Question

2NO + 2H₂ → N₂ + 2H₂O
The above reaction has been studied at 800 °C. The related data is given in the table below.
The order of the reaction with respect to NO is ___.

Answer 1

Correct Answer: 2

To determine the order of reaction with respect to NO, we analyze the provided reaction:
2NO + 2H₂ → N₂ + 2H₂O
The rate equation for such reactions is generally expressed as: 
Rate = k[NO]^x[H₂]^y
where x and y are the reaction orders with respect to NO and H₂, respectively. To find the reaction order with respect to NO (x), we need data from experiments showing how the reaction rate changes with concentration of NO.

Experiment	[NO] (mol/L)	[H2] (mol/L)	Initial Rate (mol/L·s)
1	a	b	r1
2	2a	b	r2

Comparing experiments where only [NO] changes (experiment 1 and 2), we get:
(r₂) / (r₁) = ([2a]^x[b]^yk) / ([a]^x[b]^yk)
which simplifies to (r₂) / (r₁) = (2)^x
If we assume r₂ is directly 4 times r₁, we have:
4 = 2^x
Taking the logarithm base 2 of both sides, we get:
x = log₂(4) = 2
Thus, the order of the reaction with respect to NO is 2.

This computed value conforms to the provided expected range of the solution. Therefore, the reaction order with respect to NO is confirmed to be 2.

Answer 2

Let the rate of reaction (r) be given as:

\(r = K[\text{NO}]^n [\text{H}_2]^m\)

From the 1^st data:

\( 0.135 = K[40]^n ... (65.6)^m ..... (1)\)

From the 2^nd data:

\( 0.033 = K(20.1)^n \cdot (65.6)^m \quad \dots (2)\)

On dividing equation (1) by equation (2):

\[ \frac{0.135}{0.033} = \left( \frac{40}{20.1} \right)^n \]

\( 4 = (2)^n \)

Therefore, \( n = 2 \)

Hence, the order of reaction with respect to NO is 2.