Question

a sample of carbon dioxide gas (co₂) at an initial pressure of 2.07 × 10³ torr expands inside a rigid cylinder with a moveable piston. after expansion, the pressure and volume of the co₂ gas are 1.64 × 10³ torr and 9.50 liters, respectively. what was the initial volume of the co₂ 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: Identify Boyle's Law formula

$P_1V_1 = P_2V_2$

Step2: Rearrange for initial volume

$V_1=\frac{P_2V_2}{P_1}$

Step3: Substitute values

$P_1 = 2.07\times 10^{3}$ torr, $P_2 = 1.64\times 10^{3}$ torr, $V_2 = 9.50$ L
$V_1=\frac{1.64\times 10^{3}\text{ torr}\times9.50\text{ L}}{2.07\times 10^{3}\text{ torr}}$

Step4: Calculate result

$V_1=\frac{1.64\times9.50}{2.07}\text{ L}\approx7.53\text{ L}$

Answer:

7.53