Question

a chemist prepares a mixture of dioxane and toluene at a temperature of 26.0°c. he measures out 310. ml of dioxane and mixes it with 0.92 l of toluene. he measures the volume of the solution after it is well mixed and finds that it is 1.28 l. the density of dioxane is 1.03 g/ml and the density of toluene is 0.87 g/ml.
calculate the volume percent of dioxane in this solution.
be sure your answer has the right number of significant digits.
24 %(v/v)

Explanation:

Step1: Convert volume units

Convert \(0.92\ L\) of toluene to \(mL\). Since \(1\ L = 1000\ mL\), then \(V_{toluene}=0.92\times1000 = 920\ mL\).

Step2: Calculate the volume of dioxane

Given \(V_{dioxane}=310\ mL\).

Step3: Calculate the total volume of the solution

\(V_{total}=1.28\times1000\ mL\) (since \(1\ L = 1000\ mL\)).

Step4: Calculate the volume - percent

The formula for volume - percent (\(v/v\)) is \(\text{Volume}\%=\frac{V_{solute}}{V_{solution}}\times100\). Here, the solute is dioxane. So \(\text{Volume}\%=\frac{310\ mL}{1280\ mL}\times100\).

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Rounding to two significant digits (since \(310\) has two significant digits), we get \(24\%\).

Answer:

\(24\%\)