Question

The initial volume of a gas cylinder is 750.0 \,mL. If the pressure of gas inside the cylinder changes from $840.0 \,mm$ Hg to 360.0 mm Hg, the final volume the gas will be :

• A. 1.750 L
• B. 3.60 L
• C. 4.032 L
• D. 7.50 L

Answer 1

The Correct Option is A

To solve this problem, we'll use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature is kept constant. The formula for Boyle's Law is:

P_1 V_1 = P_2 V_2

Where:

• P_1 and V_1 are the initial pressure and volume.
• P_2 and V_2 are the final pressure and volume.

Let's list the known values:

• Initial volume, V_1 = 750.0 \, \text{mL}
• Initial pressure, P_1 = 840.0 \, \text{mm Hg}
• Final pressure, P_2 = 360.0 \, \text{mm Hg}

We need to find the final volume, V_2. Using Boyle's Law:

840.0 \times 750.0 = 360.0 \times V_2

Solve for V_2:

V_2 = \frac{840.0 \times 750.0}{360.0}

V_2 = \frac{630000}{360.0}

V_2 = 1750 \, \text{mL}

Since the question provides the options in liters, convert the final volume to liters:

• 1 \, \text{mL} = 0.001 \, \text{L}
• 1750 \, \text{mL} = 1.750 \, \text{L}

Therefore, the final volume of the gas is 1.750 L. Thus, the correct answer is Option 1: 1.750 \, \text{L}.