UNIT 10 Pressure: F/A http://chemlab.truman.edu/chem130labs/calorimetryfiles/thermobackground.asp There are four variable needed to define the physical state of a gas. They are: o Temperature o Pressure o Volume o Amount of gas (moles) Relationship between pressure and volume o What happens when a balloon at the earth s surface is released into the atmosphere? As it rises, the balloon. o Boyle s law: PV = constant Your lungs work by Boyle s law. How? Relationship between temperature and volume. o Charles s law: V/T = constant Relationship between volume and quantity (moles) o The more air I blow into a balloon, the larger the balloon becomes. o Avogadro s hypothesis: V/n = constant Combining relationships. The Ideal Gas Equation. o Bole s law: V α 1/P (constant n, T) o Charle s law: V α T (constant n, P) o Avogadro s law: V α n (constant P, T) o Thus, V α nt/p o Rearranging, PV α nt o Introducing a constant, R we get:
PV = nrt (T must always be in Kelvin!) o To use this equation, we must assume some things: The gas molecules take up no space The gas molecules are so far apart that they do not interact. Question: What would happen if we did not make these assumptions? Question: What is the volume of 1 mole of an ideal gas at 0 Celsius (273.15 K) and atmospheric pressure (1 atm)? R = 0.08206 (L*atm/mol-K). Note: STP (standard temperature and pressure) is defined as 0 Celsius and 1 atm. Relating Density to the Ideal Gas Equation. o The definition of moles, n, is mass/molar mass. o If we substitute this for n in the Ideal Gas Equation we get: o Because density is mass/v, PV = (mass/molar mass)rt PV = V(d/molar mass) RT or P = (d/molar mass) RT o Rearrange this to get o Molar mass of a gas = drt/p Partial Pressures (mixtures of gases). o Dalton s Law of Partial Pressures The pressure exerted by a particular component of a mixture of gasses is called the partial pressure of that component. o Let Pt = the total pressure of the mixture o For each gas in the mixture (1, 2, 3 ): P 1 = n 1 (RT/V) P 2 = n 2 (RT/V) P 3 = n 3 (RT/V) o All gases occupy the same volume and have the same temperature, thus: P t = (n 1 + n 2 + n 3 +..)(RT/V) = n t (RT/V) o The number of moles of gas determines the total pressure of a gas mixture. Question: A mixture of 6 g of O 2 (g) and 9 g of CH4 (g) is placed in a 15 L vessel at 0 Celsius. What is the partial pressure of each gas? What is the total pressure? Partial Pressures and Mole Fractions: n 1 /n t
Question: A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5 mol percent of CO 2, 18.0 mol percent of O 2 and 80.5 percent Ar. Calculate the partial pressure of O 2 in the mixture if the total pressure is 745 torr. If this atmosphere is to be held in a 121 L space at 295 K, how many moles of O 2 are needed? Kinetic Molecular Theory of Gases. Explains the relationships between P, V, n, R, and T. o Gases consist of large numbers of molecules/atoms/particles that are in continuous random motion. o The combined volume of all the particles is negligible relative to the total volume of the container o Attractive and repulsive forces between gas molecules are negligible. o Energy can be transferred between particles during collisions but, as long as temperature remains constant, the average kinetic energy of the molecules does not change with time. o The average kinetic energy of the molecules is proportional to the absolute temperature. At a particular temperature the molecules of all gases have the same average kinetic energy. Speed of gas particles. o Although gas particles at a particular temperature have an average speed, the individual particles have different speeds. http://www.chemistry.wustl.edu/~edudev/labtutorials/coursetutorials/tutorials/airbags/gas_0 6.htm Question: A sample of oxygen gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on: 1) the average kinetic energy of the molecules 2) their average speed, 3) the number of collisions they make with the container walls per unit time.
Question: How is the average speed of gas particles in a container changed by: 1) an increase in temperature, 2) an increase in volume, 3) mixing with a sample of Ar at the same temperature. Real Gases. Deviation from ideal behavior. Question: As temperature decreases, gases deviate from ideal behavior. How and Why? Remember the assumptions we made for ideal gas behavior. Question: If the pressure of a gas increases by decreasing the volume of the container, how would this lead to a deviation from ideal gas behavior? Question: At low temperatures and high pressures, deviations from ideal gas behavior are large. Why? http://chemwiki.ucdavis.edu/physical_chemistry/physical_properties_of_matter/phases_of_mat ter/gases/real_gases Question: Describe the deviations from ideal behavior in the above graph. van der Waals Equation (real gases). Let s start with PV = nrt (P + n 2 a/v 2 )(V-nb) = nrt
Rearranged: P = nrt/v 1) First correction term: the pressure of real gas is smaller than what is calculated by the ideal gas equation. P = nrt/v- n 2 a/v 2 n 2 a/v 2 is the correction for the fact that a real gas has smaller pressure due to intermolecular forces than an ideal gas does. Rearranged: (P + n 2 a/v 2 ) =nrt/v 2) Second correction term: gases do take up space. The ideal gas law calculates a volume that is too high when you assume that gases take up no space. (P + n 2 a/v 2 ) =nrt/(v-nb) Rearranged: (P + n 2 a/v 2 )(V-nb) = nrt