# Groupwork 12 Kinetics 1

Name: ______________________________

Section: _____________________________

Student ID#:__________________________

Work in groups on these problems. You should try to answer the questions without referring to your textbook. If you get stuck, try asking another group for help.

This group work activity intends to remind you about kinetics concepts to which you were exposed in your general chemistry curriculum.

### Q1: Writing and comprehending rate expressions

Consider the reaction

$NO(g)+O_2(g)\rightarrow N_2O_3(g)$

Balance the equation, then write out the rate expressions describing the disappearance of NO and O2 and the appearance of N2O3.

If the NO gas decreases at a rate of 1.60´10-4 M/s, how fast does the O2 gas disappear?  How fast does the N2O3 gas appear?  Explain why the answers you got make sense.

### Q2: Method of initial rates

To determine the rate law for a particular reaction, we can use the method of initial rates.  By measuring the initial rate for the reaction under a range of reaction conditions, we can find the correct rate law.

Consider the reaction

$F_2(g)+2ClO_2(g)\rightarrow 2FlO_2(g)$

For this reaction, scientists collected the following data:

[F2] (M)

ClO2 (M)

Initial rate (M/s)

0.10

0.010

1.2´10-3

0.10

0.040

4.8´10-3

0.20

0.010

2.4´10-3

Use the data in the table and the expression for the yet-to-be-determined rate law

$v(t)=k[F_2]^x[ClO_2]^y$

to determine the rate law for this chemical reaction.  Can you also determine the rate constant?

### Q3: Reaction rate laws and half life

When a reaction follows first order kinetics, the equation that describes it is

$\frac{d[A]}{dt}=k[A]$

When A is a reactant, the sign of the derivative is negative leading to

$-\frac{d[A]}{dt}=k[A]$

From this expression, we can generate an integrated rate law, which is exactly what its name implies.  Rearrange the equation to derive the integrated rate law.  First, gather terms associated with A on the left side of the equation.  Gather terms associated with t, on the right side and write down the resulting expression.

Now, you should have an expression that you can integrate from [A]0 to [A] and t=0 to t.  Integrate your expression to get the integrated first order rate law.

### Q4: Half life

The half life of a reaction is the time it takes for the initial concentration to drop to half its initial value, that is $$[A]_{1/2}=[A]_0/2$$.

Substitute this into your first order integrated rate law to get and expression for the half life of a first order reaction.

The rate equation for a zero order reaction is $$v(t)=k$$.  Use $$[A]_{1/2}=[A]_0/2$$to determine an expression for the half life of a zero order reaction.