Question

A student makes three plots of their data and finds that a plot of [A] vs t is non-linear, a plot of ln[A] vs t is linear, and a plot of 1/[A] vs t is non-linear. What is the rate law of the reaction?

Answer 1

Answer:

First order reaction

Explanation:

We have to remember the kinetic equations:

Zero order: $[A]=-kt~+~[A]o$

First order: $Ln[A]=-kt~+~Ln[A]o$

Second order: $1/[A]=-kt~+~1/[A]o$

The data given by the problem is:

-)  [A] vs t is non-linear

-) Ln[A] vs t is linear

-) 1/[A] vs t is non-linear

If we have a linear behaivor (a staigth line) between Ln[A] and t we will have a first order reaction.

Answer 2

For a first order reaction, a plot of ln[A] vs t is linear while plots of [A] vs t and 1/[A] vs t are nonlinear. Hence, the reaction is first order.

For a first order reaction, the concentration of reactants decreases exponentially with time. As a result of this, the graph of concentration against time is always a curve.

However, if we write the equation of first order reaction in logarithmic form;

ln[A] = ln[A]o - kt

Where;

[A] = concentration of species at time t

[A]o = initial concentration of reactants

k = rate constant

t = time taken

A  plot ln[A] vs t, yields  a straight line graph having a negative slope. Hence, the reaction is first order.

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