# Chemistry Lab/Kinetics

Kinetics was a topic for the event Chemistry Lab in 2015 and 2016.

## Kinetics (2015)

### Kinetics: Reaction Rates

$\text{rate}=\dfrac{[\text{limiting reagent}]}{\text{time}}$. To find reaction rates, you need a table or graph showing the concentration of one of the products or reactants over a period of time. If given:

• a line graph showing concentration of a reactant, you can find reaction rate at a given instant for that reactant. It will be equal to the slope of the line tangent to the point on the graph at that instant.
• a line graph showing concentration of a product, you can find the reaction rate at at given instant for that product. It will be equal to the opposite of the slope of the line tangent to the point on the graph at that instant.
• the reaction rate for one reactant or product and the reaction equation, you can find the reaction rates for another reactant or product. Balance the equation, if necessary. Take the rate you are given, multiply by the coefficient of the reactant or product you want the rate for, and divide by the coefficient of the reactant or product whose rate you were given.

### Kinetics: Reaction Conditions

• Increasing temperature increases reaction rate.
• Increasing concentration increases reaction rate.
• Increasing particle size decreases reaction rate.
• Adding catalysts increases reaction rate.

## Rate Laws

In an equation with rate constant k and reactants A, B, and C, the rate is:

$Rate=k([A]^x)([B]^y)([C]^z)$

x, y, and z are whole numbers that indicate the concentrations' effect on reaction rate. They can be determined by using a table of data showing concentrations of reactants and resulting reaction rates. When the concentration of all reactants but one ($A$) stay the same, the concentration of that one product is multiplied by a factor of $p$, and the reaction rate is multiplied by a factor of $q$, the whole number exponent ($x$) of that product in the rate law is equal to $log(q)/log(p)$. The overall order of the reaction is equal to $x+y+z$.

### Zeroth Order Reactions

The rates of zeroth order reactions do not depend on the concentration of the reactants. The units of $k$ are $Ms^{-1}$. When graphing zeroth order reactions, two graphs can be drawn: rate vs concentration and concentration vs time. It has a half life equation as well.
Rate vs Concentration

The graph of the rate of a reaction over the concentration of the reactant yields a straight horizontal line with a slope of 0. From this graph, we can get the differential rate law, which is:

$rate = -\frac{Δ[A]}{Δt} = k$

Concentration vs Time

The graph of the concentration of a reactant over time yields a straight line with a negative slope, and the slope of this line equals $-k$. This gives us the integrated rate law, which is:

$[A] = [A]_0 - kt$

Half Life

The half-life of a zeroth order reaction is:

$t_½ = \frac{[A]_0}{2k}$

### First Order Reactions

The rates of first order reactions do depend on the concentration of the reactants and they change by the same factor. The units of $k$ are $s^{-1}$. When graphing first order reactions, two graphs can be drawn: rate vs concentration and concentration vs time. It has a half life equation as well.
Rate vs Concentration

The graph of the rate of a reaction over the concentration of the reactant yields a straight line with a positive slope. From this graph, we can get the differential rate law, which is:

$rate = -\frac{Δ[A]}{Δt} = k[A]$

Concentration vs Time

The graph of the natural log of the concentration of a reactant over time yields a straight line with a negative slope, and the slope of this line equals $-k$. This gives us the integrated rate law, which is:

$ln([A]) = ln([A]_0) - kt$ or $[A] = [A]_0e^{-kt}$

Half Life

The half-life of a first order reaction is:

$t_½ = \frac{ln(2)}{k}$

### Second Order Reactions

The rates of second order reactions increase exponentially as the concentration of the reactant increases. The units of $k$ are $M^{-1}s^{-1}$. When graphing second order reactions, two graphs can be drawn: rate vs concentration and concentration vs time. It has a half life equation as well.
Rate vs Concentration

The graph of the rate of a reaction over the concentration of the reactant yields an exponentially increasing line. From this graph, we can get the differential rate law, which is:

$rate = -\frac{Δ[A]}{Δt} = k[A]^2$

Concentration vs Time

The graph of the inverse of the concentration of a reactant over time yields a straight line with a positive slope, and the slope of this line equals $k$. This gives us the integrated rate law, which is:

$\frac{1}{[A]} = \frac{1}{[A]_0} + kt$

Half Life

The half-life of a second order reaction is:

$t_½ = \frac{1}{k[A]_0}$

## Sample Questions: Kinetics

Questions in the kinetics section might involve...

1. Reaction Rates
2. Reaction Conditions (Temperature, Concentration, Particle Size, Cataylsts)
3. Rate Laws (at state and national levels)
4. Rate Constants (at state and national levels)