Gases Chapter 5 Gases

Gases Characteristics of Gases Unlike liquids and solids, they  Expand to fill their containers.  Are highly compressible.  Have extremely low densities.

Gases Pressure is the amount of force applied to an area. Pressure Atmospheric pressure is the weight of air per unit of area. P = FAFA

Gases Units of Pressure Pascals  1 Pa = 1 N/m 2 Bar  1 bar = 10 5 Pa = 100 kPa

Gases Units of Pressure mm Hg or torr  These units are literally the difference in the heights measured in mm ( h ) of two connected columns of mercury. Atmosphere  1.00 atm = 760 torr

Gases Manometer Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel.

Gases Standard Pressure Normal atmospheric pressure at sea level. It is equal to  1.00 atm  760 torr (760 mm Hg)  kPa

Gases The pressure of a gas is measured as 49 torr. Represent this pressure in both atmospheres & pascals.

Gases Boyle’s Law The volume of a fixed quantity of gas at constant temperature is inversely proportional to the pressure.

Gases Boyle’s Law

Gases As P and V are inversely proportional A plot of V versus P results in a curve. Since V = k (1/P) This means a plot of V versus 1/P will be a straight line. PV = k

Gases Boyle’s Law - Example Sulfur dioxide, a main contributor to the formation of acid rain, is found in the exhaust of cars & power plants. Consider a 1.53 L sample of gaseous sulfur dioxide at a pressure of 5.6 x 10 3 Pa. If the pressure is changed to 1.5 x 10 4 Pa at constant temperature, what will be the new volume of the gas?

Gases Charles’s Law The volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. A plot of V versus T will be a straight line. i.e., VTVT = k

Gases Charles’s Law Example A sample of a gas at 15 0 C and 1 atm has a volume of 2.58 L. What volume will the gas occupy at 38 0 C & 1 atm?

Gases Avogadro’s Law The volume of a gas at constant temperature and pressure is directly proportional to the number of moles of the gas. Mathematically, this means V = kn

Gases

Ideal-Gas Law V  1/P (Boyle’s law) V  T (Charles’s law) V  n (Avogadro’s law) So far we’ve seen that Combining these, we get V V  nT P

Gases Ideal-Gas Equation The constant of proportionality or combined proportionality constant is known as R, the gas constant.

Gases Ideal-Gas Equation The relationship then becomes nT P V V  nT P V = R or PV = nRT

Gases Ideal Gas Law – Example I A sample of hydrogen gas has a volume of 8.56 L at a temperature of 0 0 C & a pressure of 1.5 atm. Calculate the moles of hydrogen molecules present in this gas sample.

Gases Ideal Gas Law II Suppose we have a sample of ammonia gas with a volume of 7.0 ml at a pressure of 1.68 atm. The gas is compressed to a of 2.7 ml at a constant temperature. Use the ideal gas law to calculate the final pressure.

Gases Ideal Gas Law III A sample of methane gas that has a volume of 3.8 L at 5 0 C is heated to 86 0 C at constant pressure. Calculate its new volume.

Gases Ideal Gas Law IV A sample of diborane gas (B 2 H 6 ), a substance that bursts into flame when exposed to air, has a pressure of 345 torr at a temperature of C and a volume of 3.48 L. If conditions are changed so that the temperature is 36 0 C torr, and the pressure is 468 torr, what will be the volume of the sample?

Gases Gas S-Word (Stoichiometry) Remember the volume of an ideal gas (at 0 0 C and 1 atm) is L.  Also known as STP (standard temperature and pressure) Stoichiometry is the same as chapter 3 – Remember to convert to moles, Kelvin, atmospheres, & Liters. If you use units you will know if miss conversions.

Gases Gas Stoichiometry I A sample of gas has a volume of 1.75 STP. How many moles of nitrogen are present?

Gases Gas Stoichiometry II Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. Calculate the volume of carbon dioxide produced at STP from the decomposition of 152 g of calcium carbonate.

Gases Gas Stoichiometry III A sample of methane gas having a volume of 2.80 L at 25 0 C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31 0 C and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of carbon dioxide formed at a pressure of 2.50 atm and a temperature of C

Gases Densities of Gases If we divide both sides of the ideal-gas equation by V and by RT, we get nVnV P RT =

Gases We know that  moles  molecular mass = mass Densities of Gases So multiplying both sides by the molecular mass (  ) gives n   = m P  RT mVmV =

Gases Densities of Gases Mass  volume = density So, Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas. P  RT mVmV = d =

Gases Molecular Mass We can manipulate the density equation to enable us to find the molecular mass of a gas: Becomes P  RT d = dRT P  =

Gases Gas Density/Molar Mass The density of a gas was measured at 1.50 atm and 27 0 C and found to be 1.95 g/L. Calculate the molar mass of the gas.

Gases

2009 AP® CHEMISTRY FREE-RESPONSE QUESTIONS 2. A student was assigned the task of determining the molar mass of an unknown gas. The student measured the mass of a sealed 843 mL rigid flask that contained dry air. The student then flushed the flask with the unknown gas, resealed it, and measured the mass again. Both the air and the unknown gas were at 23.0°C and 750. torr. The data for the experiment are shown in the table below. (a) Calculate the mass, in grams, of the dry air that was in the sealed flask. (The density of dry air is 1.18 g L−1 at 23.0°C and 750. torr.) Volume of sealed flask843 mL Mass of sealed flask and dry air g Mass of sealed flask and unknown gas g

Gases (b) Calculate the mass, in grams, of the sealed flask itself (i.e., if it had no air in it). (c) Calculate the mass, in grams, of the unknown gas that was added to the sealed flask.

Gases (d) Using the information above, calculate the value of the molar mass of the unknown gas. After the experiment was completed, the instructor informed the student that the unknown gas was carbon dioxide (44.0 g mol−1). (e) Calculate the percent error in the value of the molar mass calculated in part (d).

Gases Dalton’s Law of 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. In other words, P total = P 1 + P 2 + P 3 + …

Gases Dalton’s Law Mixtures of helium & oxygen can be used in scuba diving tanks to help prevent “the bends.” For a particular dive, 46 L He at 25 0 C & 1.0 atm & 12.0 L O 2 at 25 0 C & 1.0 atm were pumped into the tank with a volume of 5.0 L. Calculate the partial pressure of each gas and the total pressure in the tank at 25 0 C.

Gases Mole Fraction Mole Fraction: the ratio of the number of moles of a given component in a mixture to the total number of moles in the mixture.  Use a lower case chi (  ) from Greek alphabet

Gases Dalton’s Law II – Mole Fraction The mole fraction of nitrogen in the air is Calculate the partial pressure of N 2 in air when the atmospheric pressure is 760 torr.

Gases Partial Pressures When one collects a gas over water, there is water vapor mixed in with the gas. To find only the pressure of the desired gas, one must subtract the vapor pressure of water from the total pressure.

Gases Gas Collection Over Water A sample of solid potassium chlorate was heated in a test tube and decomposed by the reaction: The oxygen produced was collected by displacement of water at 22 0 C at a total pressure of 754 torr. The volume of the gas collected was L, & the vapor pressure of water at 22 0 C is 21 torr. Calculate the partial pressure of O 2 in the gas collected and the mass of potassium chlorate in the original sample.

Gases Kinetic-Molecular Theory This is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

Gases Main Tenets of Kinetic- Molecular Theory Gases consist of large numbers of molecules that are in continuous, random motion.

Gases Main Tenets of Kinetic- Molecular Theory The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained. Attractive and repulsive forces between gas molecules are negligible.

Gases Main Tenets of Kinetic- Molecular Theory 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.

Gases Main Tenets of Kinetic- Molecular Theory The average kinetic energy of the molecules is proportional to the absolute temperature.

Gases The Meaning of Temperature The Kelvin temperature is an index of the random motions of the particles of a gas – the higher the temperature – the greater the motion

Gases Root Mean Square Velocity The average of the squares of the velocity of gas particles M is mass in kg Remember that a joule is kg*m 2 /s 2

Gases Root Mean Square Velocity Example Calculate the root mean square velocity for the atoms in a sample of helium gas at 25 0 C. Which has more kinetic energy at 25 0 C: helium, argon, carbon dioxide, or hydrogen gas?

Gases Effusion The escape of gas molecules through a tiny hole into an evacuated space.

Gases Diffusion The spread of one substance throughout a space or throughout a second substance.

Gases Boltzmann Distributions

Gases Effect of Molecular Mass on Rate of Effusion and Diffusion

Gases Effusion Rates Calculate the ratio of effusion rates of hydrogen gas, and uranium hexafluoride, a gas used in the enrichment process to produce fuel for nuclear reactors.

Gases Real Gases In the real world, the behavior of gases only conforms to the ideal-gas equation at relatively high temperature and low pressure.

Gases Deviations from Ideal Behavior The assumptions made in the kinetic-molecular model break down at high pressure and/or low temperature.

Gases Real Gases

Gases Corrections for Non-ideal Behavior The ideal-gas equation can be adjusted to take these deviations from ideal behavior into account. The corrected ideal-gas equation is known as the van der Waals equation.

Gases The van der Waals Equation ) (V − nb) = nRT n2aV2n2aV2 (P +