For many purposes we can treat nitrogen N2 as an ideal gas at temperatures above its boiling point of −196.°C. Suppose the temperature of a sample of nitrogen gas is lowered from 18.0°C⁢ to −15.0°C, and at the same time the pressure is changed. If the initial pressure was 3.6atm and the volume decreased by 40.0%, what is the final pressure? Round your answer to the correct number of significant digits.

5.3 atm

Explanation:

We can solve this problem using the equation of state for an ideal gas, which states that:

where

p is the pressure of the gas

V is its volume

n is the number of moles

R is the gas constant

T is the absolute temperature of the gas

For a gas undergoing a transformation, n and R remain constant, so the equation can be written as

For the gas in this problem we have:

is the initial temperature of the gas

is the final temperature

is the initial pressure

, as the volume is decreased by 40.0%

Solving for , we find the final pressure of the gas:

the answer is the