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Chapter 1: Problem 20

A gas sample with a mass of 10 grams occupies 5.0 liters and exerts a pressure of 2.0 atm at a temperature of \(26^{\circ} \mathrm{C} .\) Which of the following expressions is equal to the molecular mass of the gas? The gas constant, \(R,\) is \(0.08(\mathrm{L} \times \mathrm{atm}) / \mathrm{mol} \times \mathrm{K}\) ). (A) \((0.08)(299) \mathrm{g} / \mathrm{mol}\) (B) \(\frac{(299)(0.50)}{(2.0)(0.08)} \mathrm{g} / \mathrm{mol}\) (C) \(\frac{299}{0.08} \mathrm{g} / \mathrm{mol}\) (D) \((2.0)(0.08) \mathrm{g} / \mathrm{mol}\)

Short Answer

Expert verified
None of the options is correct. The molar mass of the gas, calculated using the provided data and formula, is approximately 30 g/mol, which none of the choices matches.

Step by step solution

01

Convert Celsius to Kelvin

Temperature must be represented in Kelvin for the Ideal Gas Law. The conversion formula is \(K = ^{\circ}C + 273\). Therefore, convert the given Celsius temperature to Kelvin: \(K = 26^{\circ}C + 273 = 299K\).
02

Apply the Ideal Gas Law

Rearrange the Ideal Gas Law to solve for the number of moles, so that it becomes \(n = \frac{PV}{RT}\). Substituting the given values into the equation, we get \(n = \frac{(2.0 atm)(5.0 L)}{(0.08 L \cdot atm/mol \cdot K)(299 K)} = 0.333 mol\).
03

Calculate the Molar Mass

Use the formula for molar mass, \(M = \frac{m}{n}\), to find it. Substituting the calculated number of moles and given mass of the gas into the formula we obtain \(M = \frac{10 g}{0.333 mol} = 30 g/mol\).
04

Match the Result to the Choices

The goal is to find which of the choices matches with the calculated molar mass when calculated. None of them matches, they represent different calculations. However, if we look at choice (B), its formula looks like the formula used to solve for the number of moles (not molar mass), \(n = \frac{PV}{RT}\). If we rewrite it as molar mass \(M = \frac{m}{n}\), it becomes \(M = \frac{(2.0 atm)(0.08 L \cdot atm/mol \cdot K)}{(299 K)(0.5 mol)}\), which is still not matching the correct calculation for molar mass. So none of the options are correct for the molar mass of the gas considering the values provided in the question.

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Most popular questions from this chapter

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