Question

A 25.00 g CO2 cartridge contains 25.00 grams of CO2. A 25 x 2.4 MTB tire has a volume of about 5.30 liters. On a cool fall day (6.7 degrees Celsius), what is the maximum pressure in psi you can get with a 25.00 g CO2 inflator, assuming you are starting with a 0 psi tire?

Answer 1

Volume of the tire = 5.30 L

Maximum mass of CO₂ that can be filled in the tire from the inflator= 25.00 g

Molar mass of CO₂ = Molar mass of C + 2 x Molar mass of O

= 12 g/mol + 2 x 16 g/mol

= 12 g/mol + 32 g/mol

= 44 g/mol

Maximum number of moles of CO₂ that can be filled in the tire = 25.00 g/44.00 g/mol= 0.57 mol

Temperature T= 6.7°C = 6.7 + 273.15 K = 279.85 K (0°C = 279.15 K)

Gas constant R = 0.0821 L atm/mol K

Substituting the values in ideal gas equation

PV = nRT

P (5.30 L)= 0.57 mol x 0.0821 L atm/mol K x 279.85 K

P = 2.47 atm

1 atm = 14.70 psi

So, P = 2.47 atm x 14.70 psi/atm = 36.32 psi

So, the maximum pressure of the tire can be 36.32 psi.