Question

Keeping temperature constant the pressure of $11.2\ \text{dm}^3$ of a gas was increased from $105\ \text{kPa}$ to $420\ \text{kPa}$. What is the new volume of gas?

• A. $1.4\ \text{dm}^3$
• B. $7.0\ \text{dm}^3$
• C. $5.6\ \text{dm}^3$
• D. $2.8\ \text{dm}^3$

Hint:

Boyle's Law shows an inverse relationship. If the pressure increases by a factor of 4 (from 105 to 420), the volume must instantly decrease by that exact same factor of 4 ($11.2 / 4 = 2.8$).

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are asked to calculate the new volume of a gas when its pressure is increased at a constant temperature.

Step 2: Key Formula or Approach:
Because the temperature remains constant, the system strictly follows Boyle's Law.
The mathematical relationship for Boyle's Law is:
$$P_1V_1 = P_2V_2$$ Rearranging to solve for the final volume ($V_2$) yields:
$$V_2 = \frac{P_1 \times V_1}{P_2}$$

Step 3: Detailed Explanation:
Extract the given parameters from the problem:
Initial pressure $P_1 = 105\ \text{kPa}$
Initial volume $V_1 = 11.2\ \text{dm}^3$
Final pressure $P_2 = 420\ \text{kPa}$
Substitute these values into the rearranged formula:
$$V_2 = \frac{105 \times 11.2}{420}$$ To simplify the calculation, notice the direct relationship between the pressures: $105 \times 4 = 420$.
$$V_2 = \frac{11.2}{4}$$ $$V_2 = 2.8\ \text{dm}^3$$

Step 4: Final Answer:
The new volume of the gas is $2.8\ \text{dm}^3$, matching option (D).