Question

At constant temperature, a gas is at a pressure of 940.3 mm Hg. The pressure at which its volume decreases by 40% is mm Hg. (Nearest integer)

Answer 1

Step 1: Write the given data

• Initial pressure, \( P_{\text{initial}} = 940.3 \, \text{mm Hg} \).
• Initial volume, \( V_{\text{initial}} = 100 \, \text{units} \) (assumed). 
• Final volume, \( V_{\text{final}} = 100 - 40\% = 60 \, \text{units} \).
• Final pressure, \( P_{\text{final}} = ? \).

Step 2: Apply Boyle's Law

Boyle's law states that:

\[ P_{\text{initial}} \cdot V_{\text{initial}} = P_{\text{final}} \cdot V_{\text{final}}. \] Substitute the given values: \[ 940.3 \times 100 = P_{\text{final}} \times 60. \] Solving for \( P_{\text{final}} \): \[ P_{\text{final}} = \frac{940.3 \times 100}{60} = 1567.16 \, \text{mm Hg}. \] 

Step 3: Round to the nearest integer \[ P_{\text{final}} = 1567 \, \text{mm Hg}. \] 

Final Answer:

The pressure at which the volume decreases by 40% is \( P_{\text{final}} = 1567 \, \text{mm Hg}. \)