Question #16279

A reaction is of first order in a reactant A and of second order in a reactant B . How is the rate of this reaction affected when
a) The concentration of B alone is increased to three times?
b)The concentration of A as well as B are doubled ?

Expert's answer

Since it is given that a reaction is first order in reactant A and second order in reactant B; therefore,

r = k[A][B]^{2} …………………………. (i)

Where r is the rate of reaction and k is the rate constant of the reaction.

a)

When concentration of B alone is increased three times, let the new rate be r_{1}

r_{1} = k[A][3B]^{2} = 9k[A][B]^{2} …………………………. (ii)

Dividing eq.(ii) by eq.(i), we get

r_{1} = 9r

Therefore, the rate of the reaction would become 9 times the initial rate when the concentration of B alone is increased three times.

b)

When the concentration of both the reactants is doubled, then the rate of the reaction would be r_{2}

r_{2} = k[2A][2B]^{2} = 8k[A][B]^{2} …………………………. (iii)

Dividing eq.(iii) by eq.(i), we get

r_{2} = 8r

Therefore, the rate of the reaction would become 8 times the initial rate when the concentration of both A and B is doubled.

r = k[A][B]

Where r is the rate of reaction and k is the rate constant of the reaction.

a)

When concentration of B alone is increased three times, let the new rate be r

r

Dividing eq.(ii) by eq.(i), we get

r

Therefore, the rate of the reaction would become 9 times the initial rate when the concentration of B alone is increased three times.

b)

When the concentration of both the reactants is doubled, then the rate of the reaction would be r

r

Dividing eq.(iii) by eq.(i), we get

r

Therefore, the rate of the reaction would become 8 times the initial rate when the concentration of both A and B is doubled.

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