A chemist prepares a mixture of cyclohexane and toluene at a temperature of 15.0 °C. He measures out 1.38 L of cyclohexane and mixes it with 1.17 L of toluene. He measures the volume of the solution after it is well mixed and finds that it is 2.63 L. The density of cyclohexane is 0.78 g/ml and the density of toluene is 0.87 g/mL.

Question

Calculate the volume percent of cyclohexane in this solution.
Be sure your answer has the right number of significant digits.

Answer 1

To calculate the volume percent of cyclohexane in the solution, we can use the following formula:

\[ \text{Volume percent of cyclohexane} = \left( \frac{\text{Volume of cyclohexane}}{\text{Total volume of solution}} \right) \times 100 \]

1. Identify the volumes:

   • Volume of cyclohexane = 1.38 L
   • Total volume of the solution = 2.63 L

2. Plug the values into the formula:

\[ \text{Volume percent of cyclohexane} = \left( \frac{1.38 , \text{L}}{2.63 , \text{L}} \right) \times 100 \]

3. Calculate:

\[ \frac{1.38}{2.63} \approx 0.524 \] \[ 0.524 \times 100 \approx 52.4% \]

Since we want to ensure the answer has the correct number of significant figures, we look at the values used. The volumes of cyclohexane and the total volume were measured to three significant figures. Therefore, we should round our final answer to three significant figures as well.

Final answer:

\[ \text{Volume percent of cyclohexane} \approx 52.4% \]