A bicycle tire whose volume is 4.1 x 10-4 m3 has a temperature of 295 K and an a

Question

A bicycle tire whose volume is 4.1 x 10-4 m3 has a temperature of 295 K and an absolute pressure of 3.51 x 105 Pa. A cyclist brings the pressure up to 6.78 x 105 Pa without changing the temperature or volume. How many moles of air must be pumped into the tire?

Explanation / Answer

use ideal gas law p·V = n·R·T => n = p·V/(R·T) Initial number of moles was n1 = p1·V1/(R·T1) final number of moles in the tire is n2 = p2·V2/(R·T2) = p2·V1/(R·T1) (because temperature and volume remain unchanged. So the number of moles added is: ?n = n2 - n1 = (p2 - p1)·V1 / (R·T1) = (5.15×105Pa - 4.95×105Pa) · 3.10×10?4m³ / (8.3145J/molK · 295K) = 2.53×10?³mol

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