the reaction A+3B->2C+D is first order with respect to reactant A and second order with respect to reactant B if the concentration of A is doubled the concentration of B is halfed and the rate of the reaction would -------by a factor of --------
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To determine how the rate of the reaction will change when the concentration of reactant A is doubled and the concentration of reactant B is halved, we need to use the rate equation.
The rate equation for the given reaction is:
Rate = k[A]^x[B]^y
Where "k" is the rate constant, "[A]" and "[B]" are the concentrations of reactants A and B respectively, and "x" and "y" are the orders of reactants A and B in the reaction.
From the information given, we know that the reaction is first order with respect to reactant A (x = 1) and second order with respect to reactant B (y = 2).
So the rate equation becomes:
Rate = k[A]^1[B]^2
Now, let's consider the changes in concentration:
- Doubling the concentration of A means [A] will be multiplied by 2.
- Halving the concentration of B means [B] will be divided by 2.
Substituting these changes into the rate equation, we get:
New Rate = k(2[A])(1/2[B]^2)
= 2k[A](1/4)[B]^2
= 1/2 * (4k[A][B]^2)
= 2k[A][B]^2
Comparing the new rate equation to the initial rate equation, we see that the rate of the reaction will be doubled (increased by a factor of 2) when the concentration of A is doubled and the concentration of B is halved.