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+1 vote
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in Chemical Kinetics by (36.2k points)
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For the reaction :

2A + B → A2B

the rate = k[A][B]2 with k = 2.0 × 10-6 mol-2 L2 s-1.

Calculate the initial rate of the reaction when [A] = 0.1 mol L-1 [B] = 0.2 mol L-1.

Calculate the rate of reaction after [A] is reduced to 0.06 mol L-1.

1 Answer

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by (33.4k points)
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Best answer

Initial rate = k[A][B]2

But [A] = 0.1 M, [B] = 0.2 M and 

k = 2.0 × 10-6 mol-2 L2 s-1

∴ Initial rate

= 2.0 × 10-6 mol-2 L2 s-1 × 0.1 M × (0.2 M)2

= 8 × 10-9 M s-1

From the equation 2A + B → A2B it is clear that when 2 moles of A are used then 1 mol of B is used in the same time. Therefore, when A has been reduced to 0.06 M , 0.04 M of A and hence 0.02 M of B have reacted.

Thus,

Concentration of A left = [A] = 0.06 M

Concentration of B left = [B] = (0.2 M – 0.02 M) = 0.18 M

Rate = k[A][B]2

= 2.0 × 10-6 mol-2 L2 s-1 × 0.06 M × (0.18 M)2

= 3.89 × 10-9 M s-1

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