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vlabodo [156]
3 years ago
15

3) A certain reaction has the following general form: A + B à AB At a particular temperature the concentration versus time were

collected for this reaction, and a plot of ln[A]t versus time resulted in a straight line with a slope of −3.7 x 10−3 s−1. Show your math! (5 points) a. What is the order of the reaction? b. What is the rate constant (including units)? c. Calculate the half-life for the reaction. d. If the initial concentration of A is 0.250 M, what is the concentration after 220 seconds?
Chemistry
1 answer:
seropon [69]3 years ago
7 0

Answer:

a. First order.

b. k=3.7x10^{-3}s ^{-1}

c. t_{1/2}=187.3s

d. [A]=0.111M

Explanation:

Hello.

a. In this case since the slope is in s⁻¹ we can infer that the lineal form of the rate law is:

ln[A]=-kt+ln[A]_0

Which is also:

y=mx+b

It means that the reaction is first-order as slope equals the negative of the rate constant which also has units of first-oder reaction.

b. Since the slope is −3.7 x 10−3 s−1 the rate constant is:

k=-m\\\\k=-(-3.7x10^{-3}s ^{-1})\\\\k=3.7x10^{-3}s ^{-1}

c. For first-order reactions, the half-life is:

t_{1/2}=\frac{ln(2)}{k}\\ \\t_{1/2}=\frac{ln(2)}{3.7x10^{-3}s^{-1}}\\\\t_{1/2}=187.3s

d. In this case, since the integrated first-order rate law is:

[A]=[A]_0exp(-kt)

The concentration once 220 seconds have passed is:

[A]=0.250Mexp(-3.7x10^{-3}s^{-1}*220s)\\\\

[A]=0.111M

Regards.

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