For a reaction that is first order with respect to [D] and second order with respect to [E], which of the following will result in no change in overall reaction order?
A. Doubling [D] and halving [E]
B. Halving [D] and doubling [E]
C. Doubling [D] and doubling [E]
D. Increasing [D] by a factor of four and halving [E]
Solution: We can write the rate law based on the given.
The orders are powers in the rate law equation.
Rate = k [D][E]^2
Let's go through each answer choice to figure out the correct one.
A. Doubling [D] and halving [E]
Rate = k [2D][1/2E]^2 = 2*(1/4) = 1/2 NOT 1
The rate law would be 1/2 of the original, answer choice A is not correct
B. Halving [D] and doubling [E]
Rate = k [1/2D][2E]^2 = 1/2(4) = 2 , not correct
C. Doubling [D] and doubling [E]
Rate = k [2D][2E]^2 = 2(4) = 8 , not correct
D. Increasing [D] by a factor of four and halving [E]
Rate = k [4D][1/2E]^2 = 4(1/4) = 1
The rate stays the same! Answer choice D is the correct answer.