Question:
The volume of a gas at \(30^\circ\text{C}\) temperature and \(760\ \text{mm}\) of Hg pressure is \(100\ \text{cc}\). Then its volume at the same temperature and \(400\ \text{mm}\) of Hg pressure is
The volume of a gas at \(30^\circ\text{C}\) temperature and \(760\ \text{mm}\) of Hg pressure is \(100\ \text{cc}\). Then its volume at the same temperature and \(400\ \text{mm}\) of Hg pressure is
Show Hint
For a fixed mass of gas at constant temperature,
\[
PV=\text{constant}.
\]
Therefore, if pressure decreases, volume increases in the same ratio according to Boyle's law.
Updated On: Jun 26, 2026
- 190 cc
- 210 cc
- 150 cc
- 120 cc
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The Correct Option is A
Solution and Explanation
Step 1: Identify the gas law to be used.
Since the temperature remains constant, Boyle's law is applicable.
According to Boyle's law, \[ P_1V_1=P_2V_2 \] where \[ P_1=760\ \text{mm Hg}, \] \[ V_1=100\ \text{cc}, \] \[ P_2=400\ \text{mm Hg}. \] We have to find \[ V_2. \]
Step 2: Substitute the given values.
Using Boyle's law, \[ 760 \times 100 = 400 \times V_2 \]
Step 3: Solve for \(V_2\).
\[ V_2 = \frac{760 \times 100}{400} \] \[ V_2 = 190\ \text{cc} \]
Step 4: Verify the result.
Since pressure decreases from \[ 760\ \text{mm Hg} \] to \[ 400\ \text{mm Hg}, \] the volume should increase.
The calculated value \[ 190\ \text{cc} \] is therefore physically correct.
Step 5: Final conclusion.
Hence, the volume of the gas at \(400\ \text{mm Hg}\) pressure is \[ \boxed{190\ \text{cc}} \]
Since the temperature remains constant, Boyle's law is applicable.
According to Boyle's law, \[ P_1V_1=P_2V_2 \] where \[ P_1=760\ \text{mm Hg}, \] \[ V_1=100\ \text{cc}, \] \[ P_2=400\ \text{mm Hg}. \] We have to find \[ V_2. \]
Step 2: Substitute the given values.
Using Boyle's law, \[ 760 \times 100 = 400 \times V_2 \]
Step 3: Solve for \(V_2\).
\[ V_2 = \frac{760 \times 100}{400} \] \[ V_2 = 190\ \text{cc} \]
Step 4: Verify the result.
Since pressure decreases from \[ 760\ \text{mm Hg} \] to \[ 400\ \text{mm Hg}, \] the volume should increase.
The calculated value \[ 190\ \text{cc} \] is therefore physically correct.
Step 5: Final conclusion.
Hence, the volume of the gas at \(400\ \text{mm Hg}\) pressure is \[ \boxed{190\ \text{cc}} \]
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