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Ch.10 - Gases
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?

Verified step by step guidance
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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.
Related Practice
Open Question
Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? (a) Because Xe is a noble gas, there is less tendency for the Xe atoms to repel one another, so they pack more densely in the gaseous state. (b) Xe atoms have a higher mass than N2 molecules. Because both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser. (c) The Xe atoms are larger than N2 molecules and thus take up a larger fraction of the space occupied by the gas. (d) Because the Xe atoms are much more massive than the N2 molecules, they move more slowly and thus exert less upward force on the gas container and make the gas denser.
Textbook Question

The apparatus shown here has two gas-filled containers and one empty container, all attached to a hollow horizontal tube. When the valves are opened and the gases are allowed to mix at constant temperature, what is the distribution of atoms in each container?

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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. Assume that the containers are of equal volume and ignore the volume of the connecting tube. Which gas has the greater partial pressure after the valves are opened?

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Textbook Question

Consider the following graph. (a) If curves A and B refer to two different gases, He and O2, at the same temperature, which curve corresponds to He?

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Textbook Question

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 graph. (c) For each curve, which speed is highest: the most probable speed, the root-mean-square speed, or the average speed?

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