Question

a chemist mixes 69.1 g of water with 98.1 g of butanoic acid and 73.1 g of acetone. calculate the percent by mass of each component of this solution. round each of your answers to 3 significant digits.

Explanation:

Step1: Calculate the total mass of the solution

$$\begin{align*} \text{Total mass}&=69.1\ \text{g}+98.1\ \text{g}+73.1\ \text{g}\\ &=(69.1 + 98.1+73.1)\ \text{g}\\ &=240.3\ \text{g} \end{align*}$$

Step2: Calculate the mass percent of water

The formula for mass percent is $\text{Mass}\ \%=\frac{\text{Mass of component}}{\text{Total mass of solution}}\times100\%$.
For water:

$$\begin{align*} \text{Mass}\ \%&=\frac{69.1\ \text{g}}{240.3\ \text{g}}\times 100\%\\ &\approx\frac{69.1}{240.3}\times100\%\\ &\approx 28.8\% \end{align*}$$

Step3: Calculate the mass percent of butanoic acid

For butanoic acid:

$$\begin{align*} \text{Mass}\ \%&=\frac{98.1\ \text{g}}{240.3\ \text{g}}\times 100\%\\ &\approx\frac{98.1}{240.3}\times100\%\\ &\approx 40.8\% \end{align*}$$

Step4: Calculate the mass percent of acetone

For acetone:

$$\begin{align*} \text{Mass}\ \%&=\frac{73.1\ \text{g}}{240.3\ \text{g}}\times 100\%\\ &\approx\frac{73.1}{240.3}\times100\%\\ &\approx 30.4\% \end{align*}$$

Answer:

component	mass percent
butanoic acid	$40.8\%$
acetone	$30.4\%$