a sample of chlorine gas (cl₂) occupies a volume of 4.899 × 10⁴ milliliters at a pressure of 32.0 pounds per…

a sample of chlorine gas (cl₂) occupies a volume of 4.899 × 10⁴ milliliters at a pressure of 32.0 pounds per square inch (psi). the gas is compressed inside a rigid cylinder with a moveable piston to a final pressure of 148.0 pounds per square inch. what is the final volume of the cl₂ 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.

a sample of chlorine gas (cl₂) occupies a volume of 4.899 × 10⁴ milliliters at a pressure of 32.0 pounds per square inch (psi). the gas is compressed inside a rigid cylinder with a moveable piston to a final pressure of 148.0 pounds per square inch. what is the final volume of the cl₂ 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.

Answer

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 $P_1 = 32.0$ psi, $V_1=4.899\times 10^{4}$ mL, $P_2 = 148.0$ psi. We need to find $V_2$. Rearranging the formula for $V_2$ gives $V_2=\frac{P_1V_1}{P_2}$. Substituting the values: $V_2=\frac{32.0\times4.899\times 10^{4}}{148.0}$.

Step3: Calculate the result

$V_2=\frac{32.0\times4.899\times 10^{4}}{148.0}=\frac{1.56768\times 10^{6}}{148.0}\approx1.06\times 10^{4}$ mL.

Answer:

$1.06\times 10^{4}$