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# The reaction $A + 2B + C \to 2D + E$ is found to be 1, 2 and zero order with respect to A, B, C respectively. What will be the final rate, if concentration of each reactant is doubled?A.2 timesB.4 timesC.8 timesD.16 times

Last updated date: 11th Aug 2024
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Hint:
The rate of reaction is the speed at which a chemical reaction proceeds. It is often expressed in terms of either the concentration (amount per unit volume) of a product that is formed in a unit of time or concentration of a reactant that is consumed in a unit of time.
Formula used:
Rate$\; = {\text{ }}k{\text{ }}{\left[ A \right]^a}{\left[ B \right]^b}$
Where, k= rate constant
A and B are concentrations in mol 
a is order of reaction with respect to A
b is order of reaction with respect to B

The given reaction $A + 2B + C \to 2D + E$
Now according to the rate formula,
Rate$= {\text{ }}K{\text{ }}{\left[ A \right]^1}{\left[ B \right]^2}{\left[ C \right]^0}$...............................................(i)
Now, if the concentration of each reactant is doubled, then we will get
New Rate$= {\text{ }}k\left[ {2A} \right]^1{\text{ }}\left[ {2B} \right]^2{\text{ }}\left[ {2C} \right]^0$
$= {\text{ }}K.2{\text{ }}\left[ A \right]^1.4\left[ B \right]^2\left[ C \right]^0$
$= 8.K\left[ A \right]^1\left[ B \right]^2\left[ C \right]^0$………………………………………………….(ii)
Now dividing (ii) by (i)
We get, $\dfrac{{New\;Rate}}{{Rate}} = 8$
Therefore, the final rate will be 8 times that of initial.

Hence, option C is correct.

Note:
The factors that affect the rate of reaction are surface area of a solid reactant, temperature, nature of reactant, presence/absence of catalyst, concentration or pressure of a reactant.