The decomposition of ammonia on a platinum surface at 1129 K occurs according to the

following reaction: 2NH3 (g) �¨ N2(g) + 3H2(g). Use the following kinetic data which report the
variation of ammonia concentration in the gas phase with time to evaluate the order of reaction, rate
constant for the reaction at 1129 K and the half life. Justify why the reaction follows the order you
have determined.
[NH3] (x10-3 M) 2.10 1.85 1.47 1.23 0.86 0.57 0.34
Time (s) 0 200 400 600 800 1000 1200

please explain 'Use the following kinetic data which report the

variation of ammonia concentration in the gas phase with time to evaluate the order of reaction?' am confused I did plot found it was a 0zero order but then what.i need to know the key points of this question and what I should do when I see a question like this.thank you dr bob

To determine the order of reaction, rate constant, and half-life for the given reaction, you can use the given data and a graphical method known as the method of initial rates.

The order of reaction can be determined by examining the change in concentration of ammonia (NH3) with time. The general rate law equation for this reaction can be written as:

Rate = k[NH3]^n

Where "k" is the rate constant and "n" is the order of reaction with respect to ammonia. By comparing the rate of the reaction at different concentrations of ammonia, you can determine the order of reaction.

To find the order of reaction, you need to compare the initial rates of the reaction at two different concentrations. Let's consider the concentrations at 1.85 x 10^-3 M and 1.47 x 10^-3 M.

From the given data:
[NH3] (x10^-3 M) 1.85 1.47
Time (s) 200 400

Now, let's calculate the initial rates by taking the change in concentration divided by the change in time:

Rate1 = ([NH3]1 - [NH3]0) / (t1 - t0)
= (1.85 - 2.10) / (200 - 0)
= -0.25 / 200
= -1.25 x 10^-3 M/s

Rate2 = ([NH3]2 - [NH3]0) / (t2 - t0)
= (1.47 - 2.10) / (400 - 0)
= -0.63 / 400
= -1.575 x 10^-3 M/s

Now, since the rate law equation is Rate = k[NH3]^n, we can set up a ratio of rates and concentrations:

(Rate1 / Rate2) = ([NH3]1 / [NH3]2)^n

(-1.25 x 10^-3) / (-1.575 x 10^-3) = (1.85 x 10^-3) / (1.47 x 10^-3)^n

0.793 = 1.258^n

Now, take the logarithm of both sides to solve for "n":

log(0.793) = log(1.258^n)

-0.101 = n * log(1.258)

n = -0.101 / log(1.258)
n ≈ -0.101 / 0.100
n ≈ -1

Hence, the order of the reaction with respect to ammonia (NH3) is approximately -1.

Now let's determine the rate constant (k) using the initial rates and concentrations at any time point. Let's consider the concentrations at 1.47 x 10^-3 M.

From the given data:
[NH3] (x10^-3 M) 1.47
Time (s) 400

Using the rate law equation and the previously calculated order of reaction (-1), we substitute the values:

Rate = k[NH3]^n
-1.575 x 10^-3 = k(1.47 x 10^-3)^(-1)

Now, solve for the rate constant (k):

k = (-1.575 x 10^-3) / (1.47 x 10^-3)^(-1)
k ≈ -1.575 x 10^-3 / (1.47 x 10^-3)
k ≈ -1.072 s^-1

Hence, the rate constant (k) for the reaction at 1129 K is approximately -1.072 s^-1.

Finally, let's determine the half-life of the reaction. The half-life is the time it takes for the concentration of a reactant to decrease by half.

Using the rate law equation, we can find the half-life (t1/2):

t1/2 = 0.693 / k
t1/2 = 0.693 / (-1.072)
t1/2 ≈ -0.623 s

Note that the negative sign indicates the direction of the reaction, and the value is its magnitude. Thus, the half-life of the reaction is approximately 0.623 seconds.

To justify why the reaction follows the determined order, you can analyze the chemical equation and the reaction mechanism. In this case, the reaction is a decomposition reaction of ammonia on a platinum surface. It is reasonable to assume that the rate of decomposition is proportional to the concentration of ammonia raised to the power of -1 due to the stoichiometry of the reaction. This order indicates that the reaction is likely first order with respect to ammonia. Additionally, experimental data supports this assumption as determined from the rate law calculation.

Remember, rate law and reaction orders can only be determined experimentally and may not always correspond to the stoichiometric coefficients in the balanced equation.