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Which of the following statements is(are) true? For the false statements, correct them. a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules. b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules. c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly. d. As temperature increases, the effect of interparticle interactions on gas behavior is increased. e. At constant \(V\) and \(T\), as gas molecules are added into a container, the number of collisions per unit area increases resulting in a higher pressure. f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and moles of gas.

Step by step solution

01

Statement a: Average velocity at a constant temperature

Statement a is true. According to Graham's law of diffusion, the lighter the gas molecules, the faster their average velocity at a constant temperature. This is because the lighter molecules have less mass and hence require less energy to move at a given velocity.

02

Statement b: Average kinetic energy at a constant temperature

Statement b is false. At a constant temperature, all the gases have the same average kinetic energy. This is because the average kinetic energy of any gas is proportional to its temperature. So, regardless of the weight of the gas molecules, if they are at the same temperature, they have the same average kinetic energy.

03

Statement c: Ideal gas behavior

Statement c is true. Real gases behave most like an ideal gas when the container volume is relatively large, and the gas molecules are moving relatively quickly. This is because, under these conditions, the gas molecules are less likely to experience any significant interparticle interactions and have a negligible volume compared to the container volume, both of which are characteristics of an ideal gas.

04

Statement d: Interparticle interactions effect

Statement d is false. Actually, as temperature increases, the effect of interparticle interactions on gas behavior is decreased. This happens because at higher temperatures, gas molecules move faster and are less likely to experience significant interparticle interactions. With the decrease of interparticle interactions, the gas behaves more closely to an ideal gas.

05

Statement e: Pressure within a container

Statement e is true. At constant volume and temperature, as more gas molecules are added to a container, the number of collisions per unit area increases, leading to a higher pressure. This is demonstrated by Boyle's law, which states that the pressure of a gas is inversely proportional to its volume at constant temperature and moles of gas.

06

Statement f: Kinetic molecular theory predictions

Statement f is false. The kinetic molecular theory predicts that pressure is directly proportional to temperature at constant volume and moles of gas, not inversely proportional. This is known as Gay-Lussac's law, which states that pressure and temperature are directly proportional for a fixed amount of gas at constant volume.

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