Question

a sample of nitrogen gas (n₂) is transferred from a cylinder with a volume of 0.0152 cubic meters to an empty tank with a volume of 0.0463 cubic meters. before transfer, the pressure in the cylinder was measured to be 7.42 atmospheres (atm). what is the final pressure of the n₂ gas inside the tank? 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: Assign values

$P_1 = 7.42$ atm, $V_1=0.0152$ m³, $V_2 = 0.0463$ m³. We need to find $P_2$.

Step3: Rearrange the formula to solve for $P_2$

$P_2=\frac{P_1V_1}{V_2}$.

Step4: Substitute values and calculate

$P_2=\frac{7.42\times0.0152}{0.0463}=\frac{0.112784}{0.0463}\approx2.44$ atm.

Answer:

2.44 atm