(A) Calculate the values of the rate constant k assuming that the reaction is fi

Question

(A)Calculate the values of the rate constant k assuming that the reaction is first order.

What is the value of k at 5 s?  s-1
What is the value of k at 10 s?  s-1
What is the value of k at 15 s?  s-1
What is the value of k at 25 s?  s-1

(B)Calculate the value of k assuming that the reaction is second order.

What is the value of k at 5 s?  M-1s-1
What is the value of k at 10 s?  M-1s-1
What is the value of k at 15 s?  M-1s-1
What is the value of k at 25 s?  M-1s-1

(C)Use your results from parts A and B above to decide what the order of the reaction is for your data. (Enter 1 or 2)

(D)What is the concentration of [A] at time t=57 s?  M

Explanation / Answer

For 1st order reaction , lnCA= lnCAO- Kt

Where CA= concentration at any time t , CAO= initial concentration of reactant= 30M, and K= rate constant and t is the time requires

K=( lnCAO-lnCA)/t =ln (CAO/CA)/ t

At 5 sec, K= ln (30/14.53)/ 5 sec-1=0.1449/sec

At 10sec, K= ln (30/9.58)/10 = 0.1141/sec, at 15 sec K= ln(30/7.15)/15= 0.096/sec and 25 sec, K= ln(30/4.74)/25= .0738/sec

for

For second order reaction, KCAOt= XA/(1-XA), XA= conversion at any time= 1-CA/CAO

At 5sec, XA= 1-14.53/30= 0.516, K30*5= 0.516/(1-0.516)= 1.06, K= 1.06/(30*5)= 0.0071/M.sec

The constant rate constant values for 2nd order reaction suggests the reaction to be second order . In case of assumption of 1st order reaction, the rate constant is changing.

at t= 57sec, XA/(1-XA)= 0.0071*30*57=12.14

XA= 12.14-12.14XA

XA= 12.14/13.14= 0.9238 is the conversion

from XA= 1-CA/CAO

CA/CAO = 1-XA

CA= CAO*(1-XA)= 30*(1-0.9238)= 2.286 M

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