Doubling the concentration of B, while keeping the concentration of A constant, how is the value of k be affected? How is the rate affected?
It really depends on the reaction itself...
For example, if your hypothetical reaction x A + y B = f C, the rate will be considering reactants A and B. And, if for example, rate =k[A]^2[B] , then:
Doubling the [A] will quadruple the rate; doubling the [B] will double the rate.
You did not indicate such conditions in your problem set, so it is hard to help. Also, answering your second question:
Changing the concentration has no effect on the value of k: it is a constant at a given temperature.
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