Question

Using the data in the table, calculate the rate constant of this reaction.

A+B⟶C+D

Trial	[A] (M)	[B] (M)	Rate (M/s)
1	0.280	0.240	0.0160
2	0.280	0.576	0.0922
3	0.504	0.240	0.0288

k=

Units

Answer 1

Given.

Trial1

Concentration of A =0.280M concentration of B=0.240M,Rate =0.0160M/s

Trial 2

Concentration of A =0.280M concentration of B =0.576M rate =0.0922M/s

Trial3

Concentration of A =0.504 M concentration of B=0.240M,rate =0.0288M/s

Solution

Rate law is defined as the rate of reaction equal to product of concentration of reactants each raised to term as determined experimentally. The sum of exponents to which the concentration terms are raised is called overall order of reaction.

Suppose order with respect to A =a and and with respect to B is b.

The rate law equation is Rate =k [A]^a [B] ^{​​​​​b}

Substituting the data of each experiment, we get

Trial1)0.0160 M/s =k(0.280M)^a(0.240M)^b​​​​​​..... 1

Trial 2) 0.0922M/s =k (0.280M)^a(0.576M)^b.....2

Trial3)0.0288M/s =k(0.504M)^a(0.240M)^b.....3

Dividing 1 by 2, we get

0.0160M/s /0.0922M/s =(0.280M)^a​​​​​​(0.240)^b/(0.280M)^a(0.576)^b

0.280 M divides with 0.280M to give 1, so we are left with othe term with power b. Moreover, rate constant k also get cancelled. So, the equation we get:

0.0160M/s/0.0922M/s =(0.240)^b(0.576)^b

0.0160M/s/0.0922M/s =(0.240/0.576)^b

0.174 =(0.417)^b

Taking square root of 0.174 we get 0.417

(0.417)²=(0.417)^b

Thus,b=2.

Similarly, dividing 1 and 3 we get

0.0160M/s/0.0288M/s =(0.280M/0.504M)^a Terms with power b are same so they get cancelled and k also get cancelled, we get:

0.556 =(0.556)^a

Terms are same on the both side a=1

Hence, rate law equation is

Rate =k[A] ¹[B]²

K =Rate /[A] [B] ²

We can calculate K by putting the values from any experiment in the above given equation.

Example: taking the values from experiment 1 we get

K = 0.0160M/s/(0.280M)(0.240M)²

K =0.0160M/s /(0.280M)(0.0576M²)

K =0.0160M/s/(0.016125M³)=0.992248062M^-2/s

If we consider significant figures , then on dividing answer, should be equal to the significant figures possessed by least precise number.

0.0160 has 3 significant figures, 0.280 has 3 significant figures, 0.0576 has 3 significant figures, so answer should have 3 significant figures.

Answer, K =0.992M^-2/s

The first term on right hand has same value in numerator and denominator, so on division this value