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Chapter 5: Problem 15

How does Dalton's law of partial pressures help us with our model of ideal gases? That is, what postulates of the kinetic molecular theory does it support?

Short Answer

Expert verified
Dalton's law of partial pressures supports the kinetic molecular theory by emphasizing that gas particles are in constant, random motion, do not interact with each other, and that the pressure each gas exerts depends only on its partial pressure. This law demonstrates that the total pressure of a non-reactive gas mixture results from the sum of the individual pressures, without considering any interactions between the gases.

Step by step solution

01

Understanding Dalton's Law of Partial Pressures

Dalton's law of partial pressures states that in a mixture of non-reactive gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. Mathematically, it is expressed as: \[ P_{total} = P_1 + P_2 + P_3 + ... + P_n \] where \(P_{total}\) is the total pressure, and \(P_i\) represents the partial pressure of the individual gases in the mixture.
02

Kinetic Molecular Theory - Gas Particles are in Constant, Random Motion

According to the kinetic molecular theory, gas particles are always moving in random directions with a wide range of velocities. These particles are assumed to be in constant motion and collide with the walls of the container, exerting pressure. When multiple gases are mixed, they behave as one gas with gas particles from each gas species moving randomly and exerting pressure on the container walls.
03

Kinetic Molecular Theory - Gas Particles Don't Interact With Each Other

Another fundamental postulate of the kinetic molecular theory is that gas particles do not interact with each other. They neither attract nor repel each other. This means that the pressure each gas exerts is independent of the presence of other gas particles. Dalton's law supports this idea by showing that the total pressure exerted by a gas mixture is the sum of individual pressures, without any consideration of interactions between the gases.
04

Pressure Exerted Depends Only on Partial Pressure

Dalton's law states that the pressure exerted by each gas in a mixture depends only on its partial pressure, which is proportional to both its concentration and temperature. This is in line with the postulates of the kinetic molecular theory, which states that the pressure a gas exerts is proportional to its concentration and its temperature. Applying Dalton's law of partial pressures to ideal gas mixtures supports the idea that the total pressure exerted by the gases results solely from the addition of the partial pressures of each individual gas. No interactions between the gases need to be considered. In conclusion, Dalton's law of partial pressures supports the assertions of the kinetic molecular theory that gas particles are in constant, random motion and do not interact with each other. Additionally, the pressure exerted by a gas in a mixture depends only on its partial pressure.

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Most popular questions from this chapter

A compressed gas cylinder contains \(1.00 \times 10^{3} \mathrm{~g}\) argon gas. The pressure inside the cylinder is \(2050 .\) psi (pounds per square inch) at a temperature of \(18^{\circ} \mathrm{C}\). How much gas remains in the cylinder if the pressure is decreased to \(650 .\) psi at a temperature of \(26^{\circ} \mathrm{C} ?\)

Consider the following reaction: $$ 4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) $$ It takes \(2.00 \mathrm{~L}\) pure oxygen gas at STP to react completely with a certain sample of aluminum. What is the mass of aluminum reacted?

One of the chemical controversies of the nineteenth century concerned the element beryllium (Be). Berzelius originally claimed that beryllium was a trivalent element (forming \(\mathrm{Be}^{3+}\) ions) and that it gave an oxide with the formula \(\mathrm{Be}_{2} \mathrm{O}_{3} .\) This resulted in a calculated atomic mass of \(13.5\) for beryllium. In formulating his periodic table, Mendeleev proposed that beryllium was divalent (forming \(\mathrm{Be}^{2+}\) ions) and that it gave an oxide with the formula BeO. This assumption gives an atomic mass of \(9.0 .\) In 1894 , A. Combes (Comptes Rendus 1894, p. 1221\()\) reacted beryllium with the anion \(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}^{-}\) and measured the density of the gaseous product. Combes's data for two different experiments are as follows: If beryllium is a divalent metal, the molecular formula of the product will be \(\mathrm{Be}\left(\mathrm{C}_{3} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{2} ;\) if it is trivalent, the formula will be \(\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{3}\). Show how Combes's data help to confirm that beryllium is a divalent metal.

One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of \({ }^{12} \mathrm{C}^{16} \mathrm{O},{ }^{12} \mathrm{C}^{17} \mathrm{O}\), and \({ }^{12} \mathrm{C}^{18} \mathrm{O}\). Name some advantages and disad- vantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide.

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.
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