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

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

Step-by-step 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)

`(V_1)/(T_1)=(V_2)/(T_2)`

`V_2=(V_1* T_2)/(T_1)=(50.0 L* 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).

Answer 2

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