Question

a sample of carbon dioxide gas (co₂) is transferred from a cylinder with a volume of 0.0202 cubic meters to an empty tank with a volume of 0.0346 cubic meters. after transfer, the pressure in the tank is 1.880 × 10³ kilopascals (kpa). what was the initial pressure of the co₂ gas inside 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 formula for $P_1$

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

Step3: Substitute given values

$V_1 = 0.0202$ m³, $V_2=0.0346$ m³, $P_2 = 1.880\times 10^{3}$ kPa
$P_1=\frac{1.880\times 10^{3}\text{ kPa}\times0.0346\text{ m}^3}{0.0202\text{ m}^3}$

Step4: Calculate $P_1$

$P_1=\frac{1.880\times 10^{3}\times0.0346}{0.0202}\text{ kPa}\approx 3.21\times 10^{3}$ kPa

Answer:

$3.21\times 10^{3}$ kPa