Question

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

Trials	[A] (M)	[B] (M)	[C] (M)	Initial rate (M/s)
1	0.20	0.20	0.20	6.0x10-5
2	0.20	0.20	0.60	1.8×10−4
3	0.40	0.20	0.20	2.4×10−4
4	0.40	0.40	0.20	2.4×10−4

Given the data calculated in Parts A, B, C, and D, determine the initial rate for a reaction that starts with 0.45 M of reagent A and 0.90 M of reagents B and C?

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

Answer 1

Answer:

The given reaction is A + B + C -----> D+ E

Rate=k[A]x[B]y[C]z

Where k=rate constant, x=order with respect to A, y=order with respect to B, z=order with respect to C.

Now trial 2/trial 1 =>

k(0.2)x(0.2)y(0.6)z/k(0.2)x(0.2)y(0.2)z=(1.8 x 10-4)/(6.0 x 10-5)

3z=3=31

Therefore z=1 order with respect to C.

Now trial 3/trial 1 =>

k(0.4)x(0.2)y(0.2)z/k(0.2)x(0.2)y(0.2)z=(2.4 x 10-4)/(6.0 x 10-5)

2x=4=22

Therefore x=2 order with respect to A.

Now trial 4/trial 3 =>

k(0.4)x(0.4)y(0.2)z/k(0.4)x(0.2)y(0.2)z=(2.4 x 10-4)/(2.4 x 10-4)

2y=1=20

Therefore y=0 order with respect to B.

Rate=k[A]2[B]0[C]1

Rate=k[A]2[C]

From trail 1=>

Rate=k[A]2[C]

(6.0 x 10-5 M/s)=k(0.2 M)2(0.2 M)

k=(6.0 x 10-5 M/s)/(0.2 M)2(0.2 M)

k=0.0075 M-2 s-1.

Now given [A]=0.45 M, [B]=0.90 M, and [C]=0.90M.

Rate=k[A]2[C]

Rate=0.0075 M-2 s-1 x (0.45 M)2 x (0.90 M)

Rate=1.366 x 10-3 M/s

Therefore initial rate=1.4 x 10-3 M/s (Two significant figures)