Given the initial rate data for the reaction A + B C, determine ALM BI.M ACVA (i

Question

Given the initial rate data for the reaction A + B C, determine ALM BI.M ACVA (initial) M/s 0.215 0.150 .81 x 10 0.215 0.300 1.16×10-3 0430 0.150 a. [C] 2.32x10-3 1.80 x 10-2 Mis-1 [A][B] A[C] -3.60x 102M's-I[ATB) AC] 1.20 x 10 M'[AIB 4 4101-3,37 x 101 ABI eA[C] 4c1-8.37x10-2M4"[A]2[B] 7. The rate law for a reaction is rate k[A]?[B]. Which of the following mixtures of reactants will give the smallest initial rate? a. 1.0 MA, 1.0 M B b. 2.0 MA, 0.50 M B c. 0.50 M A, 0.50 M B d. 0.125 M A, 3.0 M B e. 1.5 MA, 0.50 M B

Explanation / Answer

Let the rate (r)= K[A]a [B]b, a and b are orders of reaction with respect to A and B respectively.

From the 1st data point, K[0.215]a [0.150]b= 5.81*10-4 (1)

From the 2nd data point, K[0.215]a [0.300]b= 1.16*10-3 (2)

Eq.2/Eq.1 gives 2b= 2, b= 1

From the 3rd data point, K[0.430]a [0.1500]b= 2.32*10-3 (3)

Eq.3/Eq.1 2a= 4, a= 2

So the rate r= K[A]2 [B]

From the 1st data point, K[ 0.215]2 [0.150] = 5.81*10-4 , K= 0.084/M2.sec

The rate law becomes r= 0.084[A]2[B] (E is correct)

2.for [A] =1 [B]=1, r = K[1][1] =K, for [A] =2M, [B]=0.5, r= K[2]2[0.5]= 2K, for [A] =0.5, [B]=0.5, rate= K*0.5*0.5*0.5= 0.125K, for [A]=0.125, [B] =3M, K= K[0.125]2*0.3=0.005K, for [A] =1.5, [B] =0.5, r= K*1.5*1.5*0.5= 1.125K

So smaller rate if for [A]= 0.125 and [B] =0.3M ( d is correct)

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