The rate constant is numerically the same for three reactions of first, second and third order respectively. Which one is true for the rates of the three reactions if the concentration of the reactant is $1$ $M$ ?

r_{1} = r_{2} = r_{3}

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r_{1} > r_{2} > r_{3}

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r_{1} < r_{2} < r_{3}

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None of the above

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Solution

The correct option is A $r_{1} = r_{2} = r_{3}$
Suppose $R_{1}, R_{2}$ and $R_{3}$ are the rates of three reactions of first, second and third order respectively, and $k$ is the rate constant all the three reactions.
$R_{1} = k [A]$
$R_{2} = k [A]^{2}$
$R_{3} = k [A]^{3}$
$[A]$ being the concentration of the reactiont $A$ in mol per lit.
Now if,
$[A] = 1$ , $R_{1} = R_{2} = R_{2}$
$[A] < 1$ , $R_{1} > R_{2} > R_{3}$
$[A] > 1$ , $R_{1} < R_{2} < R_{3}$

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The rate constant is numerically the same for three reactions of first, second and third order respectively. Which one is true for the rates of the three reactions if the concentration of the reactant is 1 M?

The rate constant is numerically the same for three reactions of first, second and third order respectively. Which one is true for the rates of the three reactions if the concentration of the reactant is $1$ $M$ ?