The problem describes Gay-Lussac's Law in which pressure of the gas is directly proportional to its absolute temperature at constant volume.
From Ideal gas equation, Gay-Lussac's Law then expressed as P=kT where k is the proportionality constant.
Given:
P_1 = 3.00 atm
T_1 = 25°C (298.15 K)
T_2 = 52°C (325.15 K)
Required:
P_2 = ?
Assumptions:
Sample of gas is an ideal gas
Constant volume
Solution:
We say subscript 1 means first state and subscript 2 means second state
P=kT
k = P/T
k_1 = k_2 since it is the proportionality constant so k in first state is equal to k to second state
Therefore,
[tex] \frac{P_1}{T_1} = \frac{P_2}{T_2} [/tex]
Substitute all known values to the equation
You will get
P_2 = [(3.00 atm)(325.15K)]/298.15K
∴ P_2 = 3.27 atm
