Question

At elevated temperatures, nitrous oxide decomposes according to the equation
2 N2O(g) → 2 N2(g) + O2(g)
Given the following data, plot the appropriate graphs to determine whether the reaction is zeroth, first, or second order. Write the rate equation for this reaction. What is the value of the rate constant for the consumption of N2O? (Use excel to work this problem out completely, show all three graphs and the equations associated with each.)

Time (min)	0	60	90	120	180
[N2O]	0.250	0.218	0.204	0.190	0.166

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

The best fist that with the best striaght line; i.e. R^2 = 1

In this case, it is FIRST ORDER

therefore

slope = -k

slope = -0.0023

k = 0.0023 1/s

The rate of reaction equation

Rate = k*C

dC/dt = 0.0023 *C