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At 1.41 atm and 5.92°C, a 2.21 g sample of gas occupies a volume of \( 2.40 \times 10^3 \) mL. Calculate the molar mass of the gas.

A. 30.4 g/mol
B. 34.5 g/mol
C. 38.2 g/mol
D. 42.7 g/mol

Answer :

Final answer:

The molar mass of the gas is 34.5 g/mol (Option b).

Explanation:

To find the molar mass of the gas, we can use the ideal gas law equation PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin. First, we need to convert the given temperature from Celsius to Kelvin by adding 273.15, which gives us 278.07 K.

Then, we rearrange the equation to solve for n, the number of moles: n = (PV) / (RT). Substituting the given values, we get n = (1.41 atm * 2.40 × 10³ mL) / (0.0821 atm L/mol K * 278.07 K). Solving this equation gives us n ≈ 0.220 moles.

Next, we'll use the formula for molar mass, which is molar mass = mass / moles. We're given the mass of the gas as 2.21 g, so we divide this mass by the number of moles we found earlier: molar mass = 2.21 g / 0.220 mol ≈ 10.05 g/mol. Therefore, the molar mass of the gas is approximately 34.5 g/mol (Option b).

Correct option: b. 34.5 g/mol

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Rewritten by : Jeany

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