Question

The thermal decomposition of NO₂ gas at elevated temperatures occurs according to the following reaction:

2 NO₂ (g) → 2 NO (g)+O₂ (g)

Experimental data for this reaction at 330°C are listed in the table: Concentration of NO₂ as a Function of Time at 330°C

Time (s)	[NO2] (M)
0	1.00 × 10−2
60	6.83 × 10−3
120	5.18 × 10−3
180	4.18 × 10−3
240	3.50 × 10−3
300	3.01 × 10−3
360	2.64 × 10−3

Prepare and turn in an appropriate graph for the zero-, first-, and second order kinetics to determine the reaction order with respect to NO₂ (g).

Determine the order of the reaction from the graph

Write the rate law expression.

Answer 1

The best way to identify fast and easy the rate of reaction AND the rate constant is via Graphical Method.

First, as the name implies, we need to graph all types of order (most common)

Zero = C vs t;

For zero order, there is no dependency of concentrations:

dC/dt = k*C^0

dC/dt = k

When developed:

C = C0 - kt

if x axis is "time" then the slope is "k", and y-intercept is initial concentration C0. y-axis if C (concentration)

First = ln(C) vs. t

For first order

dC/dt = k*C^1

dC/dt = k*C

When developed:

dC/C = k*dt

ln(C) = ln(C0) - kt

if x axis is "time" then the slope is "-k", and y-intercept is initial concentration C0. y-axis if ln(C) (natural logarithm of concentration)

Second = 1/C vs. t

For Second order

dC/dt = k*C^2

When developed:

dC/C^2 = k*dt

1/C= 1/C0 + kt

if x axis is "time" then the slope is "k", and y-intercept is initial concentration C0. y-axis if 1/(C (inverse of concentration)

Know, graph all data in the 3 graphical methods

Best fit is

2nd order

then

Rate = k*[NO2]^2

where k = slope so

k = 0.7742