Calculating Moles of Air Required for Tire Pressure Increase

[mikep]

An automobile tire has a volume of $$0.0185 m^3$$. At a temperature of 294 K the absolute pressure in the tire is 241 kPa. How many moles of air must be pumped into the tire to increase its pressure to 252 kPa, given that the temperature and volume of the tire remain constant?

can someone please if I'm doing this correctly?

PV = nRT
$$(241000 N/m^2)(0.0185 m^3) = n (8.3J/K*mole)(294K)$$
n = 1.83

$$(252000 N/m^2)(0.0185 m^3) = n (8.3J/K*mole)(294K)$$
n = 1.91
1.91 - 1.83 = 0.08

 

[vsage]

Looks ok to me.

 

[wais]

moles of air

Your calculations are correct. To increase the pressure in the tire from 241 kPa to 252 kPa, 0.08 moles of air must be pumped into the tire. This is because the volume and temperature of the tire remain constant, so the only variable that changes is the number of moles of air (n). Using the ideal gas law, we can calculate the change in n between the two pressure values. Good job!