Question

Consider the following data showing the initial rate of a reaction at several different concentrations of A.

[A](M)

0.15

0.30

0.60

Initial Rate (M/s)

0.026

0.207

1.655

What is the order of the reaction? Express as an integer.

What is the rate law?

Estimate the value of the rate constant, k.

Answer 1

The initial rate of the reaction means that the influence of the products on the reaction rate is negligible.
Hence, the rate is :
r = k[A]ⁿ where "n" being the order of the reaction.

log r = logK[A]ⁿ

log r = logK +´nlog[A]

The order can be determined by plotting log(r) vs log([A]), the slope being the order. In this case:

y = a + bx Where a = logK b = slope = n, x = log A; and y = log r

So if R² is near 1, then the reaction is of the order indicated order:

log A: -0.8239; -0.5229; -0.2218

log r: -1.5850; -0.6840; 0.2188

a = log K = 0.88317

R² = 0.999999996

b = n = 2.9961 or 3.

So the reaction order is 3.

Now that we know this the rate law would be:

r = k[A]³

Finally the value of K (two ways to do it):

a) 0.88317 = logK ---> k = 10^0.99317 = 7.6413

b) k = r/[A]³ = 0.026 / 0.15³ = 7.704

Two really close values.

Hope this helps