Question

A rigid cylinder with a movable piston contains 50.0 liters of a gas at 30.0 degree C with a pressure of 1.00 atmosphere. What is the volume of the gas in the cylinder at STP?
(1) 5.49 L (3) 55.5 L
(2) 45.0 L (4) 455 L

Answer 1

Charles law states that volume of a gas is directly proportional to temperature at constant pressure for a fixed amount of gas. the pressure at given conditions is 1.00 atm and the standard pressure at STP conditions too is 1.00 atm therefore pressure remains constant.
 V1/T1 = V2/T2
the parameters for the first instance are on the left side and parameters at STP are on the right side of the equation.
T1 - temperature in kelvin - 273 + 30.0 °C = 303 K
T2 - standard temperature - 273 K
V1 - volume - 50.0 L
substituting the values in the equation
50.0 L / 303 K = V / 273 K V = 45.0 L
answer is 2) 45.0 L

Answer 2

Answer: The volume of the gas at STP is 45.0 L. hence the correct answer is option(2).

Explanation:

Initial volume of the gas,$V_1$ = 50.0 L

Initial temperature of the gas$T_1$ =$30.0^oC=30+273 K=303 K$

$0^oC=273 K$

Final volume of the gas,$V_2$ = ?

At STP, the value of temperature is 273 K.

Final temperature of the gas$T_2$ = 273 H

Charles' Law: The volume is directly proportional to the temperature of the gas at constant pressure and number of moles.

$V\propto T$    (At constant pressure and number of moles)

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

$V_2=\frac{V_1\times T_2}{T_1}=\frac{50.0 L\times 273 K}{303 K}=45.0495 L\approx 45.0 L$

The volume of the gas at STP is 45.0 L. hence the correct answer is option(2).