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Pressure has more of an effect on gaseous reactions than on reactions in any other phase of matter. This is because the particles of a gas are spread far apart and move around freely. The amount of pressure on the system determines how much room these particles have to move around.
The pressure and volume of a gas are inversely proportional. Therefore, as you increase the pressure on a gas, the volume decreases. This means that as the pressure on a gas increases, the gas has less space to spread out and the particles are closer together.
A chemical reaction proceeds because reacting particles collide at the appropriate angle and with enough force to cause a reaction. The more often the particles collide, the more likely it is that a "successful collision" will occur. As the volume of a gas decreases, the particles are naturally forced closer together. Therefore, they will collide more often and the rate of the reaction will increase.
By the end of this section, you will be able to:
The gas laws that we have seen to this point, as well as the ideal gas equation, are empirical, that is, they have been derived from experimental observations. The mathematical forms of these laws closely describe the macroscopic behavior of most gases at pressures less than about 1 or 2 atm. Although the gas laws describe relationships that have been verified by many experiments, they do not tell us why gases follow these relationships. The kinetic molecular theory (KMT) is a simple microscopic model that effectively explains the gas laws described in previous modules of this chapter. This theory is based on the following five postulates described here. (Note: The term “molecule” will be used to refer to the individual chemical species that compose the gas, although some gases are composed of atomic species, for example, the noble gases.)
The test of the KMT and its postulates is its ability to explain and describe the behavior of a gas. The various gas laws can be derived from the assumptions of the KMT, which have led chemists to believe that the assumptions of the theory accurately represent the properties of gas molecules. We will first look at the individual gas laws (Boyle’s, Charles’s, Amontons’s, Avogadro’s, and Dalton’s laws) conceptually to see how the KMT explains them. Then, we will more carefully consider the relationships between molecular masses, speeds, and kinetic energies with temperature, and explain Graham’s law. The Kinetic-Molecular Theory Explains the Behavior of Gases, Part IRecalling that gas pressure is exerted by rapidly moving gas molecules and depends directly on the number of molecules hitting a unit area of the wall per unit of time, we see that the KMT conceptually explains the behavior of a gas as follows:
Molecular Velocities and Kinetic EnergyThe previous discussion showed that the KMT qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a more quantitative fashion to derive these individual laws. To do this, we must first look at velocities and kinetic energies of gas molecules, and the temperature of a gas sample. In a gas sample, individual molecules have widely varying speeds; however, because of the vast number of molecules and collisions involved, the molecular speed distribution and average speed are constant. This molecular speed distribution is known as a Maxwell-Boltzmann distribution, and it depicts the relative numbers of molecules in a bulk sample of gas that possesses a given speed (Figure 2). The kinetic energy (KE) of a particle of mass (m) and speed (u) is given by: [latex]\text{KE}=\frac{1}{2}m{u}^{2}[/latex] Expressing mass in kilograms and speed in meters per second will yield energy values in units of joules (J = kg m2 s–2). To deal with a large number of gas molecules, we use averages for both speed and kinetic energy. In the KMT, the root mean square velocity of a particle,urms, is defined as the square root of the average of the squares of the velocities with n = the number of particles: [latex]{u}_{rms}=\sqrt{\overline{{u}^{2}}}=\sqrt{\frac{{u}_{1}^{2}+{u}_{2}^{2}+{u}_{3}^{2}+{u}_{4}^{2}+\dots }{n}}[/latex] The average kinetic energy, KEavg, is then equal to: [latex]{\text{KE}}_{\text{avg}}=\frac{1}{2}{mu}_{\text{rms}}^{2}[/latex] The KEavg of a collection of gas molecules is also directly proportional to the temperature of the gas and may be described by the equation: [latex]{\text{KE}}_{\text{avg}}=\frac{3}{2}RT[/latex] where R is the gas constant and T is the kelvin temperature. When used in this equation, the appropriate form of the gas constant is 8.314 J/K (8.314 kg m2s–2K–1). These two separate equations for KEavg may be combined and rearranged to yield a relation between molecular speed and temperature: [latex]\frac{1}{2}{mu}_{\text{rms}}^{2}=\frac{3}{2}RT[/latex] [latex]{u}_{\text{rms}}=\sqrt{\frac{3RT}{m}}[/latex]
Calculate the root-mean-square velocity for a nitrogen molecule at 30 °C. Check Your LearningCalculate the root-mean-square velocity for an oxygen molecule at –23 °C. If the temperature of a gas increases, its KEavg increases, more molecules have higher speeds and fewer molecules have lower speeds, and the distribution shifts toward higher speeds overall, that is, to the right. If temperature decreases, KEavg decreases, more molecules have lower speeds and fewer molecules have higher speeds, and the distribution shifts toward lower speeds overall, that is, to the left. This behavior is illustrated for nitrogen gas in Figure 3. At a given temperature, all gases have the same KEavg for their molecules. Gases composed of lighter molecules have more high-speed particles and a higher urms, with a speed distribution that peaks at relatively higher velocities. Gases consisting of heavier molecules have more low-speed particles, a lower urms, and a speed distribution that peaks at relatively lower velocities. This trend is demonstrated by the data for a series of noble gases shown in Figure 4. The PhET gas simulator may be used to examine the effect of temperature on molecular velocities. Examine the simulator’s “energy histograms” (molecular speed distributions) and “species information” (which gives average speed values) for molecules of different masses at various temperatures. The Kinetic-Molecular Theory Explains the Behavior of Gases, Part IIAccording to Graham’s law, the molecules of a gas are in rapid motion and the molecules themselves are small. The average distance between the molecules of a gas is large compared to the size of the molecules. As a consequence, gas molecules can move past each other easily and diffuse at relatively fast rates. The rate of effusion of a gas depends directly on the (average) speed of its molecules: [latex]\text{effusion rate}\propto {u}_{\text{rms}}[/latex] Using this relation, and the equation relating molecular speed to mass, Graham’s law may be easily derived as shown here: [latex]{u}_{\text{rms}}=\sqrt{\frac{3RT}{m}}[/latex] [latex]m=\frac{3RT}{{u}_{rms}^{2}}=\frac{3RT}{{\overline{u}}^{2}}[/latex] [latex]\frac{\text{effusion rate A}}{\text{effusion rate B}}=\frac{{u}_{rms\text{A}}}{{u}_{rms\text{B}}}=\frac{\sqrt{\frac{3RT}{{m}_{\text{A}}}}}{\sqrt{\frac{3RT}{{m}_{\text{B}}}}}=\sqrt{\frac{{m}_{\text{B}}}{{m}_{\text{A}}}}[/latex] The ratio of the rates of effusion is thus derived to be inversely proportional to the ratio of the square roots of their masses. This is the same relation observed experimentally and expressed as Graham’s law.
The kinetic molecular theory is a simple but very effective model that effectively explains ideal gas behavior. The theory assumes that gases consist of widely separated molecules of negligible volume that are in constant motion, colliding elastically with one another and the walls of their container with average velocities determined by their absolute temperatures. The individual molecules of a gas exhibit a range of velocities, the distribution of these velocities being dependent on the temperature of the gas and the mass of its molecules. Key Equations
Glossarykinetic molecular theory: theory based on simple principles and assumptions that effectively explains ideal gas behavior root mean square velocity (urms): measure of average velocity for a group of particles calculated as the square root of the average squared velocity |