5 Gases Contents 5-1 Gases and Pressure 5-2 Relation Between Pressure and Volume of a Gas 5-3 Relations Between Volume and Temperature 5-4 Standard Temperature and Pressure 5-5 Gay-Lussac’s Law of Combining Volumes and Avogadro’s Law 5-6 The Ideal Gas Equation and Its Uses 5-7 Dalton’s Law of Partial Pressures 5-8 The Kinetic-Molecular Theory 5-9 Real Gases

Why Study Gases? 1. Many elements and compounds are gases under everyday conditions. N 2, H 2, O 2, O 3, F 2, Cl 2, He, Ne, Ar, Kr, Xe, Rn, CO 2, CO, NO 2, SO 2, NH 4, etc. 2. Many chemical reactions involve gases as reactants or products or both. 3. Earth’s weather is largely the result of changes in the properties of the mixture of gases called air.

Elements that exist as gases at 25 0 C and 1 atmosphere 5.1

Characteristics of Gases Gases occupy containers uniformly and completely. Gases always form homogeneous mixtures with other gases Gases are highly compressible and occupy the full volume of their containers. Gases can be expanded infinitely. When a gas is subjected to pressure, its volume decreases.

Gas properties can be modeled using math. Model depends on: V = volume of the gas (L) T = temperature (K) n = amount (moles) P = pressure (atmospheres) Characteristics of Gases Gas experiments revealed that these four variables will affect the state of a gas. These variables are related through equations know as the gas laws.

Units of Pressure 1 pascal (Pa) = 1 N/m 2 =1kg/(m∙s 2 ) 1 atm = 760 mmHg = 760 torr 1 atm = 101,325 Pa (~10 5 ) Barometer Pressure = Force Area 1.0 N is the force required to accelerate 1.0 kg 1.0 m/s Gases and Pressure Pressure is the force acting on an object per unit area.

The air in Earth’s atmosphere is attracted to earth by gravity and pushes against every surface it touches.

Atmosphere Pressure and The Barometer If a tube is inserted into a container of mercury open to the atmosphere, the mercury will rise 760 mm up the tube. Atmospheric pressure is measured with a barometer. Standard atmospheric pressure is the pressure required to support 760 mm of Hg in a column. Units: 1 atm = 760 mmHg = 760 torr =  105 Pa = kPa.

Atmosphere Pressure and The Manometer The pressures of gases not open to the atmosphere are measured in manometers. A manometer consists of a bulb of gas attached to a U-tube containing Hg: –If P gas < P atm then P gas + P h2 = P atm. –If P gas > P atm then P gas = P atm + P h2.

The Gas Laws: Boyle’s Law The Pressure-Volume Relationship: Weather balloons are used as a practical consequence to the relationship between pressure and volume of a gas. As the weather balloon ascends, the volume increases. As the weather balloon gets further from the earth’s surface, the atmospheric pressure decreases. Boyle’s Law: At constant temperature, the volume of a sample is inversely proportional to the pressure of the gas. Boyle used a manometer to carry out the experiment. 5-2 Relation Between Pressure and Volume of a Gas

Boyle’s Law

Mathematically: A plot of V versus P is a hyperbola. Similarly, a plot of V versus 1/P must be a straight line passing through the origin. The Value of the constant depends on the temperature and quantity of gas in the sample. The Pressure-Volume Relationship

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? Solution: at constant temperature: P 1 x V 1 = P 2 x V 2 P 1 = 726 mmHg V 1 = 946 mL P 2 = ? V 2 = 154 mL P 2 = P 1 x V 1 V2V2 726mmHg×946mL 154ml = = 4.46×10 3 mmHg 5.3

We know that hot air balloons expand when they are heated. Charles’s Law: At constant pressure, the volume of a sample of a gas is directly proportional to the Kelvin or absolute temperature. Mathematically: Charles’s Law 5-3 Relations Between Volume and Temperature

Plotting Charles’s Law A plot of V versus T is a straight line. When T is measured in  C, the intercept on the temperature axis is  C. We define absolute zero, 0 K =  C. Note the value of the constant reflects the assumptions: amount of gas and pressure.

All gases will solidify or liquefy before reaching zero volume.

Variation of gas volume with __________________ at constant ________________. 5.3 V  TV  T V = constant x T V 1 /T 1 = V 2 /T 2 T (K) = t ( 0 C) Charles’ Law Temperature must be in _Kevin._

A sample of carbon monoxide gas occupies 3.20 L at C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant? V 1 = 3.20 L T 1 = K V 2 = 1.54 L T 2 = ? T 2 = V 2 x T 1 V1V1 = = 5.3 V 1 /T 1 = V 2 /T 2

5-4 Standard Temperature and Pressure Standard Temperature: 0 ℃ or K Standard Pressure: 760mmHg or 1 atm or ×10 5 Pa STP: standard temperature and pressure

The Quantity-Volume Relationship: Gay-Lussac’s Law of combining volumes: at constant temperature and pressure, the volumes of gases involved in chemical reactions are ratios of small whole numbers. 5-5 Gay-Lussac’s Law of Combining Volumes and Avogadro’s Law

Avogadro’s Hypothesis: equal volumes of gas at the same temperature and pressure will contain the same number of molecules. Avogadro’s Law: the volume of a gas at constant temperature and pressure is directly proportional to the number of molecules of the gas, n. Mathematically: We can show that 22.4 L of any gas at STP contain 6.02  gas molecules.

__________________ Law V  number of moles (n) V = constant x n V 1 /n 1 = V 2 /n Constant _________

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? 4NH 3 + 5O 2 4NO + 6H 2 O __ mole NH 3 __ mole NO At constant T and P __ volume NH 3 __ volume NO 5.3

Consider the three gas laws. We can combine these into a general gas law: Boyle’s Law: Charles’s Law: Avogadro’s Law: The Ideal Gas Equation

If R is the constant of proportionality (called the gas constant), then The ideal gas equation is: The Ideal Gas Constant 5-6 The Ideal Gas Equation and Its Uses

We define STP (standard temperature and pressure) = 0  C, K, 1 atm. Volume of 1 mol of gas at STP is: Applying The Ideal Gas Equation

Argon is an inert gas used in light bulbs to retard the vaporization of the filament. A certain light bulb containing argon at 1.20 atm and 18 0 C is heated to 85 0 C at constant volume. What is the final pressure of argon in the light bulb (in atm)? PV = nRT n, V and R are _________________ nR V = P T = constant P1P1 T1T1 P2P2 T2T2 = P 1 = 1.20 atm T 1 = 291 K P 2 = ? T 2 = 358 K P 2 = P 1 x T2T2 T1T1 = 1.20 atm x 358 K 291 K = _________ atm 5.4

For an ideal gas, calculate the following quantities: (a) the pressure of the gas if 1.04 mol occupies 21.8 L at 25 o C; (b) the volume occupied by 6.72 x mol at 265 o C and pressure of 23.0 torr; (c) the number of moles in 1.50 L at 37 o C and 725 torr; (d) the temperature at which mol occupies 15.0 L at 2.54 atm.

Relating the Ideal-Gas Equation and the Gas Laws If PV = nRT and n and T are constant, then PV = constant and we have Boyle’s law. Other laws can be generated similarly. In general, if we have a gas under two sets of conditions, then

A sample of argon gas is confined to a 1.00-L tank at 27.0 o C and 1 atm. The gas is allowed to expand into a larger vessel. Upon expansion, the temperature of the gas drops to 15.0 o C, and the pressure drops to 655 torr. What is the final volume of the gas?

Density has units of mass over volume. Rearranging the ideal-gas equation with M as molar mass we get Molar Mass

The molar mass of a gas can be determined as follows:. Gas Densities What is the density of carbon tetrachloride vapor at 714 torr and 125 o C? Class Guided Practice Problem

Volumes of Gases in Chemical Reactions The ideal-gas equation relates P, V, and T to number of moles of gas. The n can then be used in stoichiometric calculations

The safety air bags in automobiles are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN 3 : 2 NaN 3 (s)  2 Na(s) + 3N 2 (g) If an air bag has a volume of 36 L and is filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26 o C, how many grams of NaN 3 must be decomposed? Class Guided Practice Problem

Density (d) Calculations d = m V = PMPM RT Molar Mass ( M ) of a Gaseous Substance dRT P M = 5.4 How do we arrive at these equations?? Let’s see…

PV = nRT (1) (2) (3) (4) (5) P = nRT V Divide by V Divide by RT P RT n V = m M = = n n = number of moles m = mass in grams M = molar mass sub. (4) into (3) m MVMV P RT Multiply by M

(7) = m V (8) (9) = M dRT P Multiply by RT and divide by P in order to Solve for M (6) = m V PMPM RT Since d and = m V PMPM RT d = PMPM RT

Density (d) Calculations d = m V = PMPM RT m is the mass of the gas in g M is the molar mass of the gas Molar Mass ( M ) of a Gaseous Substance dRT P M = d is the density of the gas in g/L 5.4

Gas Mixtures and Partial Pressures Since gas molecules are so far apart, we can assume they behave independently. Dalton’s Law: in a gas mixture the total pressure is given by the sum of partial pressures of each component: Each gas obeys the ideal gas equation: Combining the equations we get: 5-7 Dalton’s Law of Partial Pressures

Dalton’s Law of ___________________ V and T are constant P1P1 P2P2 P total = P 1 + P 2 5.6

Consider a case in which two gases, A and B, are in a container of volume V. P A = n A RT V P B = n B RT V n A is the number of moles of A n B is the number of moles of B P T = P A + P B X A = nAnA n A + n B X B = nBnB n A + n B P A = X A P T P B = X B P T P i = X i P T 5.6 X is the mole fraction

A sample of natural gas contains 8.24 moles of CH 4, moles of C 2 H 6, and moles of C 3 H 8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C 3 H 8 )? P i = X i P T X propane = P T = 1.37 atm = __________ P propane = x 1.37 atm= __________ atm 5.6

Collecting Gases over Water

It is common to synthesize gases and collect them by displacing a volume of water. To calculate the amount of gas produced, we need to correct for the partial pressure of the water: Collecting Gases over Water

Theory developed to explain gas behavior. Theory of moving molecules. Assumptions: –Gases consist of a large number of molecules in constant random motion. –Volume of individual molecules negligible compared to volume of container. –Intermolecular forces (forces between gas molecules) negligible. 5-8 The Kinetic-Molecular Theory

Assumptions: –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 gives us an understanding of pressure and temperature on the molecular level. Pressure of a gas results from the number of collisions per unit time on the walls of container. Kinetic Molecular Theory

Magnitude of pressure given by how often and how hard the molecules strike. Gas molecules have an average kinetic energy. Each molecule has a different energy. Kinetic Molecular Theory

As kinetic energy increases, the velocity of the gas molecules increases. Root mean square speed, v, is the speed of a gas molecule having average kinetic energy. Average kinetic energy, E, is related to root mean square speed: Kinetic Molecular Theory

As volume increases at constant temperature, the average kinetic of the gas remains constant. Therefore, u is constant. However, volume increases so the gas molecules have to travel further to hit the walls of the container. Therefore, pressure decreases. If temperature increases at constant volume, the average kinetic energy of the gas molecules increases. Therefore, there are more collisions with the container walls and the pressure increases. Application to Gas Laws

From the ideal gas equation, we have For 1 mol of gas, PV/RT = 1 for all pressures. In a real gas, PV/RT varies from 1 significantly. The higher the pressure the more the deviation from ideal behavior. Real Gases: Deviations from Ideal Behavior 5-9 Real Gases

From the ideal gas equation, we have For 1 mol of gas, PV/RT = 1 for all temperatures. As temperature increases, the gases behave more ideally. The assumptions in kinetic molecular theory show where ideal gas behavior breaks down: –the molecules of a gas have finite volume; –molecules of a gas do attract each other Real Gases: Deviations from Ideal Behavior

As the pressure on a gas increases, the molecules are forced closer together. As the molecules get closer together, the volume of the container gets smaller. The smaller the container, the more space the gas molecules begin to occupy. Therefore, the higher the pressure, the less the gas resembles an ideal gas. Real Gases: Deviations from Ideal Behavior

As the gas molecules get closer together, the smaller the intermolecular distance. Real Gases: Deviations from Ideal Behavior

The smaller the distance between gas molecules, the more likely attractive forces will develop between the molecules. Therefore, the less the gas resembles and ideal gas. As temperature increases, the gas molecules move faster and further apart. Also, higher temperatures mean more energy available to break intermolecular forces. Real Gases: Deviations from Ideal Behavior

Therefore, the higher the temperature, the more ideal the gas. Real Gases: Deviations from Ideal Behavior Correction for attractive force between molecules Correction for volume of molecules