Question

calculate the volume, in l, of a sample of an ideal gas at 5.75 atm if it occupies 5.08 l at 3.02 atm at the same temperature. report your answer with the correct number of significant figures.

Explanation:

Step1: Identify the gas law

This is a Boyle's Law problem, which states that for a fixed amount of ideal gas at constant temperature, \( P_1V_1 = P_2V_2 \). Here, \( P_1 = 3.02 \, \text{atm} \), \( V_1 = 5.08 \, \text{L} \), \( P_2 = 5.75 \, \text{atm} \), and we need to find \( V_2 \).

Step2: Rearrange the formula

From \( P_1V_1 = P_2V_2 \), we solve for \( V_2 \): \( V_2=\frac{P_1V_1}{P_2} \)

Step3: Substitute the values

Substitute \( P_1 = 3.02 \, \text{atm} \), \( V_1 = 5.08 \, \text{L} \), and \( P_2 = 5.75 \, \text{atm} \) into the formula:
\( V_2=\frac{3.02 \, \text{atm} \times 5.08 \, \text{L}}{5.75 \, \text{atm}} \)

Step4: Calculate the result

First, multiply the numerator: \( 3.02 \times 5.08 = 15.3416 \)
Then divide by the denominator: \( \frac{15.3416}{5.75} \approx 2.668 \)
Considering significant figures, \( 3.02 \) (3 sig figs), \( 5.08 \) (3 sig figs), \( 5.75 \) (3 sig figs), so the result should have 3 sig figs. So \( V_2 \approx 2.67 \, \text{L} \)

Answer:

\( 2.67 \, \text{L} \)