Question

At constant temperature, a gas occupies a volume of 200 mL at a pressure of 500 mm Hg. What will be its volume at 800 mm Hg pressure?

• A. \(280 \text{mL}\)
• B. \(125 \text{mL}\)
• C. \(100 \text{mL}\)
• D. \(350 \text{mL}\)

Hint:

At constant temperature, pressure times volume stays constant.

Answer 1

The Correct Option is B

Step 1: Identify the law
At constant temperature the volume of a fixed amount of gas is inversely proportional to its pressure. This is Boyle's law: \(P_1V_1 = P_2V_2\).

Step 2: Substitute
\(P_1 = 500\) mm Hg, \(V_1 = 200\) mL, \(P_2 = 800\) mm Hg.
\[ V_2 = \frac{500 \times 200}{800} = \frac{100000}{800} = 125\ \text{mL} \]

Step 3: Check
Pressure has increased, so volume must fall below \(200\) mL. Only \(125\) mL and \(100\) mL are lower, and \(100\) mL would need a pressure of \(1000\) mm Hg. The values \(280\) and \(350\) mL are higher than \(200\) mL, so they are impossible.

Final Answer:
The gas occupies 125 mL at 800 mm Hg. \[ \boxed{\text{(B)}\ 125\ \text{mL}} \]