Ch.10 - Gases

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.10 - Gases

Problem 81

Chapter 10, Problem 81

Place the following gases in order of increasing average molecular speed at 25 °C: O2, Ar, CO, HCl, CH4.

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

Understand that the average molecular speed of a gas is related to its molar mass and temperature. According to the kinetic molecular theory, the average speed of gas molecules is inversely proportional to the square root of the molar mass of the gas.

Use the formula for average molecular speed: \( v = \sqrt{\frac{3RT}{M}} \), where \( v \) is the average speed, \( R \) is the ideal gas constant, \( T \) is the temperature in Kelvin, and \( M \) is the molar mass of the gas in kilograms per mole.

Convert the temperature from Celsius to Kelvin by adding 273.15 to the Celsius temperature: \( 25 + 273.15 = 298.15 \) K.

Calculate the molar mass for each gas: O2 (32 g/mol), Ar (40 g/mol), CO (28 g/mol), HCl (36.5 g/mol), CH4 (16 g/mol).

Rank the gases in order of increasing average molecular speed by comparing their molar masses. The gas with the highest molar mass will have the lowest average speed, and the gas with the lowest molar mass will have the highest average speed.

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 will effuse faster than heavier gases. Understanding this principle is crucial for predicting the average molecular speeds of different gases at a given temperature.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. It posits that the average kinetic energy of gas molecules is directly proportional to the temperature of the gas in Kelvin. This theory helps in understanding how temperature affects molecular speed and the distribution of speeds among gas molecules.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In the context of gas behavior, molar mass is a key factor in determining the average speed of gas molecules; lighter gases (lower molar mass) will generally move faster than heavier gases at the same temperature.

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Textbook Question

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (a) number of molecules?

(b) Calculate the rms speed of NF₃ molecules at 25 °C.

Suppose you have two 1-L flasks, one containing N2 at STP, the other containing CH4 at STP. How do these systems compare with respect to (c) average kinetic energy of the molecules?

The temperature of a 5.00-L container of N₂ gas is increased from 20 °C to 250 °C. If the volume is held constant, predict qualitatively how this change affects the following: (b) the rootmean-square speed of the molecules. (c) the strength of the impact of an average molecule with the container walls. (d) the total number of collisions of molecules with walls per second.

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