Collision Theory

Collision Theory attempts to explain reaction rates.  It is based on the basic ideas:

• Molecules must collide to react.
• Concentration affects the rate.  A higher concentration allows for more particles to have a chance of colliding, therefore increasing the rate.  Fewer particles would lessen the chance of collision, therefore slowing the rate.
• Molecules must collide hard enough (but not too hard) to cause a reaction.
• Temperature and rate are related.
• Only a small number of collisions actually result in a reaction.

Activation Energy is the energy needed to form an activated complex or transition state so a reaction can occur.  In other words, how much energy is needed to get the reaction started.  Think of it as the amount of energy it takes to cut up all the vegetables you need to prepare a meal.

Take the synthesis reaction that forms hydrogen iodide gas.

Before the hydrogen and iodine can combine, the diatomic molecules must be broken apart in a redox reaction.  After the positive hydrogen ions and the iodine ions have been formed, the electrostatic force (attraction of a + for a -) will pull the ions together.

This reaction needs energy to break up the diatomic molecules and form ions.  This is the activation energy.  The H+ and I- are the activated complex (the transition state or intermediate step) in the mechanism of the reaction.

Chemical Kinetics

The Rate of Reaction is measured by the change in molarity over time.  By convention, we use the decreasing molarity of the reactants instead of the increasing molarity of the products.  The rate of a reaction depends upon many factors: the number of molecules, how fast they are moving, how they are colliding, …  Because of this, reaction rate is not linear, it is an exponential decay.

Instantaneous rate is the rate at a specific moment in time.  It is determined by the slope of the tangent line to the curve.  The only way to determine this without calculus is to graph the data and manually approximate a tangent line.

Average rate is the rate between 2 specific times.  It is determined by the slope of the line between the 2 times on the curve.  You do not need an actually graph the data to determine average rate, just use the (time, molarity) as (x,y) and determine the slope by ∆x/∆y.

The formula for the rate law for an equation is always    rate=k[reactant]^order

The power or order of the reaction for each reactant must be determined from experimental data.  The total order for a reaction is equal to the sum of the orders for each reactant. 

• This method requires that a reaction be run several times.
• The initial concentrations of the reactants are varied.
• The reaction rate is measured just after the reactants are mixed.
• Eliminates the effect of the reverse reaction.

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.

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.

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.

The Basic Gas Laws and the Combined Gas Law

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.

Gases: Atmospheric Pressure

Gases exert pressure by applying a force when they collide with a surface.  That surface can be the interior walls of an scuba tank or your skin.  Remember we are surrounded by gases all the time.  We breathe the oxygen, and add to the carbon dioxide when we exhale.  The atmosphere is composed of many gases, but it is primarily nitrogen (~79%), with oxygen (~19%), and very little quantities of many other gases including carbon dioxide, argon, nitrogen compounds, unburned hydrocarbons, ozone, ...

The atmosphere is composed of gas particles from high above the earth to here on the surface.  All of them moving and colliding.  Here at the surface, we actually feel the "weight" of all those gas particles from the top of our head all the way to outer-space.  This is called atmospheric pressure. The normal pressure exerted by the atmosphere at sea level is 1 atmosphere (atm).

Gases: 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.