How to find the percent composition of a mixture in AP Chemistry: an example

A 26.5 g mixture of $\ce{Na2CO3}$ and $\ce{KCl}$ contains 4.60 g of $\ce{Na}$. What percent of the mixture is $\ce{Na2CO3}$ by mass?

• A) 40.0%
• B) 80.0%
• C) 17.4%
• D) 60.0%

Solving this Problem

Whenever we are solving for percent composition, we are trying to figure out what percent of the entire mixture is made up by a given compound. Remember that to find the percent we use a fraction (part / whole) where the mass of the given compound is on top, and the mass of the entire mixture is on bottom. This gives us the percent in decimal form, and the last step to convert to a percent form is to multiply by 100. These steps combined are represented by the formula below:

In this specific problem we want to find the percent composition of $\ce{Na2CO3}$, so we need to find its mass and then we can divide by the given mass of the entire mixture, 26.5 g.

Step 1

We must convert from grams of $\ce{Na}$ to grams of $\ce{Na2CO3}$ in order to use the percent composition formula. If you need a refresher on stoichiometry, check out our stoichiometry problem walkthrough or practice the unit 1.1 and 4.5 Check Your Understanding Quiz in your AP Chemistry course.

First we convert the 4.60 g of $\ce{Na}$ into moles of $\ce{Na}$ by dividing by the molar mass of $\ce{Na}$, 22.99 g/mol. Then we convert moles of $\ce{Na}$ into moles of $\ce{Na2CO3}$ using the ratio in the formula, where every 1 mol of $\ce{Na2CO3}$ contains 2 mol of $\ce{Na}$. Finally we convert moles of $\ce{Na2CO3}$ into grams by multiplying by its molar mass, 105.99 g/mol.

Step 2

Now that we have the mass of $\ce{Na2CO3}$, it is time to plug in our numbers to the percent composition formula. If you understand what this formula is doing, then there is no need to memorize it. The mass of $\ce{Na2CO3}$ over the mass of the whole mixture gives us decimal composition, then multiply by 100 to get the percent composition.

So after calculating, we get a final answer of 40.0% - meaning that 40.0% of the total mass of the mixture is made up by $\ce{Na2CO3}$. The correct answer is A! You should also understand that this means the remaining 60.0% of the mixture's mass is made up by $\ce{KCl}$, but for this problem we are done.

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