Cyclists sometimes use pressurized carbon dioxide inflators to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide.
At 301 K , to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.08 L mountain bike tire?
(Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.)
Express your answer to three significant figures with the appropriate units.

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Tringa0 Tringa0 · Answer 1 · 2019-11-25T09:30:51+01:00

Answer:

Pressure of the carbon dioxide gas in the bicycle tire is 28.2 psi.

Explanation:

Using ideal gas equation:

PV = nRT

where,

P = Total Pressure of gas =?

V = Volume of gas = 3.08 L

n = number of moles of gas = [tex]\frac{16.0 g}{44 g/mol}=0.3636 mol[/tex]

R = Gas constant = 0.0821 L.atm/mol.K

T = Temperature of gas = 301 K

Putting values in above equation, we get:

[tex](P\times 3.08 L)=0.3636\times (0.0821L.atm/mol.K)\times 301K\\\\P=2.92 atm[/tex]

P = 2.92 atm = 42.91 psi(1 atm =14.6959 psi)

Gauge pressure = Total pressure - Atmospheric pressure

= P - 14.7 psi = 42.91 psi - 14.7 psi = 28.21 psi ≈ 28.2 psi

Pressure of the carbon dioxide gas in the bicycle tire is 28.2 psi.