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Ch.10 - Gases
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.10 - GasesProblem 9c
Chapter 10, Problem 9c

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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insert step 1: Understand the three types of molecular speeds in a gas: the most probable speed (v_p), the average speed (v_avg), and the root-mean-square speed (v_rms).
insert step 2: Recall the relationships between these speeds: v_p < v_avg < v_rms for a given temperature.
insert step 3: Analyze the graph to identify the curves representing each of these speeds.
insert step 4: Compare the positions of the peaks and the spread of the curves to determine which speed is highest for each curve.
insert step 5: Conclude that the root-mean-square speed is typically the highest among the three speeds for each curve.

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Key Concepts

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

Most Probable Speed

The most probable speed is the speed at which the maximum number of particles in a gas sample are moving at a given temperature. It is derived from the Maxwell-Boltzmann distribution and represents the peak of the distribution curve, indicating the most common speed among the particles.
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Most Probable Speed Example

Root-Mean-Square Speed

The root-mean-square (RMS) speed is a measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of the speeds. It provides a way to quantify the kinetic energy of the gas particles and is always greater than or equal to the average speed.
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Root Mean Square Speed Formula

Average Speed

The average speed of gas particles is calculated by taking the total distance traveled by all particles divided by the total time taken. It is a straightforward arithmetic mean and typically falls between the most probable speed and the root-mean-square speed, reflecting the overall motion of the gas.
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Average Bond Order
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?

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?

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

Textbook Question

Consider the following samples of gases:

If the three samples are all at the same temperature, rank them with respect to (a) total pressure

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?