The kinetics of the catalytic decomposition of NH3 into N2 and H2 on a hot tungsten filament at 1100 °C was investigated by Kunsman. He measured the times (t1/2) required for half of NH3 to decompose at different initial NH3 pressures, as shown below:

Question

The kinetics of the catalytic decomposition of NH3 into N2 and H2 on a hot tungsten filament at 1100 °C was investigated by Kunsman. He measured the times (t1/2) required for half of NH3 to decompose at different initial NH3 pressures, as shown below:

P (torr) t1/2 (minutes)
265 7.6
130 3.7
58 1.7
Determine (i) the order of the reaction and (ii) the rate constant.

Answer 1

a). NH3== N2 + H2

BAlance:

2NH3 == N2 + 3H2
-r= kC(NH3)2

>> Therefore th order of rxn is 2nd order

Answer 2

To determine the order of the reaction and the rate constant, we can use the integrated rate law equation for a first-order reaction:

ln([A]t/[A]0) = -kt

Where:
[A]t = concentration of the reactant at time t
[A]0 = initial concentration of the reactant
k = rate constant
t = time

In this case, since we are given the half-life (t1/2), we can rewrite the equation as:

ln(1/2) = -kt1/2

Taking the natural logarithm (ln) of both sides gives:

ln(1/2) = -kt1/2

Now, we can rearrange the equation to solve for k:

k = -ln(1/2) / t1/2

To determine the order of the reaction (i), we need to plot the natural logarithm of the initial NH3 pressure (P0) against the natural logarithm of the half-life (t1/2). If the resulting graph is a straight line, the reaction is first-order with respect to NH3.

Let's calculate the rate constant and the order of the reaction.

First, let's calculate the rate constant (k) using the given half-life values:

For P = 265 torr, t1/2 = 7.6 minutes
k1 = -ln(1/2) / 7.6

For P = 130 torr, t1/2 = 3.7 minutes
k2 = -ln(1/2) / 3.7

For P = 58 torr, t1/2 = 1.7 minutes
k3 = -ln(1/2) / 1.7

To find the average value of k, we can sum up the three values and divide by 3:

k = (k1 + k2 + k3) / 3

Now, let's calculate the order of the reaction (i) by plotting the natural logarithm of the initial NH3 pressure (P0) against the natural logarithm of the half-life (t1/2).

Take the natural logarithm of the initial NH3 pressure (P0) values:

ln(P0) = ln(265), ln(130), ln(58)

Plot these values on the x-axis against the natural logarithm of the half-life (t1/2) on the y-axis. If the resulting graph is a straight line, the reaction is first-order with respect to NH3, and the slope of the line represents the order of the reaction.

By following these steps, you should be able to determine the order of the reaction (i) and the rate constant.