Unit 8 Gases

Characteristics of Gases Gases can be elements or molecules at room temp (298K) Elemental gases Diatomic H2, O2, N2, F2, Cl2 Monatomic - Noble gases Molecular gases Following slide Gases expand to fill their containers Compressible Gases form homogeneous mixtures with each other

Pressure Pressure is force applied over an area P = F/A Gases molecules are pulled downward by gravity causing atmospheric pressure Pressure is measured using a barometer Standard atmospheric pressure is measured at sea level Units of pressure 1atm = 760mmHg = 760 torr = 1.01325x105 Pa = 101.325 kPa

Conversion Practice Perform the following conversions Convert 0.357 atm to torr Convert 6.6x10- 2 torr to atm Convert 147.2 kPa to torr Answers: 271torr, 8.7x10- 5atm, 1104torr

Measuring Pressure in the lab Barometer measures atmospheric pressures Manometer can be used to measure pressure of an enclosed gas

Using a Manometer to Measure Pressure On a certain day the barometer in a laboratory indicates that the atmospheric pressure is 764.7 torr. A sample of gas is placed in a vessel attached to an open ended mercury manometer. A meter stick is used to measure the height of the mercury above the bottom of the manometer. The level of the mercury in the open-end arm of the manometer has a height of 136.4mm and that in the arm that is in contact with the gas has a height of 103.8mm. What is the pressure of the gas in atmospheres and in kPa?

Gas Laws Four variables determine the state of a gas n = number of moles (mol) P = pressure (atm, mmHg, torr) V = volume (L) T = temperature (K) Gas laws show the relationships between them

Boyle's Law As pressure decreases volume increases As pressure increases volume decreases What type of relationship is this? Boyle's Law = The volume of a fixed quantity of gas maintained at constant temperature is ________ proportional to the pressure. PV = constant Constant depends on temperature and amount of gas

Relationship between P and V

Charles Law As temperature increases volume increases As temperature decreases volume decreases What type of relationship is this? Charles law = The volume of a fixed amount of gas maintained at constant pressure is ________ proportional to its absolute temperature. V/T = constant Constant depends on amount of gas and pressure

Relationship between V and T

Gay-Lussac's Law Law of combining volumes = At a given temperature and pressure, the volumes of gases which react are ratios of small whole numbers.

Avogadro's Law As the amount of gas increases volume increases As the amount of gas decreases volume decreases What type of relationship is this? Avogadro's Law = The volume of a gas maintained at constant temperature and pressure is ________ proportional to the number of moles of gas. V = constant x n Constant depends on the temperature and pressure

Using the Gas Laws Suppose we have a gas confined to a piston. Consider the following changes: Heat the gas from 298K to 360K, while maintaining pressure Move the piston to reduce the volume of gas from 1L to 0.5L Inject additional gas through the gas inlet valve. Indicate whether each of the following changes will occur Decrease the distance between molecules Increase the pressure of the gas Increase the total mass of the gas Increase the number of moles of gas

Ideal Gas Law Boyle's Law → V α 1/P (constant n, T) Charles's Law → V α T (constant n, P) Avogodro's Law → V α n (constant P, T) V α nT/P → V = R(nT/P) PV = nRT = ideal gas equation R = gas constant Ideal gases behavior can be described by this equation. At STP, 1 mole of a gas has a volume 22.4L STP = 0°C, 1 atm

Ideal Gas Constant

Using the Ideal Gas Law If n and T are held constant P1V1=P2V2 If V and n are held constant P1/T1=P2T2 If P and n are held constant V1/T1=V2/T2 If nothing is held constant P1V1/T1 = P2V2/T2

Gas Laws The gas pressure in an aerosol can is 1.5atm at 25°C. Assuming that the gas inside obeys the ideal gas equation, what would the pressure be if the can were heated to 450°C? A large natural gas storage tank is arranged so that the pressure is maintained at 2.20atm. On a cold day in December when the temperature is -15°C, the volume of the gas in the tank is 28,500ft3. What is the volume of the same quantity of gas on a warm July day when the temperature is 31°C? Answer: 3.6atm, 33,600ft3

An inflated balloon has a volume of 6 An inflated balloon has a volume of 6.0L at sea level and is allowed to ascend in altitude until the pressure is 0.45atm. During ascent the temperature of the gas falls from 22°C to -21°C. Calculate the volume of the balloon at its final altitude. A 5.0mol sample of oxygen gas is confined at 0°C in a cylinder with a movable piston. The gas has an initial pressure of 1.0atm. The gas is then compressed by the piston so that its final volume is half the initial volume. The final pressure of the gas is 2.2atm. What is the final temperature in degree Celsius? Answer: 11L, 27°C

Using the Ideal Gas Law The ideal gas law can be used to find density and the molar mass of a gas How? Higher molar mass and pressure = more dense gas Higher temperature = less dense gas

Finding Density What is the density of carbon tetrachloride at 714 torr and 125°C? R = 0.0821L·atm/mol·K The mean molar mass of the atmosphere at the surface of Titan, Saturn's largest moon, is 28.6g/mol. The surface temperature is 95K and the pressure is 1.6atm. Assuming ideal behavior, calculate the density of Titan's atmosphere. Answer: 4.43g/L , 5.9g/L

Finding Molar Mass A series of measurements is made to determine the molar mass of an unknown gas. First, a large flask is evacuated and found to have a mass of 134.567g. It is then filled with the gas to a pressure of 735 torr at 31°C and reweighed; its mass is now 137.456g. Finally, the flask is filled with water at 31°C and found to weigh 1067.9g. (The density of water at this temperature is 0.997g/mL) Answer: 79.7g/mol

Finding Molar Mass Calculate the average molar mass of dry air if it has a density of 1.17g/L at 21°C and 740.0 torr? Answer: 29.0g/mol

Gas Laws and Stoichiometry The safety air bags in automobiles are inflated by nitrogen gas generated by the rapid decomposition if sodium azide (NaN3) 2NaN3(s) → 2Na(s) + 3N2(g) If an air bag has a volume of 36L and is to be filled with nitrogen gas at a pressure of 1.15atm at a temperature of 26.0°C, how many grams of NaN3 must be decomposed? Answer: 72g NaN3

Gas Laws and Stoichiometry In the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presence of a suitable catalyst to form nitric oxide and water vapor. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g) How many liters of ammonia at 850°C and 5.00atm are required to react with 1.00mol of oxygen in this reaction? Answer: 14.8L

Gas Mixtures and Partial Pressures The total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone. Pt = P1 + P2 + P3 + ...... → Dalton's Law of Partial Pressures If each gas obeys the ideal-gas equation Pt = nt(RT/V) Total pressure at constant temperature and volume is determined by the number of moles.

Total Pressure A gaseous mixture made from 6.00g O2 and 9.00g CH4 is placed in a 15.0L vessel at 0°C. What is the partial pressure of each gas and what is the total pressure in the vessel? What is the total pressure exerted by a mixture of 2.00g of H2 and 8.00g of N2 at 273K in a 10.0L vessel? Answer: 0.281atm, 0.841atm, 1.122atm; 2.86atm

Partial Pressures and Moles Fractions We can relate the amount of a gas to its partial pressure. P1 = n1RT/V = n1 Pt ntRT/V nt Mole fraction (X) shows the ratio of the moles of one of the gases in a mixture to the total number of moles n1/nt = X1 The partial pressure of a gas is equal to its mole fraction multiplied by the total pressure P1 = X1 Pt

Mole Fractions A study of the effects of certain gases on plant growth requires a synthetic atmosphere composed of 1.5mol percent CO2, 18.0mol percent O2, and 80.5mol percent Ar. Calculate the partial pressure of oxygen in the mixture is the total pressure is to be 745torr. If this atmosphere is to be held in a 120L space at 295K, how many moles of oxygen are needed? Answer: 134torr, 0.872mol

Kinetic Molecular Theory The kinetic molecular theory explains what happens to gas particles as temperature and pressure change. Gases consist of large numbers of molecules that are in continuous, random motion. The volume of all the molecules of the gas is negligible compared to the total volume in which the gas is contained. Attractive and repulsive forces between gas molecules are negligible.

Kinetic Molecular Theory 4) Energy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant. 5) The average kinetic energy of the molecules is proportional to the absolute temperature. At any given temperature the molecules of all gases have the same average kinetic energy. The pressure of a gas is caused by collisions of molecules with the walls of the container. If two gases have the same temperature they have the same average kinetic energy.

Speed and Kinetic Energy Molecules in a gas have an average kinetic energy Momentum is conserved but speed is not Root mean squared speed (u) is directly proportional to the average kinetic energy

Applying the Kinetic Molecular Theory What effect does increasing the volume at constant temperature have on pressure? Why? What effect does increasing the temperature at constant volume have on constant pressure? Why?

Applying the Kinetic Molecular Theory A sample of O2 gas initially at STP is compressed to a smaller volume at constant temperature. What effect does this change have on a) the average kinetic energy of the O2 molecules; b) the average speed of O2 molecules; c) the total number of collisions with the container walls in a unit time? How is the rms speed of nitrogen molecules is a gas sample changed by a) an increase in temperature; b) an increase in the volume of the sample; c) mixing with a sample of Ar at the same temperature?

Effusion and Diffusion At a given temperature, the average kinetic energy for all gases is the same but their speeds are not. RMS (u) = √(3RT/M) What happens to RMS as molar mass increases? Effusion = gas escaping through a tiny hole Diffusion = spread of one substance through another one

Real Gases The ideal gas equation is useful for approximation but all real gases of deviate from this behavior. High pressures cause gases to deviate from from ideal behavior (P>10atm) Low temperatures cause gases to deviate from ideal behavior. Under what conditions can you assume ideal behavior?

Real Gases In ideal gases, molecules are assumed to occupy no space. Real gases molecules do have finite volumes. The volume of a real gas is higher than that of an ideal gas.

Real Gases In ideal gases molecules have no attractions. Real gas molecules do attract each other. Real gases have lower pressures than ideal gases.

Van der Waals Equation Van der waals equation P = nRT/(V - nb) – n2a/V2 Volume is decreased by nb which accounts for the volume of the gas Pressure is decreased by n2a/V2 which accounts for the attractive forces inbetween gas molecules. a and b different for every gas.

Integrative Practice Cyanogen, a highly toxic gas, is composed of 46.2%C and 53.8%N by mass. At 25°C and 751 torr, 1.05g of cyanogen occupies 0.500L What is the molar mass of cyanogen? What is the molecular formula of cyanogen? Answer: 52g/mol, C2N2