Unit 4: Gases

We live in a solution of gases: nitrogen, oxygen and other gases surround and support us. In this chapter we will focus on the behavior of gases and the laws that govern that behavior.

5.2 Pressure: The result of molecular collisions Properties of Gases

Gases are compressibleGases uniformly fill any containerGases mix easily with other gases

Units of pressuremm Hg (millimeters of mercury) – also called torr (for Torricelli!)

760 mmHg = 760 torr = 1 atmSI unit of pressure is N/m2 or Pascal (Pa)

1 atm = 101,325 Pa = 101.325 kPa

Barometers & ManometersManometer- instrument used for measuring pressure

Gas pressure less than atmospheric pressure (gas pressure = atm. pressure - height of Hg)

Gas pressure more than atmospheric pressure (gas pressure = atm pressure + height of Hg)

In 1643, Evangelista Torricelli invented the barometer, an instrument for measuring atmospheric pressure. Atmospheric pressure results from gravity’s pull on air masses.How Torricelli’s barometer worked

Dish filled with mercury with a closed tubeOutside pressure causes mercury level to rise and fall

Manometer- instrument used for measuring pressureGas pressure less than atmospheric pressure

(gas pressure = atm. pressure - height of Hg)Gas pressure more than atmospheric pressure

(gas pressure = atm pressure + height of Hg) Note: Read about how blood pressure cuffs work on Pg. 199!

5.3 The Simple Gas LawsBoyle’s Law- Robert Boyle performed the first quantitative study of gases in the 1600s.

Found that pressure and volume are inversely relatedAn ideal gas- gas that obeys Boyle’s law at all times

Example: We inhale by increasing our lung volume. A woman has an initial lung volume of 2.75 L, which is filled with air at an atmospheric pressure of 1.02 atm. If she increases her lung volume to 3.25 L without inhaling any additional air, what is the pressure in her lungs?

Boyle’s LawP1V1 = P2V2 P1 = V2

V1 P2

Charles’ Law- Jacques Charles, a French scientist, determined in the late 1700s that the volume of a gas is directly proportional to Kelvin temperatureThe temperature must be in Kelvin!The volume of a gas at absolute zero is zero (can that be true?)

Example: A sample of gas has a volume of 2.80 L at an unknown temperature. When the sample is submerged in ice water at a temperature of 0.00oC, its volume decreases to 2.57 L. What was the initial temperature in Kelvin and Celsius?

Avogadro’s Law- Amadeo Avogadro determined in 1811 that equal volumes of gases at the same temperature and pressure contain the same number of moles (it doesn’t matter the identity of the gas!!!)For a gas of constant temperature and pressure, the volume is directly proportional to the number of moles of gas.

Example: A male’s athlete in a kinesiology research study has a lung capacity of 6.15 L during a deep inhalation. At this volume, his lungs contain 0.254 moles of air. During exhalation, his lungs decreases to 2.55L. How many moles of gas did the athlete exhale? Assume constant temperature and pressure.

Combined Gas Law- all of the relationships we have discussed so far can be combined in to a single law“Peas and Vegetables on the Table”

Ideal Gas Law- also combines Boyle’s Charles’ and Avogadro’s LawsP = pressure (atm)V = volume (L)R = 0.08206 Latm/molK (proportionality constant)n = number of moles of gas present (mol)T = temperature in Kelvin

Example- The gas pressure inside an aerosol can is 1.5 atm at 25oC. Assuming that the gas is ideal, what would the pressure be if the can were heated to 450oC?

Charles’ LawV1 = V2

T1 T2

Avogadro’s LawV1 = V2

n1 n2

Combined Gas LawP1V1 = P2V2

n1T1 n2T2

Ideal Gas LawPV = nRT

Example: A quantity of helium gas occupies a volume of 16.5 L at 78oC and 45.6 atm. What is the volume at STP?

Example: Many gases are shipped in high pressure containers. If a steel tank whose volume is 50.0L contains O2 gas at a total pressure of 1500 kPa at 23oC, what mass of oxygen does it contain?

5.5 Applications of the Ideal Gas Law: Molar Volume, Density and Molar Mass of a GasThe volume of 1 mole of an ideal gas at STP is constant. We can use this volume for stoichiometry!Molar volume of an ideal gas at STP = 22.42 L (Note: some gases behave more ideally than others)Prove it!

Example: Calcium Hydride reacts with water to produce hydrogen gas and calcium hydroxide. This reaction is used to generate hydrogen gas to inflate life rafts and for similar uses where a simple compact means of H2

generation is desired. Assuming complete reaction with water, how many grams of calcium hydride are required to fill a 5.50 L balloon to a total pressure of 1.12 atm at 15oC.

Example: How many liters of nitrogen gas are required to produce 115 grams of NH3 at STP?

Molecular Weight and Density of a GasThe molar mass of a gas can be determined from the measured density of a gas.

n = mass (g) so if P = nRT MW (g/mol) V

Plugging in for “n” we get: P = mRT V(MW)

Since density (d) = m/V : P = dRT MW

Example: Calculate the molecular weight of a gas if 0.608 grams occupies 750 mL at 385 mm Hg and 35oC.

5.6 Mixtures of Gases and Partial PressuresFor a mixture of gases in a container, the total pressure exerted is the sum of the pressures that each gas would exert if it were alone.Ptot = P1 + P2 + P3 + P4 … OR Ptot = n1RT + n2RT + n3RT + … = ntotRT

V V V VExample: A 1L mixture of helium, neon, and argon has a total pressure of 662 mm Hg at 298 K. If the partial pressures of helium is 341 mm Hg, and the partial pressure of neon is 112 mm Hg, what mass of argon is present in the sample?

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.

Mole Fraction Χ1 = moles1

total moles

Molecular Weight Kitty CatMW = dRT

P

The partial pressure of a particular component of a gaseous mixture is the mole fraction of that component times the total pressure.

P1 = Χ1 (Ptot)When gases are collected over water, we must adjust for the pressure of the water vapor.

Ptot = Pgas + PH2O

Example: A sample of hydrogen gas is mixed with water vapor. The mixture has a total pressure of 755 torr and the water vapor has a partial pressure of 24 torr. What amount (in moles) of hydrogen gas is contained in 1.55 L of this mixture at 298 K?

Example: If a 0.20 L sample of O2 at 0oC and 1.0 atm of pressure and a 0.10 L sample of N2 at 0oC and 2.0 atm of pressure are both placed in a 0.40 L container at 0oC, what is the total pressure in the new container?

5.7 Gases in Chemical Reactions (Gas Stoichiometry)Example: Methanol (CH3OH) can be synthesized by the reaction: CO (g) + 2 H2 (g) CH3OH (g)What volume (in liters) of hydrogen gas, at a temperature of 355 K and a pressure of 738 mm Hg, do we need to synthesize 35.7 grams of methanol?

Example: How many grams of water form when 1.24 L of H2 gas at STP completely reacts with O2? 2 H2 (g) + O2 2 H2O (g)

5.8 Kinetic Molecular Theory (KMT) of GasesThe Kinetic Molecular Theory of gases is a simple model that attempts to explain the properties of an ideal gas. NOTE: There is no such thing as an ideal gas! No gas acts ideally at all times, however EVERY gas acts ideally under certain circumstances.KMT states that gases consist of particles that have the following properties:

1. The particles are so small compared to the distances between them that the volume of the individual particles can be assumed to be negligible (zero).

2. The particles are in constant motion. The collisions of the particles with the walls of the container are the cause of the pressure exerted by the gas.

3. The particles are assumed to exert no forces on each other; they are assumed neither to attract nor to repel each other.

4. The average kinetic energy of a collection of gas particles is assumed to be directly proportional to the Kelvin temperature of the gas.

Real gases don’t conform to these assumptions!Kelvin temperature is an index of the random motions of the particles of a gas, with higher temperatures meaning greater motion.

KEavg = 3/2 RTR = 8.3148 J/KmolKE units are J/mol

Root mean square velocity- this is a measure of the average speed of particles. It is INDIRECTLY proportional to the molar mass (MW) of the gas. At any given temperature, lighter molecules have higher root mean square velocities (are moving faster)

Example: Calculate the root mean square velocity in m/s of O2 molecules at 27oC.

Calculate the average KE of the same molecules.

Real gases have many collisions between particles. The average distance a particle travels between collisions in a particular gas sample is called the mean free path. These collisions produce a huge variation in velocities. As the temperature increases the range of velocities is greater.

Root Mean Square Velocity

μrms = 2√ 3 RTMM = molar mass of gas in kgThe units of μrms is m/s

5.9 Effusion & DiffusionDiffusion- the mixing of gasesEffusion- the passage of a gas through a tiny hole into an evacuated chamber.

Graham’s Law of Effusion- the rate of effusion of a gas is inversely proportional to the square root of the mass of its particles.

Rate of Effusionof Gas1Rate of Effusionof Gas2

= 2√MW 2MW 1Lighter gases effuse and diffuse faster than heavier gases.

Example: An unknown gas effuses at a rate that is 0.462 times that of nitrogen gas (at the same temperature). Calculate the molar mass of the unknown gas in g/mol.

5.10 Real GasesNo gas exactly follows the ideal gas law. A real gas exhibits behavior closest to ideal behavior at LOW PRESSURE and HIGH TEMPERATURE,

At high temperatures, there is less interaction between particles because they are moving too fast.

At high concentrations, gases have much greater attractive forces between particles. This causes particles to hit the walls of the container with less force (producing less pressure than expected).At high pressure (small volume), the volume of the particles becomes significant, so that the volume available to the gas is significantly less than the container volume,Attractive forces are greatest for large, complex molecules.

We can use the

Van der Waals equation to adjust for departures from ideal conditions:

PV = nRT becomes:

a= correction for pressure that takes into account the intermolecular attractions between molecules. It increases with an increase in MW and an increase in molecular complexity.b = correction for the finite volume of the gas molecules. It is a measure of the actual volume occupied by the gas molecules. It increases with an increase in mass of the molecule or in the complexity of the structure.

We can look up the values of a&b for common gases in Table 5.5

Practice: The graph below shows PV/RT for carbon dioxide at three different temperatures. Rank the curves in order of increasing temperature.