Question

C) The reactant concentration in a first-order reaction was 8.40×10−2 M after 30.0 s and 1.50×10−3 M after 100 s . What is the rate constant for this reaction?

D)The reactant concentration in a second-order reaction was 0.320 M after 250 s and 7.40×10−2 M after 750 s . What is the rate constant for this reaction? Express your answer with the appropriate units. Include an asterisk to indicate a compound unit with mulitplication, for example write a Newton-meter as N*m.

Answer 1

For a first order reaction

-ln(1-XA)= kt ,k= rate constant

XA= Conversion= 1-CA/CAO, where CA= initial concentration= 1.5*10-3 M at 30 sec and CAO= initial concentration= 8.4*10-2 M

1-XA= CA/CAO= 1.5*10^-3/ 8.4*10^-2   = 0.017857

-ln (0.017857)= k*30

4.025352 =k*30 and K = 4.025352/30= 0.134178 sec-1

2. For a second order reaction XA/(1-XA)= KCAOt

XA=1-CA/CAO

(1-CA/CAO)/ CA/CAO= KCAO*t

(CAO-CA)/CA= KCAOt (1)

For two different concentrations and time intervals equation (1) becomes

(CAO-0.320)/0.32= k*CAO* 250 (2), 3.125*(CAO-0.320)= k*250 (2A)

CAO-7.4*10-2)/7.4*10-2= k*CAO*750 (3), 13.51(CAO- 7.4*10^-2)= 750*k (3A)

Dividing 3A and 2A gives

(CA-7.4*10-2)= 13*(CA-0.32) ,CA=0.3405

From XA= 1-CA/CAO= 1- 0.32/0.3405=0.06= K*0.3405*250s

K= 0.06/0.3405*250 =0.00705/M.s