For the reaction A+B+CD+E, the initial reaction rate was measured for various in

Question

For the reaction A+B+CD+E, the initial reaction rate was measured for various initial concentrations of reactants. The following data were collected:

What is the value of the rate constant k for this reaction?

Express your answer to three significant figures and include the appropriate units. Indicate the multiplication of units explicitly either with a multiplication dot or a dash.

Trial [A]
(M) [B]
(M) [C]
(M) Initial rate
(M/s) 1 0.50 0.50 0.50 1.5×104 2 0.50 0.50 1.50 4.5×104 3 1.00 0.50 0.50 6×104 4 1.00 1.00 0.50 6×104

Explanation / Answer

rate of reaction = k*[A]a*[B]b[C]c

Now,

1.5*10-4 = k*(0.5)a*(0.5)b*(0.5)c.............(1)

4.5*10-4 = k*(0.5)a*(0.5)b*(1.5)c.............(2)

6.0*10-4 = k*(1.0)a*(0.5)b*(0.5)c.............(3)

6.0*10-4 = k*(1.0)a*(1.0)b*(0.5)c.............(4)

Now, (2)/(1)

3 = (3)c

or, c = 1 ..........(5)

(3)/(1) we get

4 = (2)a

or, a = 2 ..........(6)

(4)/(3) we get

1 = (2)b

or, b = 0

Thus, rate of reaction = k*[A]2*[C]1

Now, 1.5*10-4 = k*(0.5)2*(0.5)

or, rate constant,k = 1.2*10-3

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