Gases Chapter 10

Characteristics of Gases Expand to fill a volume (expandability) Compressible Readily forms homogeneous mixtures with other gases Have extremely low densities. These behaviors are due to large distances between the gas molecules.

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

Units of Pressure Pascals Bar mm Hg or torr Atmosphere 1 Pa = 1 N/m2 1 bar = 105 Pa = 100 kPa 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

Pressure Conversion Factors 1 atm = 760 mmHg 1 atm = 760 torr 1 atm = 1.01325  105 Pa 1 atm = 101.325 kPa.

Manometer Used to measure the difference in pressure between atmospheric pressure and that of a gas in a vessel. Manometer at <, =, > P of 1 atm

Example 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-end mercury manometer. A meter stick is used to measure the height of the mercury above the bottom of the manometer. Level of the mercury in the open end arm of the manometer has a measured height of 136.4 mm, and that in the arm that is in contact with the gas has a height of 103.8 mm. What is the pressure of the gas? What is the pressure of the gas in kPa

The Gas Laws There are four variables required to describe a gas: Amount of substance Volume of substance Pressures of substance Temperature of substance The gas laws will hold two of the variables constant and see how the other two vary.

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

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

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

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

A sample of carbon monoxide gas occupies 3. 20 L at 125 0C A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

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

Ammonia burns in oxygen to form nitric oxide (NO) and water vapor Ammonia burns in oxygen to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

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

The Ideal Gas Equation Combine the gas laws (Boyle, Charles, Avogadro) yields a new law or equation. Ideal gas equation: PV = nRT R = gas constant = 0.08206 L.atm/mol-K P = pressure (atm) V = volume (L) n = moles T = temperature (K)

The conditions 0 0C and 1 atm are called standard temperature and pressure (STP). Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L. R = 0.082057 L • atm / (mol • K)

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

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

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

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

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

C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l) Gas Stoichiometry What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C6H12O6 (s) + 6O2 (g) 6CO2 (g) + 6H2O (l)

Gas Mixtures and Partial Pressures Dalton’s Law Dalton’s Law - In a gas mixture the total pressure is given by the sum of partial pressures of each component: Pt = P1 + P2 + P3 + … - The pressure due to an individual gas is called a partial pressure.

PA = nART V PB = nBRT V XA = nA nA + nB XB = nB nA + nB PT = PA + PB Consider a case in which two gases, A and B, are in a container of volume V. PA = nART V nA is the number of moles of A PB = nBRT V nB is the number of moles of B XA = nA nA + nB XB = nB nA + nB PT = PA + PB PA = XA PT PB = XB PT Pi = Xi PT where i is the mole fraction (ni/nt).

A sample of natural gas contains 8. 24 moles of CH4, 0 A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?

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.

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

Kinetic-Molecular Theory Theory developed to explain gas behavior To describe the behavior of a gas, we must first describe what a gas is: Gases consist of a large number of molecules in constant random motion. Volume of individual molecules negligible compared to volume of container.

Kinetic-Molecular Theory Intermolecular forces (forces between gas molecules) negligible. Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature. Average kinetic energy of molecules is proportional to temperature.

Kinetic-Molecular Theory ε = ½ mu2

Application to the Gas laws Effect of Volume increase at constant temperature More space Fewer collisions u is unchanged Effect of a temperature increase at constant volume Less Space More collisions Increase in u

Molecular Effusion and Diffusion Consider two gases at the same temperature: the lighter gas has a higher u than the heavier gas. Mathematically: The lower the molar mass, M, the higher the u for that gas at a constant temperature.

Molecular Effusion and Diffusion

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

Diffusion The spread of one substance throughout a space or throughout a second substance. NH4Cl NH3 17 g/mol HCl 36 g/mol

Molecular Effusion and Diffusion Graham’s Law of Effusion Graham’s Law of Effusion – The rate of effusion of a gas is inversely proportional to the square root of its molecular mass. Gas escaping from a balloon is a good example.

Molecular Effusion and Diffusion Diffusion and Mean Free Path Diffusion of a gas is the spread of the gas through space. Diffusion is faster for light gas molecules. Diffusion is slowed by gas molecules colliding with each other. Average distance of a gas molecule between collisions is called mean free path.

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

Real Gases: Deviations from Ideal Behavior From the ideal gas equation, we have PV = nRT This equation breaks-down at High pressure At high pressure, the attractive and repulsive forces between gas molecules becomes significant. Small volume At small volumes, the volume due to the gas molecules is a source of error.

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

Corrections for Nonideal 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.

Real Gases: Deviations from Ideal Behavior The Van der Waals Equation Two terms are added to the ideal gas equation to correct for volume of molecules and one to correct for intermolecular attractions. a and b are constants, determined by the particular gas.

The van der Waals Equation ) (V − nb) = nRT n2a V2 (P +

Example Consider a sample of 1.00 mol of carbon dioxide gas confined to a volume of 3.000L at 0.0 C. Calculate the pressure of the gas using the van der waals equation