Ch.10 - Gases

Brown - Chemistry: The Central Science 15th Edition

Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook

Brown 15th Edition

Ch.10 - Gases

Problem 8

Chapter 10, Problem 8

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 (d) the rate of effusion through a pinhole leak?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780137542970

Verified step by step guidance

Step 1: Understand the concept of effusion, which is the process by which gas molecules escape through a small hole into a vacuum. The rate of effusion is inversely proportional to the square root of the molar mass of the gas, according to Graham's law of effusion.

Step 2: Write down Graham's law of effusion: \( \text{Rate of effusion} \propto \frac{1}{\sqrt{M}} \), where \( M \) is the molar mass of the gas.

Step 3: Identify the molar masses of the gases involved. For \( N_2 \), the molar mass is approximately 28 g/mol, and for \( CH_4 \), the molar mass is approximately 16 g/mol.

Step 4: Compare the rates of effusion for \( N_2 \) and \( CH_4 \) using Graham's law. Since the rate of effusion is inversely proportional to the square root of the molar mass, calculate the ratio of the rates: \( \frac{\text{Rate of effusion of } CH_4}{\text{Rate of effusion of } N_2} = \sqrt{\frac{M_{N_2}}{M_{CH_4}}} \).

Step 5: Conclude that the gas with the lower molar mass, \( CH_4 \), will effuse faster than \( N_2 \) because the rate of effusion is inversely proportional to the square root of the molar mass.

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. In this scenario, comparing nitrogen (N2) and methane (CH4), we can determine their effusion rates based on their respective molar masses.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For nitrogen (N2), the molar mass is approximately 28 g/mol, while for methane (CH4), it is about 16 g/mol. The difference in molar mass between these two gases is crucial for applying Graham's Law to predict their effusion rates.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is defined as a temperature of 0 degrees Celsius (273.15 K) and a pressure of 1 atmosphere (atm). At STP, one mole of an ideal gas occupies 22.4 liters. This standardization allows for consistent comparisons of gas behavior, including effusion rates, under controlled conditions.

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Related Practice

Textbook Question

A thin glass tube 1 m long is filled with Ar gas at 101.3 kPa, and the ends are stoppered with cotton plugs as shown below. HCl gas is introduced at one end of the tube, and simultaneously NH3 gas is introduced at the other end. When the two gases diffuse through the cotton plugs down the tube and meet, a white ring appears due to the formation of NH4Cl1s2. At which location—a, b, or c—do you expect the ring to form?

Consider the following graph. (b) If A and B refer to the same gas at two different temperatures, which represents the higher temperature?

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Textbook Question

Consider the following samples of gases:

If the three samples are all at the same temperature, rank them with respect to (c) density

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Textbook Question

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube closed at both ends.

a. How many blue gas molecules are in the left container?

b. How many red gas molecules are in the middle container?

c. When the valves are opened and the gases are allowed to mix at constant temperature, how many atoms of each type of gas end up in the originally empty container? Assume that the containers are of equal volume and ignore the volume of the connecting tube. [Section 10.4]

Textbook Question

You have a sample of gas in a container with a movable piston, such as the one in the drawing. b. Redraw the container to show what it might look like if the external pressure on the piston is increased from 1.0 atm to 2.0 atm while the temperature is kept constant.

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