Dalton’s Law of Partial Pressure

A 1-L flask is filled with 1.10g of argon at 25 ∘C. A sample of ethane vapor is added to the same flask until the total pressure is 1.40atm .

What is the partial pressure of argon, P(Ar), in the flask?

What is the partial pressure of ethane, P(ethane), in the flask?

Biochemical Applications of the Gas Laws

The various gas laws can be used to describe air, which is a mixture of gases. In some cases, these laws have direct application to the air that we breathe.

A.)  How long does it take a person at rest to breathe one mole of air if the person breathes 80.0mL/s of air that is measured at 25 ∘C and 755 mmHg?

B.)  Typically, when a person coughs, he or she first inhales about 2.30L of air at 1.00 atm and 25 ∘C. The epiglottis and the vocal cords then shut, trapping the air in the lungs, where it is warmed to 37 ∘C and compressed to a volume of about 1.70 L by the action of the diaphragm and chest muscles. The sudden opening of the epiglottis and vocal cords releases this air explosively. Just prior to this release, what is the approximate pressure of the gas inside the lungs?

C.)  Helium-oxygen mixtures are used by divers to avoid the bends and are used in medicine to treat some respiratory ailments. What percent (by moles) of He is present in a helium-oxygen mixture having a density of 0.538g/L at 25 ∘C and 721 mmHg?

 

Partial Pressure and the Ideal Gas Law

The ideal gas law, PV=nRT is independent of the kind of gas. In other words, the pressure exerted by a given number of ideal gas particles is the same whether the sample consists of all one type of particle or a mixture of different kinds of particles.

Therefore, the pressure exerted by a mixture of gases can be expressed as follows:

Ptotal=(n1+n2+n3+⋯)RTV=ntotalRTV

A partial pressure is the pressure exerted by just one type of gas in a mixture. A partial pressure is calculated using only the number of moles of that particular gas, instead of the total number of moles:

P1=n1RTV, P2=n2RTV, P3=n3RTV,etc.

The sum of the partial pressures is equal to the total pressure in the mixture:

Ptotal=P1+P2+P3+⋯

Air is about 78.0% nitrogen molecules and 21.0% oxygen molecules. Several other gases make up the remaining 1% of air molecules.  What is the partial pressure of nitrogen in air at atmospheric pressure (1 atm)? Assume ideal behavior.

Application of Empirical Gas Law Relationships

A number of empirical relationships or laws exist among the parameters used to describe the behavior of gases (for example, Avogadro’s law and the relation of molecular velocity to temperature from kinetic molecular theory).  Some of these laws relate initial and final conditions of two changing parameters while all other parameters are held constant (for example, Boyle’s law for pressure-volume relationships).  Other relationships, such as the ideal gas law, relate parameters without need for initial and final conditions.

Classify each situation by the equation that would quantify it.

1. A container of ammonia cleaner is stored in the janitor’s closet off a lecture hall after being used at night for cleaning. The container has a very small hole in the lid. The next morning the entire lecture hall smells of ammonia. How would you calculate the speed of the ammonia molecules as they move out into the lecture hall?
2. The pressure on a tire pump is read. The handle of the pump is pushed down as far as possible. The reading of the pressure on the gauge is taken again. How would you calculate the final pressure?
3. The burner under a hot air balloon is ignited and the balloon expands. How would you calculate the expanded volume of the balloon?
4. A front-end collision causes the air bag in an automobile to deploy by the reaction of sodium azide to produce nitrogen gas. How would you calculate how much sodium azide is needed to fill a standard size bag with nitrogen under STP conditions?
5. Aerosol cans have a label that warns the user not to use them above a certain temperature and not to dispose of them by incineration. Even an empty can contains residual gaseous propellant. If the residual pressure in the can is 1.31 atm when it is sitting on a shelf near a furnace, how could you calculate the pressure when the can is placed on top of the furnace where the temperature reaches the boiling point of water?
6. In an automobile engine, at the end of the upstroke the piston is at its maximum height in a cylinder of exact dimensions. At this time, a precisely measured mixture of fuel and oxidant ignites to form gaseous products. If the ignition temperature is known, how could you calculate the pressure inside the cylinder just before the piston moves downward?

Calculate Delta H

Calculate ΔH∘ in kilojoules for the reaction of ammonia (ΔH∘f=−46.1 kJ/mol) with O2 to yield nitric oxide NO (ΔH∘f=91.3 kJ/mol) and H2O(g) (ΔH∘f=−241.8 kJ/mol), a step in the Ostwald process for the commercial production of nitric acid.

Calculating Delta H

When a solution containing 8.00 g of NaOH in 50.0 g of water at 25.0 ∘C is added to a solution of 8.00 g of HCl in 250.0 g of water at 25.0 ∘C in a calorimeter, the temperature of the solution increases to 33.5 ∘C.

Assuming that the specific heat of the solution is 4.18 J/(g⋅∘C) and that the calorimeter absorbs a negligible amount of heat, calculate ΔH in kilojoules for the reaction

NaOH(aq)+HCl(aq)→NaCl(aq)+H2O(l)

Calculating Delta H

When 25.0 mL of 1.0 M H2SO4 is added to 50.0mL of 1.0 M NaOH at 25.0 ∘C in a calorimeter, the temperature of the aqueous solution increases to 33.9 ∘C.

Assuming that the specific heat of the solution is 4.18 J/(g⋅∘C), that its density is 1.00 g/mL, and that the calorimeter itself absorbs a negligible amount of heat, calculate ΔH in kilojoules for the reaction.

H2SO4(aq)+2NaOH→2H2O(l)+Na2SO4(aq)

 

Using the Law of Conservation of Energy

Imagine that your water heater has broken, but you want to take a bath. You fill your bathtub with 25 kg of room-temperature water (about 25 ∘C). You figure that you can boil water on the stove and pour it into the bath to raise the temperature.

1.)  How much boiling water would you need to raise the bath to body temperature (about 37 ∘C)? Assume that no heat is transferred to the surrounding environment.

2.)  The amount of boiling water required to raise the temperature of 25.0 kg of water in the bath to body temperature is 4.80 kg.  In this process, the heat lost by the boiling water is equal to the heat gained by the room-temperature water. How much heat was transferred in this process?

Heat Capacity

Heat capacity, C, is the amount of energy required to raise the temperature of a substance by exactly 1 degree Celsius. The energy needed to warm an object increases as the mass of that object increases. We see this in our everyday life. For example, we know that it takes much more energy to heat a large tank of water than a small cup. Because of this dependence on mass, experimentally determined heat capacities are always reported in terms of the amount of the substance that is heated. One method is to report how much energy it takes to raise the temperature of one mole of a substance by exactly 1 degree Celsuis. This value is the molar heat capacity, which has the symbol Cp.The molar heat capacity is given in the units J/(mol⋅∘C). A second method is to report how much energy it takes to raise the temperature of one gram of a substance by exactly 1 degree Celsius. This value is thespecific heat, which has been given the symbol Cs. The units for specific heat are J/(g⋅∘C).

The heat capacity of a substance is therefore related to the energy q needed to raise its temperature by an amount ΔT. That is, q=nCpΔT, where n denotes the number of moles of the substance, or q=mCsΔT, where m denotes the number of grams of the substance.

1.)  It takes 53.0J to raise the temperature of an 11.4g piece of unknown metal from 13.0∘C to 24.3∘C. What is the specific heat for the metal?

2.)  The molar heat capacity of silver is 25.35 J/mol⋅∘C. How much energy would it take to raise the temperature of 11.4g of silver by 10.7∘C?

3.)  What is the specific heat of silver?

Coffee Cup Calorimetry

Calorimetry is a method used to measure enthalpy, or heat, changes that occur during chemical processes. Two common calorimeters are constant-pressure calorimeters and constant-volume (or “bomb”) calorimeters. Bomb calorimeters are used to measure combustion and other gas-producing reactions, where the reaction is observed in a strong, sealed vessel. A simple constant-pressure calorimeter can be made from a foam coffee cup and a thermometer; energy changes in a reaction are observed via a temperature change of the solution in the cup. The idea behind calorimeters is that if they are sufficiently insulated from the outside environment, any energy gained or lost in the chemical reaction will be directly observable as a temperature and/or pressure change in the calorimeter.

A total of 2.00 mol of a compound is allowed to react with water in a foam coffee cup and the reaction produces 133g of solution. The reaction caused the temperature of the solution to rise from 21.0 to 24.7∘C. What is the enthalpy of this reaction? Assume that no heat is lost to the surroundings or to the coffee cup itself and that the specific heat of the solution is the same as that of pure water.