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

• A. 190 cc
• B. 210 cc
• C. 150 cc
• D. 120 cc

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.

Answer 1

The Correct Option is A

Step 1: Apply Boyle's law (constant temperature).
\( P_1 V_1 = P_2 V_2 \). Given \( P_1 = 760\,\text{mm Hg} \), \( V_1 = 100\,\text{cc} \), \( P_2 = 400\,\text{mm Hg} \).

Step 2: Solve for \( V_2 \).
\[ V_2 = \frac{P_1 V_1}{P_2} = \frac{760\times100}{400} = 190\,\text{cc} \] \[ \boxed{190\,\text{cc}} \]