Answer to Question #143986 in General Chemistry for gia

Question #143986
Consider the reaction A + B --> products

From the following data obtained at a certain temperature, determine the rate law, the order of the reaction, and calculate the rate constant k.

Experiment 1: [A] = 1.50 M; [B] = 1.50 M; Initial Rate = 3.20 x 10-1 M/s

Experiment 2: [A] = 1.50 M; [B] = 2.50 M; Initial Rate = 3.20 x 10-1 M/s

Experiment 3: [A] = 3.00 M; [B] = 1.50 M; Initial Rate = 6.40 x 10-1 M/s
1
Expert's answer
2020-11-18T13:40:19-0500

Rate = k[A]a[B]b

"\\frac{Rate_1}{Rate_2} = (\\frac{[A_2]}{[A_1]})^a \\times (\\frac{[B_2]}{[B_1]})^b"

"\\frac{3.2 \\times 10^{-1}}{3.2 \\times 10^{-1}} = (\\frac{[1.5]}{[1.5]})^a \\times (\\frac{[2.5]}{[1.5]})^b"

"1 = 1^a \\times 1.67^b"

b = 0

"\\frac{Rate_3}{Rate_1} = (\\frac{[A_3]}{[A_1]})^a \\times (\\frac{[B_3]}{[B_1]})^b"

"\\frac{6.4 \\times 10^{-1}}{3.2 \\times 10^{-1}} = (\\frac{[3.0]}{[1.5]})^a \\times (\\frac{[1.5]}{[1.5]})^b"

"2 = 2^a \\times 1^b"

a = 1

Thus,

Rate = k[A]

Overall order of reaction = a + b = 1 + 0 = 1

Reaction is the first order.

Substituting values from Exp. 1 into the rate low:

"3.2 \\times 10^{-1} = k \\times 1.5"

"k = 0.213 \\;s^{-1} = 2.13 \\times 10^{-1} \\;s^{-1}"


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