Question

Calculate the pressure in atm of 2.50 liters of CH4 gas at STP, if the volume is reduced to 2.00 liters and the temperature is raised to 227oC.

Answer 1

Given

At STP , Temperature is 273.15 K and Pressure is 1 atm.

Initial volume of methane gas ( V ₁ ) = 2.50 L

Initial temperature of methane gas ( T ₁) = 273.15 K

Initial pressure of methane gas ( P ₁) = 1 atm

Final volume of methane gas ( V ₂ ) = 2.00 L

Final temperature of methane gas ( T ₂) = 500.15 K

Final pressure of methane gas ( P ₂) =?

We have relation , P V = n R T

where, P is a pressure of a gas, V is a volume of a gas, n is no. of moles of gas, R is a gas constant and T is temperature of gas.

From above relation, we can write P ₁ V ₁ = n R T ₁ (1) & P ₂ V ₂= n R T ₂ (2)

Divide equation 2 by 1 , we get ( P ₂ V ₂ ) / ( P ₁ V ₁ ) = T ₂ / T ₁

( P ₂ 2.00 L ) / ( 1 atm 2.50 L ) = 500.15 K / 273.15 K

( P ₂ 2.00 L ) / ( 1 atm 2.50 L ) = 1.831

( P ₂ 2.00 L ) = 1.831 ( 1 atm 2.50 L )

P ₂ = 1.831 ( 1 atm 2.50 L ) / 2.00 L = 2.29 atm

ANSWER : Pressure of methane gas = 2.29 atm