A solution of ethanol is prepared by combining \(22.5 \mathrm{~g}\) of ethanol with \(49.6 \mathrm{~g}\) of water. What is the percent composition by mass of alcohol in this solution?

Short Answer

Expert verified
The percent composition by mass of alcohol in this solution is \(31.2\%\).

Step by step solution

01

Identify the given values

We are given the mass of ethanol (\(m_{ethanol}\)) and the mass of water (\(m_{water}\)), which are: - \(m_{ethanol} = 22.5~g\) - \(m_{water} = 49.6~g\) We will use these values to find the mass percentage of ethanol in the solution.
02

Calculate the total mass of the solution

We need to find the total mass of the solution, which can be found by adding the masses of ethanol and water: Total Mass = \(m_{ethanol} + m_{water}\) Total Mass = \(22.5~g + 49.6~g = 72.1~g\)
03

Calculate the mass percentage of ethanol

Now, we will apply the formula for mass percentage to find the mass percentage of ethanol: Mass Percentage = \((m_{ethanol} / Total Mass) × 100\) Mass Percentage = \((22.5~g / 72.1~g) × 100\) Mass Percentage = \((0.312~g) × 100\) Mass Percentage = \(31.2\%\) Hence, the percent composition by mass of alcohol in this solution is \(31.2\%\).

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