Question

A gas occupies a volume of $4.2~dm^3$ at $101~kPa$ pressure. What volume will the gas occupy if the pressure is increased to $235~kPa$ keeping the temperature constant?

• A. $1.8~dm^3$
• B. $3.6~dm^3$
• C. $0.9~dm^3$
• D. $2.1~dm^3$

Hint:

If pressure increases at constant temperature, volume decreases according to Boyle’s law.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is another application of Boyle's Law. At a constant temperature, pressure and volume are inversely related. When pressure increases, volume must decrease proportionately.
Key Formula or Approach:
\[ P_1 V_1 = P_2 V_2 \] Step 2: Detailed Explanation:
Given:
\(P_1 = 101\text{ kPa}\)
\(V_1 = 4.2\text{ dm}^3\)
\(P_2 = 235\text{ kPa}\)

Applying the formula:
\[ 101 \times 4.2 = 235 \times V_2 \]
\[ V_2 = \frac{101 \times 4.2}{235} \]
\[ V_2 = \frac{424.2}{235} \approx 1.805\text{ dm}^3 \]
Rounding to the nearest provided option gives \(1.8\text{ dm}^3\).
Step 3: Final Answer:
The new volume is \(1.8\text{ dm}^3\).