Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problem 87

Chapter 5, Problem 87

A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the second gas.

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Use Graham's law of effusion, which states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass: \( \frac{\text{Rate}_1}{\text{Rate}_2} = \sqrt{\frac{M_2}{M_1}} \).

Identify the known values: \( \text{Rate}_1 = \frac{1}{76} \) for neon and \( \text{Rate}_2 = \frac{1}{155} \) for the unknown gas.

Substitute the rates into Graham's law equation: \( \frac{\frac{1}{76}}{\frac{1}{155}} = \sqrt{\frac{M_2}{M_1}} \).

Solve for \( \frac{M_2}{M_1} \) by squaring both sides of the equation.

Use the known molar mass of neon (20.18 g/mol) to find the molar mass of the unknown gas, \( M_2 \), and identify the gas based on its molar mass.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases effuse faster than heavier gases. The relationship can be expressed mathematically as (Rate1/Rate2) = √(Molar Mass2/Molar Mass1), allowing for the comparison of effusion rates between two gases.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It is a critical factor in determining the behavior of gases, including their rates of effusion. For noble gases, molar masses vary significantly, which influences their effusion rates and can be used to identify unknown gases when compared to known values.

Noble Gases

Noble gases are a group of elements in Group 18 of the periodic table, known for their low reactivity due to having a full valence shell of electrons. Common noble gases include helium, neon, argon, krypton, xenon, and radon. Each noble gas has a distinct molar mass, which is essential for calculations involving effusion and can help identify unknown gases based on their effusion rates.

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