Question

a sealed syringe contains 47.32 milliliters of helium gas (he) at a pressure of 15.66 pounds per square inch (psi). the plunger of the syringe is depressed until the gas has a pressure of 20.22 pounds per square inch. what is the final volume of the he gas in the syringe? 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 $P_1 = 15.66$ psi, $V_1=47.32$ mL, and $P_2 = 20.22$ psi. We need to find $V_2$. Rearranging the formula for $V_2$ gives $V_2=\frac{P_1V_1}{P_2}$.

Step3: Calculate $V_2$

$V_2=\frac{15.66\times47.32}{20.22}=\frac{741.9212}{20.22}\approx36.7$ mL

Answer:

$36.7$