divided into the weight of the FFA in that sample.

To calculate FFA% from a titration value the formula is:

FFA% = (v - b) x N x 28.2 / w

v is the volume in ml of titration solution

b is the volume in ml of the blank

N is the normality of the titration solution

w is the weight of the sample of oil in grams

Since in the homebrew titration we do not record the blank, we set it to 0 here.

For N we use 1 gram/Liter or 0.025N for NaOH

For w we use 1ml of oil, which typically weighs 0.92grams

28.2 is the molecular weight of oleic acid divided by ten.

When we plug everything in we get:

**FFA% = 0.766t** - for NaOH titrations**FFA% = 0.546t** - for KOH titrations

t is our titration results in milliliters.

Note that since we estimated both the density of our oil sample and the molecular weight of the average fatty acid in our oil, the result will also be an estimate. Even though it is an estimate, it is close enough for our use.

### Acid Number

Acid Number, normally measured in biodiesel rather than WVO, is the amount of KOH in mg needed to react with the acid in an amount of oil in grams. The Acid Number is one of the ASTM tests for finished biodiesel.

ASTM D 664 Determination of Acid Number by Potientiometric Titration.

Max value for finished biodiesel = 0.50 mg/g

AN = (v - b) x N x 56.1 / w

v is the titration volume in ml

b is the blank in ml

N is the normality of the KOH solution

w is the weight of sample in g

Since we are using 1g/L of KOH for our titration then N=1/56.1

Of course then N and 56.1 cancel each other out and our AN is now

AN = (v-b)/w or

**AN = 1.08t **

where t is the results of a standard homebrew style KOH titration

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To see the relationship between AN and FFA% we can solve both equations for common values or:

AN/56.1 = (v - b) x N / w

And

FFA%/28.2 = (v - b) x N / w

Now combine the equations for

AN/56.1 = FFA%/28.2

Or

**AN= 1.99FFA% **

### Related Links

## Biodiesel Analytical MethodsPublication Type: Subcontractor report (PDF 2.1 MB) Authors: J. Van Gerpen, B. Shanks, and R. Pruszko, Iowa State University, D. Clements, Renewable Products Development Laboratory , G. Knothe, USDA/NCAUR Publication Date: July 2004 |

### Comments:

**Lthem001****2012-07-11 23:22**

I am having a hard time understanding the equation for FFA %. I don't not understand how (v-b)x N x 28.2/w = .546t for KOH = FFA%. From my understanding v= the amount of KOH solution that is need in the titration, I don't not understand what b or blank is. N is in relation to moles KOH? I understand what w is and why we are using 28.2. If you could please help that would be great. I do not want to use a standard of FFA% = .546t I would like to be accurate and precise.

**Rickdatech 2012-07-12 13:47**

The formula comes from chemistry. It is based on the fact that the number of molecules of FFA in our oil sample is exactly the same as the number of molecules of KOH in our titration. What makes it so complicated is that when we titrate, it gives us the number of milliliters of a solution of KOH and water. First we have to extract how many molecules of KOH we used from the milliliter number. That gives us molecules of FFA. Then we have to convert from molecules of FFA to a weight of FFA. To make that percentage FFA we divide the weight of the FFA in the sample by the weight of the sample.

In the chemistry laboratory, they use a more generalized titration than we use in home brew biodiesel. It is not any more precise than the home brew method, just different. They take two measurements, v and b, and subtract one from the other to get the same number of milliliters of KOH (t) that we get when we titrate. so '(v-b)' can be thought of as a single number 't', our titration number.

The second difference is that we use a specific mixture of KOH and water to titrate. We use one gram of KOH in one liter of water. Chemists in a laboratory use premixed solutions with different ratios of KOH and water, so they need a more generalized formula.