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You want to find how much of A was left after the reaction. As 0.034 molB was formed and as the ratio of A:B = 2:1, you know that 0.034*2 = 0.068mol A has reacted. This means that 0.153-0.068 = 0.085A was left = [a]t
The initial concentration of A is .153. The question is asking for the rate constant expressed for the rate constant of A, so you convert .034M B into units of A by multiplying by the mol ratio, 2molA/1molB. This gives you that the change in concentration of A is .068M. To find the final concentration of A, you subtract your initial A, .153 minus your change, .068. This gives you the final concentration of A which you can then plug into the rate equation.
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