Question

For the reaction $4N{{H}_{3}}\left( g \right)+5{{O}_{2}}\left( g \right)~\to 4NO\left( g \right)+6{{H}_{2}}O\left( g \right)$ , the rate of reaction in terms of disappearance of $N{{H}_{3}}$ is $-\dfrac{d[N{{H}_{3}}]}{dt}$ , then write the rate expression in terms of concentration of ${{O}_{2}}$ , NO and ${{H}_{2}}O$ .

Answer 1

Hint: The rate of disappearance of ammonia means we have to divide the total equation with four because four moles of ammonia are involved in the given chemical reaction. Then we can make the disappearance of ammonia while writing the rate expression of the chemical reaction.

Complete answer:
- In the question it is given that the rate of reaction in terms of disappearance of $N{{H}_{3}}$ is $-\dfrac{d[N{{H}_{3}}]}{dt}$ .
- But in the given reaction there is an involvement of 4 moles of ammonia.
\[4N{{H}_{3}}\left( g \right)+5{{O}_{2}}\left( g \right)~\to 4NO\left( g \right)+6{{H}_{2}}O\left( g \right)\]
 - But in the rate of the expression the number of moles of ammonia is not mentioned means we have to consider it as one mole of ammonia.
- If we consider one mole of ammonia the chemical reaction is going to convert as follows.
\[N{{H}_{3}}\left( g \right)+\dfrac{5}{4}{{O}_{2}}\left( g \right)~\to NO\left( g \right)+\dfrac{6}{4}{{H}_{2}}O\left( g \right)\]
- Now we have to write the rate expression in terms of concentration of ${{O}_{2}}$ , NO and ${{H}_{2}}O$ from the above chemical equation.
- The rate of expression in terms of oxygen = $-\dfrac{5}{4}\dfrac{d[{{O}_{2}}]}{dt}$
- The rate expression in terms of NO = $-\dfrac{d[NO]}{dt}$
- The rate expression in terms of water = $-\dfrac{3}{2}\dfrac{d[{{H}_{2}}O]}{dt}$
- Therefore the total rate expression in terms of disappearance of ammonia is
\[-\dfrac{d[N{{H}_{3}}]}{dt}=-\dfrac{5}{4}\dfrac{d[{{O}_{2}}]}{dt}=-\dfrac{d[NO]}{dt}=-\dfrac{3}{2}\dfrac{d[{{H}_{2}}O]}{dt}\]

Note:
Rate expression of a chemical reaction represents the number of moles of each reactant and products involved in the chemical reaction. By using rate expression we can write the chemical reactions very easily without any confusion.