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?
Ch.10 - Gases
Chapter 10, Problem 10c
Consider the following samples of gases:
If the three samples are all at the same temperature, rank them with respect to (c) density
Verified step by step guidance1
Step 1: Recall that the density of a gas is given by the formula: Density = mass/volume. In this case, we are not given the mass or volume of the gases, but we know that all gases at the same temperature and pressure occupy the same volume. Therefore, the density of a gas is directly proportional to its molar mass.
Step 2: Identify the molar mass of each gas. The molar mass of a gas can be found by adding up the atomic masses of all the atoms in a molecule of the gas. For example, the molar mass of O2 (oxygen) is approximately 32 g/mol, the molar mass of N2 (nitrogen) is approximately 28 g/mol, and the molar mass of He (helium) is approximately 4 g/mol.
Step 3: Rank the gases by their molar mass. The gas with the highest molar mass will have the highest density, and the gas with the lowest molar mass will have the lowest density.
Step 4: Therefore, the order of the gases from highest to lowest density is O2 > N2 > He.
Step 5: Remember that this ranking is based on the assumption that all gases are at the same temperature and pressure. If the temperature or pressure changes, the density of the gases may also change.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ideal Gas Law
The Ideal Gas Law, represented as PV = nRT, relates the pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T) of an ideal gas. This law helps in understanding how changes in these variables affect the behavior of gases, including their density, which is defined as mass per unit volume.
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Density of Gases
Density is a physical property defined as mass divided by volume (ρ = m/V). For gases, density can vary significantly with changes in temperature and pressure. At constant temperature, the density of a gas is influenced by its molar mass; heavier gases will generally have higher densities than lighter gases under the same conditions.
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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 gases, a higher molar mass indicates a greater mass of gas molecules in a given volume, leading to higher density. Thus, when comparing gases at the same temperature, those with higher molar masses will rank higher in density.
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Related Practice
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?
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
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
The graph below shows the change in pressure as the temperature increases for a 1-mol sample of a gas confined to a 1-L container. The four plots correspond to an ideal gas and three real gases: CO2, N2, and Cl2. (a) At room temperature, all three real gases have a pressure less than the ideal gas. Which van der Waals constant, a or b, accounts for the influence intermolecular forces have in lowering the pressure of a real gas?
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