Question

a sample of argon gas (ar) at an initial pressure of 772 kilopascals (kpa) is transferred from a tank with a volume of 0.0370 cubic meters to an empty cylinder. after transfer, the pressure of the gas in the cylinder is 2.210×10³ kilopascals. what is the final volume of the ar gas inside 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: Identify Boyle's Law formula

Boyle's Law is $P_1V_1 = P_2V_2$, where $P_1$ and $V_1$ are initial pressure and volume, and $P_2$ and $V_2$ are final pressure and volume.

Step2: Substitute given values

We have $P_1 = 772$ kPa, $V_1=0.0370$ m³, $P_2 = 2.210\times 10^{3}$ kPa. Rearranging for $V_2$ gives $V_2=\frac{P_1V_1}{P_2}$. Substituting values: $V_2=\frac{772\times0.0370}{2.210\times 10^{3}}$.

Step3: Calculate the result

$V_2=\frac{772\times0.0370}{2.210\times 10^{3}}=\frac{28.564}{2210}\approx0.0129$ m³.

Answer:

$0.0129$ cubic meters