At NTP the volume of a gas is 40 mL . If pressure is increased to 800 mm of Hg at the same temperature what will be the volume of the gas ?

Options

A. 38 mL
B. 22400 mL
C. 240 mL
D. 431 mL

Explanation

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

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial volume \( V_1 = 40 \, \text{mL} \)
- Initial pressure \( P_1 = 760 \, \text{mm of Hg} \) (at NTP)
- Final pressure \( P_2 = 800 \, \text{mm of Hg} \)
- Final volume \( V_2 = ? \)

2. **Write Down Boyle's Law:**
\[ P_1 V_1 = P_2 V_2 \]

3. **Rearrange the Formula to Solve for \( V_2 \):**
\[ V_2 = \frac{P_1 V_1}{P_2} \]

4. **Substitute the Known Values into the Equation:**
\[ V_2 = \frac{760 \, \text{mm of Hg} \times 40 \, \text{mL}}{800 \, \text{mm of Hg}} \]

5. **Calculate \( V_2 \):**
- First, calculate the numerator:
\[ 760 \times 40 = 30400 \, \text{mm of Hg} \cdot \text{mL} \]
- Now divide by the final pressure:
\[ V_2 = \frac{30400}{800} = 38 \, \text{mL} \]

6. **Conclusion:**
The final volume of the gas when the pressure is increased to 800 mm of Hg at the same temperature is \( V_2 = 38 \, \text{mL} \).

### Final Answer:
The volume of the gas at 800 mm of Hg is **38 mL**.

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