Questions: 4. A gas occupies 3.5 L at 1.0 atm . Find the volume of the gas when the pressure is 1140 mm Hg .

Solution Steps

We are given the initial volume and pressure of a gas and need to find the new volume when the pressure changes. The initial conditions are:

• Initial volume, \( V_1 = 3.5 \, \text{L} \)
• Initial pressure, \( P_1 = 1.0 \, \text{atm} \)

The final pressure is given as \( 1140 \, \text{mm Hg} \).

To use Boyle's Law, which states that \( P_1 V_1 = P_2 V_2 \), we need consistent units for pressure. Convert the final pressure from mm Hg to atm: \[ 1 \, \text{atm} = 760 \, \text{mm Hg} \] \[ P_2 = \frac{1140 \, \text{mm Hg}}{760 \, \text{mm Hg/atm}} = 1.5 \, \text{atm} \]

Boyle's Law relates the pressure and volume of a gas at constant temperature: \[ P_1 V_1 = P_2 V_2 \] Substitute the known values into the equation: \[ 1.0 \, \text{atm} \times 3.5 \, \text{L} = 1.5 \, \text{atm} \times V_2 \]

Rearrange the equation to solve for \( V_2 \): \[ V_2 = \frac{1.0 \, \text{atm} \times 3.5 \, \text{L}}{1.5 \, \text{atm}} \] \[ V_2 = \frac{3.5}{1.5} \, \text{L} = 2.3333 \, \text{L} \]

Final Answer