Imagine a car tire that contains 5.1 moles of air when at a gauge pressure of 2.1×10^5n/m2 (the pressure above atmospheric pressure) and a temperature of 27 degrees c. the temperature increases to 37 degrees c, the volume decreases to 0.8 times the original volume, and the gauge pressure decreases to 1.6×10^5n/m2.
how many moles of air are left in the tire?

To solve this problem it is necessary to use the concepts given through the ideal gas equation.

For this it is defined that

Where,

P = Pressure

V = Volume

R = Gas ideal constant

T = Temperature

n = number of moles.

In this problem we have two states in which the previous equation can be applied, so

From the first state we can calculate the Volume

Replacing

From the state two we can calculate now the number of the moles, considering that there is a change of 0.8 from Volume 1, then

Therefore there are 3.3moles of air left in the tire.

found in the nucleus

has mass of one amu