At 297 k , to what pressure can the carbon dioxide in the cartridge inflate a 3.79 l mountain bike tire? (note that the gauge pressure is the difference between the total pressure and atmospheric pressure. in this case, assume that atmospheric pressure is 14.7 psi.)

23.226 psi

Explanation:

From the source,

The mass of the carbon dioxide is:- 16.0 g

Molar mass of carbon dioxide = 44.01 g/mol

The formula for the calculation of moles is shown below:

Thus,

Moles of = 0.3636 moles

Volume = 3.79 L

n = 0.3636 mol

Temperature = 297 K

Using ideal gas equation as:

PV=nRT

where,  

P is the pressure

V is the volume

n is the number of moles

T is the temperature  

R is Gas constant having value = 0.0821 L.atm/K.mol

Applying the equation as:

P × 3.79 L = 0.3636 mol × 0.0821 L.atm/K.mol × 297 K

⇒P = 2.34 atm

Also,  1 atm = 14.7 psi

So, Pressure = psi = 37.926 psi

THus, pressure by the gas is:-

P = Total pressure - Atmospheric pressure = 37.926 - 14.7 psi = 23.226 psi

The carbon dioxide in the cartridge inflate a 3.79 L mountain bike tire to 23.226 psi pressure.