Question

s.1 boyles law: pressure and volume relationships of gases ne7 a sample of oxygen gas (o₂) occupies a volume of 18.8 liters at a pressure of 7.60×10³ torr. the gas is compressed inside a rigid cylinder with a moveable piston to a final pressure of 1.40×10⁴ torr. what is the final volume of the o₂ 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. liters

Explanation:

Step1: Identify Boyle's Law formula

$P_1V_1 = P_2V_2$

Step2: Define the given values

$P_1=7.60\times 10^{3}\text{ torr}$, $V_1 = 18.8\text{ L}$, $P_2=1.40\times 10^{4}\text{ torr}$

Step3: Solve for $V_2$

$V_2=\frac{P_1V_1}{P_2}=\frac{(7.60\times 10^{3}\text{ torr})\times18.8\text{ L}}{1.40\times 10^{4}\text{ torr}}$
$V_2=\frac{7.60\times18.8\times 10^{3}}{1.40\times 10^{4}}\text{ L}=\frac{142.88\times 10^{3}}{1.40\times 10^{4}}\text{ L}$
$V_2=\frac{142.88}{1.40}\times10^{3 - 4}\text{ L}\approx102.057\times10^{- 1}\text{ L}\approx10.2\text{ L}$

Answer:

$10.2$ liters