How Much Energy is Released?

How much energy (in kilojoules) is released when 7.40g of water at 39.0∘C is cooled to -18.0∘C? The heat of fusion of water is 6.01 kJ/mol, and the molar heat capacity is 36.6 J/(K⋅mol) for ice and 75.3 J/(K⋅mol) for liquid water.

What is the Radius of a Tungsten atom?

The length of a unit-cell diagonal that passes through the center atom in tungsten is equal to 549 pm.

What is the radius (in picometers) of a tungsten atom?

What is the entropy of vaporization?

Naphthalene, better known as “mothballs,” has bp= 218∘C and ΔHvap = 43.3kJ/mol.

What is the entropy of vaporization, ΔSvap [in J/(K⋅mol)] for naphthalene?

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?

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?