Question

a sample of chlorine gas (cl₂) is transferred from a 5.00-liter cylinder to an empty 12.5-liter tank. after transfer, the pressure in the 12.5-liter tank is 5.40 pounds per square inch (psi). what was the initial pressure of the cl₂ gas inside the cylinder? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary. psi save answer

Explanation:

Step1: Identify the gas law

For a gas at constant temperature and amount (since it's transferred, the moles are constant), Boyle's Law applies. Boyle's Law is \( P_1V_1 = P_2V_2 \), where \( P_1 \) is the initial pressure, \( V_1 \) is the initial volume, \( P_2 \) is the final pressure, and \( V_2 \) is the final volume.

Step2: List the known values

We know:

• \( V_1 = 5.00 \, \text{L} \) (initial volume of the cylinder)
• \( V_2 = 12.5 \, \text{L} \) (final volume of the tank)
• \( P_2 = 5.40 \, \text{psi} \) (final pressure in the tank)
• We need to find \( P_1 \) (initial pressure in the cylinder)

Step3: Rearrange Boyle's Law to solve for \( P_1 \)

From \( P_1V_1 = P_2V_2 \), we can solve for \( P_1 \) by dividing both sides by \( V_1 \):
\( P_1=\frac{P_2V_2}{V_1} \)

Step4: Substitute the known values into the formula

Substitute \( P_2 = 5.40 \, \text{psi} \), \( V_2 = 12.5 \, \text{L} \), and \( V_1 = 5.00 \, \text{L} \) into the formula:
\( P_1=\frac{5.40 \, \text{psi} \times 12.5 \, \text{L}}{5.00 \, \text{L}} \)

Step5: Perform the calculation

First, calculate the numerator: \( 5.40 \times 12.5 = 67.5 \)
Then divide by the denominator: \( \frac{67.5}{5.00}=13.5 \)

Answer:

13.5