Chemistry 1350 week of notes
Chemistry 1350 week of notes Chem 1301-2
Popular in Principles of Chemistry I
Popular in Chemistry
This 4 page Class Notes was uploaded by Brianna Carmony on Sunday March 20, 2016. The Class Notes belongs to Chem 1301-2 at Baylor University taught by John Olson in Winter 2016. Since its upload, it has received 11 views. For similar materials see Principles of Chemistry I in Chemistry at Baylor University.
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Date Created: 03/20/16
• The stoichiometry for reactions that involve gases that employs lab line to mole line conversion based on the ideal gas equation of state is also presented. • Finally the kinetic theory of gases is given which gives a much better understanding of the properties of gases and also suggests experimental methods for separating the components of gas mixtures. • If the set of properties that satisfy the criteria above are chosen to be the pressure (P), temperature (T), volume that the gas occupies (V) and the amount of gas given as the number of moles (n), this choice will result in simple relations (laws) between these properties. All of these properties refer to the state of a gas at equilibrium. • It is straightforward to show that each of these four properties satisfy the first criteria. In order to study a given amount of gas, it is necessary to confine it since otherwise it would constantly diffuse and there are numerous pieces of glassware (graduated cylinder, volumetric flask, etc. ) where the volume of the gas can be read directly. The temperature can be read from a thermometer placed in contact with the gas. • The second experimental gas law was discovered by Jacques Charles in 1787 and is known as Charles's Law. • In his studies, the amount of gas and the pressure of the gas were held constant. Below is shown some data along with a plot that represents this type of experiment for a fixed amount of nitrogen at 1atm pressure. • The solid line passes through the data points (x) and the dashed line is an extrapolation to V=0L. As one sees, V is linearly dependent on t so that • • • • is the general equation for V. For t=0 C V=5.6L so that a =5.6L. Using the first two sets o o of data points gives b=0.6L/30 C =0.02L/ C so that • • • and setting V=0L gives t=280 C. With more accurate data one finds that when V=0L, o o the temperature is 273 C. The studies by Charles found that the temperature of 273 C for V=0L was obtained for all gases irregardless of the constant pressure or the amount of gas. This suggest that the above equation for V can be simplified by choosing a temperature scale that is zero for V=0L so that a=0. This scale is called the Kelvin scale or absolute temperature scale and its relation to the centigrade or Celcius scale is • • . • • With temperature defined in degrees Kelvin, Charles’ Law takes the simple form • • • • where K Cs a constant under the conditions of Charles’ experiments. One also sees that o the temperature must be given in degrees Kelvin since, for example, 10 C would give a negative volume which is physically meaningless. If the gas goes from an initial state to a final state under constant pressure and amount of gas, Charles’ Law takes the form • • • • which allows one to, knowing the initial values and one of the final values, determine the other final value. • • EXERCISE • o • to, from the first pair of data points (30. C,5.0L), predict the volumes for the other temperatures in the previous table. • • The temperature was used as a property because it is easy to measure and gives a simple, in mathematical terms, law. • But the question still remains as to what the temperature means in terms of fundamental properties of the gas such a volume, pressure, energy, etc. which can be understood from basic physics. The common temperature of 0K for V=0L seems somewhat elusive to understand. • It is known that the gas consists of particulate matter but how can this be interpreted in terms of properties of particles? This will be returned to later. • The final gas law was produced by GayLussac and Amadeo Avogadro and is known as Avogadro's Hypothesis. This was previously discussed in the section “Dalton’s Theory” of “Experimental Laws and Dalton’s Theory” and a review of this would be helpful. • Avogadro’s Hypothesis states that, if the temperature and pressure of the gas are held constant, the volume that the gas occupies is proportional to the number of moles of the gas. This can be expressed in the form of an equation as • • • where n is the number of moles, K As a proportionality constant and P and T are held constant. Under the conditions of constant temperature and pressure, the initial values of V and n are related to the final values by • • • • which allows one to predict a final value if the initial values and the other final value are known. • What is most interesting about this law is that the dependence is on the number of moles of the gas, not on what the gas is (e.g. oxygen or hydrogen) or the mass of the gas. • For example, one mole of oxygen would have a mass sixteen times greater than one mole of hydrogen. But this law says that, at the same temperature and pressure, one mole of oxygen and one mole of hydrogen would occupy the same volume. • Moreover, a mixture of a half mole of oxygen and a half mole of hydrogen under the same conditions would still occupy the same volume. • The three experimental laws introduced above can be combined into one equation called the ideal gas equation of state. • As pointed out in “Properties of Matter”, an equation of state is a mathematical expression involving the minimum set of chosen properties such that, if all but one property is known, the final one is determined by this equation and the state of the gas (specification of its properties) is determined. • It was also pointed out that one of the conditions for being a property was that it had to be independent of how the system was prepared. Due to this condition, any pathway that leads to the same state of the system can be used. • The gas laws established by Boyle, Charles and Avogadro led to simple relations between the four properties of a gas, the pressure (P), the temperature (T), the volume (V) and the number of moles (n) and they were combined to give the ideal gas equation of state • This set of properties were chosen because they completely specified the state of a gas, were easily measurable and led to this simple equation of state. • However this equation of state is a law, not a theory, and hence does not provide an explanation for it. From Dalton’s Theory, one knows that the gas and the walls of the container it is in consists of small atomic or molecular particles. It is also reasonable to assume that the gas particles are in a state of movement and they are colliding with other gas particles and with the atoms in the walls of the container. • It will be shown in the future that the gas particles interact with each other with attractive forces and that there are attractive forces between the gas particles and the atoms in the walls of the container. • The objective of the theory, to be developed here, is to explain the macroscopic properties of the gas, P, T, V and n in terms of the microscopic properties of the gas particles such as mass, velocity, position, force and energy. • It will be assumed that there are no reactions taking place and that the gas is in a state of equilibrium, i.e., single values for the macroscopic properties. • The macroscopic property that can be directly connected to microscopic properties is the pressure which is the force divided by the area. • This is because the force is due to collisions of gas particles with the walls of the container. • Given the initial positions, velocities and forces acting on all gas particles, one could, in principle, treat the gas particles as miniature billiard balls and solve Newton’s equation of motion • What one should notice is that at the hot temperature, T , aH reater number of molecules have larger speeds in comparison to the curve at the lower temperature T . C • The most probable speed corresponds to the maximum in the curve. One sees that as the temperature increases, this most probable speed also increases. • This theory can be used to obtain an explanation of the gas laws. For example, the ideal gas equation of state says that, no matter what the gas is, the same number of moles of a gas occupying the same volume at the same pressure will always have the same pressure. • To see this, consider the gases helium and argon and let an equal number of moles of each gas be present in two identical containers (same V) at the same temperature of 25 C. o As found above, u frmsHe is 1.36x10 m/s and, from Eq. (57), u for Arrms 431m/s. the molar kinetic energy for He and Ar are both 3.7kJ/mole. • Therefor, since n and V are the same for both gases, both gases have the same pressure. The reason for this on a more fundamental level is that the pressure, is due to force divided by the area and the force, is the product of the mass times the change in velocity times the number of collisions with the wall. • Argon has a larger mass but its u rmssmaller so that the change in velocity is smaller and the number of collisions is smaller. Therefor, the increase in mass is compensated with the decrease in u rms that the pressure is the same. • The kinetic theory can also be used for gas mixtures by summing over each component in the mixture to give the total pressure. • For a mixture of gases A and B with no intermolecular forces, each component can be treated separately so that it is not difficult to show that for N particles of gas A and N A B particles of gas B, the total pressure would become which is Dalton's Law of Partial Pressures derived from the kinetic theory of gases.
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