Hi can i get help in this problem. Hopefully i can get help in this. Work or exp

Question

Hi can i get help in this problem. Hopefully i can get help in this. Work or explanation should help me understand the problem.Thank you.

Some measurements of the initial rate of a certain reaction are given in the table below. Ne H2 initial rate of reaction 18.0 M/s 0.836 M 1.02 M 0.836 M 1.21 M 25.3 M/s 254. M/s 3.14 M 1.02 M Use this information to write a rate law for this reaction, and calculate the value of the rate constant k. Round your value for the rate constant to 2 significant digits. Also be sure your answer has the correct unit symbo x10 rate k

Explanation / Answer

In order to calculate the rate law expression for a A+B reaction, we need to apply Initial Rates Method.

Note that the generic formula goes as follows:

r = k [A]^a [B]^b

Note that if we got at least 3 sets of point, in which we have A and B constant, then we could use:

r1 / r2 = (k1 [A]1^a [B]1^b) / (k2 [A]2^a [B]2^b)

If we assume K1 and K2 are constant, then K1= K2 cancel each other

r1 / r2 = ([A]1^a [B]1^b) / ( [A]2^a [B]2^b)

Then, order according to [A] and [B]

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

If we get two points in which A1 = A2, then we could get B, and vise versa for A...

From the data shown in YOUR table

Choose point 1 and 2...

r1 / r2 = ([A]1/[A2])^a * ([B]1/[B]2)^b

substitute

(18) / (25.3) = (0.836/0.836)^a * (1.02/1.21)^b

Cleary, the coefficient cancels:

0.7114= 1 * (0.842)^b

solve,

ln(0.7114) / ln(0.842) = b

b = 1.980= 2

Choose now points 2 and 3:

r2 / r3 = ([A]2/[A]3)^a * ([B]2/[B]3)^b

substitute

(18/254) = (0.836/3.14)^a * (1.02/1.02)^b

Cleary, the coefficient cancels:

0.070866= (0.26624)^a * 1

solve,

ln(0.070866) / ln(0.26624) = a

a = 2

so...

a = 2, b = 2

then

r = k [A]^a [B]^b

so

r = k [A]^2 [B]^2

For "k" value... choose any point in your set of data, I will choose 1 for simplicity

substitute data

18 = k*(0.836^2)(1.02^2)

K = (18)/((0.836^2)(1.02^2)) = 24.75 1/(M^4s)

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