How many moles of gas must be forced into a 4.6 L tire to give it a gauge pressure of 34.2 psi at 30 degrees C? The gauge pressure is relative to atmospheric pressure. Assume that atmospheric pressure is 14.9 psi so that the total pressure in the tire is 49.1 psi.

when the total pressure = P gauge + P baro

= 34.2 psi + 14.9 Psi = 49.1 psi

when we convert P = 49.1 from Psi to atm it will be = 3.34 atm

so, by using the ideal gas equation:

PV = nRT

when P is the pressure in atm = 3.34 atm

and V is the volume in L = 4.6 L

n is the number of moles of the gas

R is the gas constant = 0.0821 atm L / mol K

T is the temperature in Kelvin = 30°C + 273 = 303 K

so by substitution in the ideal gas equation:

∴ n = PV / RT

= 3.34 atm * 4.6 L / 0.0821 atm L/mol K * 303 K

= 0.618 moles

∴ there is 0.618 moles of gas