Asample of a gas has a pressure of 3.00 atm at 25°c. what would the gas pressure be at 52°c, if the volume remains constant?

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, 

Substitute all known values to the equation
You will get
P_2 = [(3.00 atm)(325.15K)]/298.15K
∴ P_2 = 3.27 atm

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