Gases: Partial Pressure

Pressure is the force applied by the particles of a gas colliding with a surface such as the walls of a container.  If there is a mixture of gases, each individual type of gas particle will exert a pressure.  This is partial pressure, or the pressure exerted by a specific component of a gas mixture.

Dalton's Law of Partial Pressure states that the total pressure exerted by a mixture of gases will be the sum of the individual pressures of each of its components.

This concept can be combined with the ideal gas law to solve for the total pressure in a gas mixture.

Gases: Avogadro's Principle

Avogadro's Principle states that equal volumes of gases at equal temperature and pressure, will contain the same number of particles.  Therefore now we can have a molar volume, just as we have a molar mass.

The molar volume of any gas at STP is 22.4 L.  This can be determined by using the ideal gas law.
REMEMBER! This only applies to a GAS at STP.

We can now apply this concept to chemical reactions.  If a reaction takes place at constant temperature and pressure, the ratio of all the gases (reactants and products) will be the same as the mole ratio.

Gases: Ideal Gas Law

In Ideal Gas Law calculations there is only one set of conditions (P,V,T), but we've added the idea of mass.

Gases: Combined Gas Laws

If the number of gas particles does not change, the pressure, volume and temperature will always combine to form a constant.  Because of this, the pressure times the volume and divided by the Kelvin temperature always be equal.  1 represents the initial conditions and 2 is the final conditions.

This is called the Combined Gas Law

By holding one of the three conditions constant, we can look at the relationship between any 2 of the variables.

Boyle's Law stated that if temperature is held constant, the pressure and volume for a sample of gas will be inversely proportional.  In other words, if the kinetic energy of a system is held constant, the force applied by its particles will be inversely proportional to the size of the container.  If the particles are moving at the same speed and the volume is decreased, the particles will hit the walls more often and apply more force.  If the volume is increased, the pressure will decrease.

Charles' Law states that if pressure is held constant, the volume and temperature will be directly proportional.  In other words, if the force applied by the particles on the walls of their container is constant, changes in the space occupied by the gas and their average kinetic energy must be directly proportional.  If you increase the temperature of a sample of gas, the particles will move faster.  To maintain a constant pressure (force on the walls), the container must get bigger.

Gay-Lussac's Law states that if the volume is held constant, the pressure and temperature must be directly proportional.  In other words, if the amount of space is constant (the container can't get bigger or smaller), if the particles move faster (temperature increases) they will have to collide with the walls of their container more, therefore more force.

Calculations:

1. Label all given information. (P, T or V and 1 or 2)
   Remember it really doesn't matter what you label 1 or 2, but it IS IMPORTANT that you keep the SET of conditions together.
2. Choose the correct formula and solve for the unknown algebraically.
3. Substitute in the given information using both the value and UNIT.  Be careful to substitute the correct values 1 and 2 and to cancel the units.  You may need to use a conversion to make the units cancel.
4. Don't forget that STP means Standard Temperature and Pressure.  These are a set of conditions!
5. Don't forget that temperature must ALWAYS be in Kelvin.
   To convert Celsius to Kelvin, add 273.  To return to Celsius from Kelvin, subtract 273.

Gases: Standard Conditions, II

For gas laws, standard pressure is considered the average pressure at sea level or 1 atmosphere (atm).

There are several other units used for pressure.

Using a barometer with mercury, standard atmospheric pressure will support a column of mercury 760 mm high.  This became a unit, or  mmHg.  Another name for mmHg is torr.

1 atm = 760 mmHg = 760 torrs

The SI unit is the pascal (Pa) which is equal to 1 Newton/meter² . 

1 atm = 101.325 kiloPascals (kPa)

Gases: Standard Conditions

For gases, standard temperature is considered the freezing point of water, 0˚C.  This causes a problem with mathematical calculations.  Temperature can be positive, negative or 0.  A positive ratio can't equal a negative number, and multiplying or dividing by 0 is 0 or undefined respectively.  To avoid this mathematical problem, the Celsius scale was shifted down to absolute zero. By using linear regression and Charles' Law, it is possible to determine the coldest possible temperature, or  -273.15˚C.

This new scale was called the Kelvin scale in honor of Lord Kelvin.  The gradations of the Kelvin scale are exactly the same as on the Celsius scale, the only difference is that 0 has been shifted to -273.  Therefore there are no negative values on the Kelvin scale.

Temperature is a measurement of the average kinetic energy of the particles of a substance.  If the lowest possible temperature is -273.15˚C, that means that the average kinetic energy must be 0, or that all molecular motion stops.

ALL CALCULATIONS IN GAS LAWS MUST ALWAYS BE CONVERTED TO KELVIN. To convert a Celsius temperature into Kelvin, just add 273.  To convert back from Kelvin to Celsius, just subtract 273.  *Note- by convention the degree symbol is not used for Kelvin.

The Nature of Gases

When you look around, you don't see or notice the gases around you.  It appears that we are surrounded by empty space, but there are actually molecules of gases and particles in constant motion.

All gases:

1. Gases have mass.
2. Gases are compressible. The particles can be pushed closer together, decreasing the volume.
3. Gases will expand their container. The particles can move farther part, increasing the volume.
4. Gases diffuse. The particles expand to fill their container, therefore they mix and equally distribute themselves throughout the space.
5. Gases exert pressure.  Gases apply a force by colliding with a surface.
6. Pressure is related to temperature.  Temperature is average kinetic energy.  The higher the temperature, the more energy, therefore momentum each pas particle has.

The Kinetic Molecular Theory (KMT) states that gases are composed of tiny particles in constant motion. In reality, gases are effected by many variables.  Some have a large effect like temperature, while others have very effect, such as intermolecular forces.  In science, we simplify this concept by ignoring the smaller influences.  We call this an ideal gas.

Ideal gasses are assumed to:

1. be composed of small hard particles.
2. have an insignificant volume in comparison to the space they occupy.
3. have only empty space between the particles.
4. have no attractive or repulsive forces between the particles.
5. are in constant, random, straight line motion.
6. only change path when they collide with each other or the walls of their container.

Enthalpy of Formation and Enthalpy of Reaction

∆Hr is the enthalpy for the entire reaction, EXACTLY as it is written.  If you change the coefficients or states, you will also change the heat absorbed or evolved.


∆Hf is the enthalpy of formation.  It is the heat absorbed or given off for the synthesis of ONE mole of specific substance in a specific state.  Remember this is ONLY for a SYNTHESIS reaction.  Because it is always for 1 mole, the units of ∆Hf will always be kJ/mole. The ∆Hf for a free element in its state a standard conditions will always equal 0 kJ.

The wonderful thing about heat of formation is that you can use tables to look up specific substances in given states, then use the ∆Hf to find the ∆Hr.  The heat of the entire reaction is equal to the sum of all the heat from the product side minus the heat from the reactant side.  Remember that in science, ∆ means change or difference and we always use FINAL - INITIAL.

Here's an example:

First, you need a balanced reaction with states.  Remember that ∆Hf is given in kJ/mole, so you will need to multiply by the number of moles in the balanced reaction (the coefficients).  You need states to choose the correct value from the table.

The enthalpy of the reaction therefore is:

By using the tables, ∆Hr = -89.3 kJ

Try another example

Hess' Law of Heat Summation

Hess' Law of Heat Summation states that the enthalpy of a net reaction is equal to the sum of the individual steps.  The reason this works is that enthalpy is a state function.  All that matters is where you start and where you end; it is path independent.

One way of using this concept is to add up several equations, and by canceling out the extraneous substances.  Think of this process like putting a jig-saw puzzle together.  Try to find what matches best to start with, then add the other reactions as needed.  Remember that you final equation must look EXACTLY like the reaction you were given.  The states and coefficients must be the same.

 In this example you are given 3 reactions to put together- a,b, and c.  You want your final answer to look EXACTLY like the original equation.  To do this, you need to start with a, reverse b (remember to make the negative positive), then multiply c by 1/2 and add.  Remember that whatever you do to the reaction you must do the same thing to the ∆Hr.

Law of Conservation of Energy

In thermochemistry we decide on the boundaries of the problem.  In other words, we define thesystem.  We could define a system as only a piston, as the engine, the car, the car in the garage or the entire universe.  Obviously, the smaller the system, the easier the problem will be.  Anything not IN the system is considered surroundings. If energy is lost to a system (exothermic), that means that the surroundings have gained the energy (endothermic).

There are 3 basic types of systems:

• open systems allow for the exchange of both matter and energy
• closed systems allow energy to move but not matter
• isolated systems cannot exchange matter nor energy with their surroundings

Now the Law of Conservation of Energy makes more sense- 

The amount of energy in the universe is constant, 

therefore energy is neither created nor destroyed, just converted.  

That means that energy could be lost to a system, BUT it will be gained by the surroundings.  Energy can also convert from one type to another.  For instance mechanical energy could be converted into heat energy through friction.

We use the term internal energy to mean the total amount of energy in a system- kinetic, potential, heat, work, ...  Although we can't calculate the exact amount of internal energy, it is possible to determine the CHANGE in internal energy or ∆E.  

In science we always calculate a change (∆) by subtracting the FINAL - INITIALvalues. We must define the way we subtract because it will determine the sign of the value.  The the final value is larger than the initial value, the change will be positive- for Energy that means ∆E>0 or endothermic.  If the final value is smaller than the initial value, the change will be negative- ∆E<0 or exothermic.

The change in internal energy to a system is the sum of the the heat (q) added to the system and the work (w) done on a system.  

∆E = q + w

While the math is very simple, the problem is interpreting the signs of the values of heat and work.  Refer to the chart for hints.  Remember compressed or decreased volume is positive (work done ON the system),expand or increase volume is negative (work done BY the system).

Exothermic & Endothermic

Thermochemistry is the study of energy changes in a chemical reaction.  First, you must understand a few basic definitions about energy from a physics standpoint.  Energy is defined as the ability to perform work. Work is a force applied through a distance, and force is defined as a push or a pull.  Therefore energy is the ability to make something move through a distance.  In physics, we are generally thinking about making an object move- like a ball rolling down a hill or dropping a rock.  For chemistry, we are concerned about the constant movement of atoms, ions and molecules.

Energy is measure in 2 different units.  A Joule (J) is defined as a Newton*meter.  A Newton is the metric unit of force.  Remember Sir Isaac Newton's 2nd law of motion states that a Force=mass*acceleration (F=ma).  In SI units, a Newton (N) = mass (kg) * acceleration (m/s^2).  So if work is defined as a force applied through a distance, a Joule is a Newton*meter.

Another unit of energy is the calorie (cal).  A calorie is defined as the amount of energy needed to raise the temperature of 1.0 g of water 1 C.  Temperature is the average amount of Kinetic Energy (E of motion) is a substance.  So a calorie is basically the amount of energy we need to add to 1g of water to make it's molecules move faster, so that it raises the temperature of the water 1 C.

Since we have 2 units, we need a conversion to change one unit to another.

 1 calorie = 4.184 Joules

You've probably heard about calories before in relation to food.  These are actually Calories, with a large C.  Sometimes manufacturers and advertisers mix them up, but a food Calorie is actually a kilocalorie.

If a system LOSES energy, it is called EXOTHERMIC.  Since heat is leaving the system, it will feel hot when you touch it.  The energy is leaving the system and going into your finger.

If a system GAINS energy, it is called ENDOTHERMIC.  Since heat is being added to the system, it will feel cool when you touch it.  The energy is leaving your finger and entering the system.