Question

a sample of nitrogen gas (n₂) occupies a volume of 0.0333 cubic meters at a pressure of 1,682 kilopascals (kpa). the gas expands inside a rigid cylinder with a moveable piston to a final pressure of 644 kilopascals. what is the final volume of the n₂ gas in the cylinder? assume ideal gas behavior and a constant temperature. write your answer to the correct number of significant figures. round if necessary.

Explanation:

Step1: Recall Boyle's Law formula

$P_1V_1 = P_2V_2$

Step2: Identify given values

$P_1 = 1682\ kPa$, $V_1=0.0333\ m^3$, $P_2 = 644\ kPa$

Step3: Solve for $V_2$

$V_2=\frac{P_1V_1}{P_2}=\frac{1682\ kPa\times0.0333\ m^3}{644\ kPa}$
$V_2=\frac{55.9106\ kPa\cdot m^3}{644\ kPa}\approx0.0868\ m^3$

Answer:

$0.0868$ cubic meters