# Using Equations to Solve Chemical Mixture Problems

Instructor: Michelle Vannoy
Science and math are like siblings. Where you find one, you may find the other. When solving chemical mixture problems knowing about percent concentration and systems of equations is a must. This lesson will show the mathematical applications for determining the amount of acid in a mixture.

## Is this Greek??

Your chemistry lab professor has asked you to determine the amount of acid in several different mixtures. Your professor promises you that there is plenty of information given to solve the problems, but you are not so sure. It all looks like Greek to you. However, if you remember what you learned in algebra about equations and system of equations, it is a breeze. The first step in solving one of these problems is to organize your information. One way to do this is to set up a table. This method takes a little extra time but makes the process a whole lot easier.

## How do I start?

Let's start with an easy problem first. You have 10 liters of 40% hydrogen peroxide (H2 O2) solution and you are asked to determine the amount of the solution that is hydrogen peroxide and the amount that is water. The first thing you should do is make a table to organize your information.

Volume % Concentration as a Decimal Amount
H2 O2 10 L .40

To turn the percent into a decimal, we just divide by 100. Remember from your previous math experience that in a word problem the word 'of' always means multiply. 40% hydrogen peroxide solution means that 40% of the solution is hydrogen peroxide and the other 60% is water. To solve you just simply multiply from left to right across the table: 10*0.40 = 4 liters of hydrogen peroxide. This means that the solution is 4 liters hydrogen peroxide and 6 liters water.

Now that you have a better understanding of what the problem is asking you and how to set it up, let's look at a problem that is a little more difficult. You are given 75 liters of 25% HCl (hydrochloric acid) mixed with 35 liters of 7% HCl. How much of the solution's volume is acid, and what is the percent concentration of the final solution?

First, you need to determine which solution is the strong solution, the solution with the highest percent concentration of acid, and which is the weak solution, the solution with the lowest percent concentration of acid.

Volume % Acid as a Decimal Amount of Acid
Strong Solution 75L .25
Weak Solution 35L .07
Total Mixture

Step 2- Multiply straight across each row and fill in the values.

Volume % Acid as a Decimal Amount of Acid
Strong Solution 75L .25 18.75 L
Weak Solution 35L .07 2.45 L
Total Mixture

Step 3- Determine the total volume by adding down the column and the total amount of acid by adding down that column.

Volume % Acid as a Decimal Amount of Acid
Strong Solution 75L .25 18.75
Weak Solution 35L .07 2.45
Total Mixture 110L
21.2 L

Determine the percent concentration of the solution by setting up a ratio between the total amount of the acid in the solution and the total volume of the solution.

Volume % Acid as a Decimal Amount of Acid
Strong Solution 75L .25 18.75
Weak Solution 35L .07 2.45
Total Mixture 110L 21.2/110 = .1927 21.2 L

Multiply this decimal by 100 to determine the percentage. The new solution contains 21.2 L of HCl and is a 19.27% concentration.

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