Question

Palladium dissolves gaseous hydrogen at 100 degreeC until the resulting material has a hydrogen content of about PdH_0.75 (i.e. almost 1000 volumes H_2 at N.T.P per volume Pd). When this is heated up in a vacuum the hydrogen is removed. At 100 degreeC palladium-hydrogen powder is heated and the value of n with time (in the formula PdH_n) is given by the following data: Plot this data according to zero, first and second order plots. What is the order with respect to dissolved hydrogen?

Answer 1

Zeroth Order Rate Law

Rate=−d[A]/dt=k[A]^o

[A]=−kt+[A]^o

So for this a plot of concentration of A versus time will give a straight line

But in this case the plot does not give a straight line so it is not zero order reaction

0.8 0.7 0.6 0.5 c 0.4 0.3 0.2 0.1 10 15 20 25 漠) time

For a first order reaction

The rate law.

Rate=−d[A]/dt=k[A]

Here

ln([A]_t/[A]^o)=−kt

So a plot of ln(A) versus t will give a straight line

But in this case a lot of ln(n) versus time does not give a straight line so it is not first order

15 20 25 漠) 10 -1 -2 -5 -6 time

For a second order reaction

second-order rate law

d[A]/dt=−k[A]²

yields

1/[A]=1/[A]o+kt

So a plot of 1/[A] versus time should give a straight line

In this case a plot of 1/n versus time gives a straight line

So the order of this reaction with respect to the dissolved hydrogen is second order.

30 15 20 10 0 time