Question

What additional information is needed to solve this problem: If a sample of a gas 12.0 o C and 1.06 atm pressure is moved to a 2.30 L container at 24.9 0 C, what is the final pressure of the gas?

Answer 1

The additional information required to solve this problem is the initial volume.

the final pressure P₂ of the gas is 1.108 atm

Step-by-step explanation:

Given that :

A sample of gas at initial temperature
`T_1 = 12.0^0 \ C` = (12+273)K = 285 K

Pressure (P₁) = 1.06 atm

Initial Volume (V₁) = unknown ???

Final Volume (V₂) = 2.30 L

final temperature
`T_2 = 24.9^0 \ C` = (24.9 +273)K = 297.9 K

Find the final Pressure (P₂)

The relation between: Pressure, Volume and Temperature can be gotten from the ideal gas equation :

PV = nRT

The Ideal Gas Equation is also reduced to the General Gas Law or the combined Gas Law by assuming that n= 1 .

From ; PV = nRT

`(PV)/(T) = R \ \ ( constant) \ if \ n=1`

∴
`(P_1V_1)/(T_1) = (P_2V_2)/(T_2) = (P_3V_3)/(T_3)...= (P_nV_n)/(T_n) \ \ \ ( n \ constant)`

The additional information required to solve this problem is the initial volume.

This expression is a combination of Boyle's Law and Charles Law. From the combined Gas Law , it can be deduced that at constant volume, the pressure of a given mass(mole) of gas varies directly with absolute temperature.

∴
`(P_1)/(T_1) = (P_2)/(T_2)` if n & Volume (V) are constant .

`P_2 = (1.06*297.9)/(285)`

P₂ = 1.108 atm

Thus, the final pressure P₂ of the gas is 1.108 atm