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A company that produces footballs uses a proprietary mixture of ideal gases to inflate their footballs. If the temperature of 230 grams [g] of gas mixture in a 15-liter [L] tank is maintained at 465 degrees Rankine [°R] and the tank is pressurized to 135 pound-force per square inch [psi], what is the molecular weight of the gas mixture in units of grams per mole [g/mol]?

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MathPhys

Answer:

35 g/mol

Explanation:

Convert to SI units.

465 R × 5/9 = 258.3 K

Assuming the pressure is absolute pressure:

135 psi × (101.3 kPa / 14.7 psi) = 930.3 kPa

Ideal gas law:

PV = nRT

(930.3 kPa) (15 L) = n (8.314 kPa L / mol / K) (258.3 K)

n = 6.50 mol

The molar mass is therefore:

230 g / 6.50 mol = 35.4 g/mol

Rounded to two significant figures, the molar mass is 35 g/mol.

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