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Question: If the rate respect to \({{\text{O}}_{2\;\;}}\), \(NO\), \(N{O_2}\) are \( - \dfrac{{\vartriangle \l...

If the rate respect to O2    {{\text{O}}_{2\;\;}}, NONO, NO2N{O_2} are −△[O2    ]△t  =  −12△[NO]△t    =  +12△[NO2]△t - \dfrac{{\vartriangle \left[ {{{\text{O}}_{2\;\;}}} \right]}}{{\vartriangle {\text{t}}}}\; = \; - \dfrac{1}{2}\dfrac{{\vartriangle \left[ {NO} \right]}}{{\vartriangle {\text{t}}}}\;\; = \; + \dfrac{1}{2}\dfrac{{\vartriangle \left[ {N{O_2}} \right]}}{{\vartriangle {\text{t}}}} , then the corresponding chemical equation is 2NO  +  O2  →  NO22NO\; + \;{{\text{O}}_2}\; \to \;N{O_2}.
A.True
B.False

Explanation

Solution

We are calculating the rate of the reaction. We should know about the rate of a reaction. Rate of a reaction is defined as the speed at which the reactants in a given reaction are converted into products. It gives us the idea about the time taken by the reaction to be completed. We will see how to calculate the rate of reaction later.

Complete answer:
Let’s suppose a simple reaction
aA  +  bB  →  cCaA\; + \;bB\; \to \;cC
here A and B are the reactants and C is the product and a, b, c are the stochiometric coefficients of A, B and C.
Rate equation for above reaction is given as
r=−1a△[A]△t  =  −1b△[B]△t    =  +1c△[C]△t  r = - \dfrac{1}{a}\dfrac{{\vartriangle \left[ A \right]}}{{\vartriangle {\text{t}}}}\; = \; - \dfrac{1}{b}\dfrac{{\vartriangle \left[ B \right]}}{{\vartriangle {\text{t}}}}\;\; = \; + \dfrac{1}{c}\dfrac{{\vartriangle \left[ C \right]}}{{\vartriangle {\text{t}}}}\;
where r is the rate of reaction, △[A]\vartriangle \left[ A \right] is the change concentration of reactant A, △[B]\vartriangle \left[ B \right] is the change in concentration of reactant B, △[C]\vartriangle \left[ C \right] is the change in concentration of product C, △t\vartriangle {\text{t}}is the change in time. A negative sign is written before reactants concentration which denotes that the concentration of reactant is decreasing with time.
Let’ see the rate equation given to us
r=−△[O2    ]△t  =  −12△[NO]△t    =  +12△[NO2]△tr = - \dfrac{{\vartriangle \left[ {{{\text{O}}_{2\;\;}}} \right]}}{{\vartriangle {\text{t}}}}\; = \; - \dfrac{1}{2}\dfrac{{\vartriangle \left[ {NO} \right]}}{{\vartriangle {\text{t}}}}\;\; = \; + \dfrac{1}{2}\dfrac{{\vartriangle \left[ {N{O_2}} \right]}}{{\vartriangle {\text{t}}}}
From this equation we can identify that 1  mole    1\;mole\;\;of Oxygen is reacting with 2  mole    2\;mole\;\;of Nitric oxide to give 1  mole    1\;mole\;\;of Oxygen. But the reaction given to us suggests that 2  mole    2\;mole\;\;of Nitric Oxide reacts with 1  mole    1\;mole\;\;of Oxygen to give 1  mole    1\;mole\;\;of Nitrogen dioxide.
The reaction does not match with the rate equation.
Hence option (B) is the correct answer.

Note:
The given reaction is wrong because it is not balanced when 2  mole    2\;mole\;\; of Nitric oxide reacts with 1  mole    1\;mole\;\;of Oxygen it should give 1  mole    1\;mole\;\; of Oxygen. So, the rate equation is correct but the reaction is wrong. The correct reaction will be 2NO  +  O2  →  2NO22NO\; + \;{{\text{O}}_2}\; \to \;2N{O_2}.