Use this data to do the following: 1. calculate the first-order rate constant fo

Question

Use this data to do the following: 1. calculate the first-order rate constant for each pH 2. calculate the half-life for each pH. 3. graph rate vs pH

moles released time (hr pH7.0 PH 6.0 pH5.0 pH 4.0 PH 3.0 0 0.00E+00 0.1 4.98E-04 0.25 1.23E-03 0.5 2.44E-03 0.75 3.61E-03 1 4.76E-03 1.5 6.96E-03 2 9.06E-03 3 1.3OE-02 4 1.65E-02 0.00E+00 0.00E+00 0.00E 00 0.00E 00 2.20E-03 3.94E-03 5.65E-03 8.24E-03 5.32E-03 9.27E-03 1.30E-02 1.81E-02 1.01E-02 1.68E-02 2.26E-02 2.97E-02 1.43E-02 2.30E-02 2.97E-023.70E-02 1.81E-02 2.80E-02 3.49E-024.17E-02 2.45E-02 3.54E-02 4.17E-02 4.66E-02 2.97E-02 4.03E-02 4.55E-02 4.86E-02 3.70E-02 4.57E-02 4.86E-02 4.98E-02 4.17E-02 4.81E-02 4.96E-02 5.00E-02

Explanation / Answer

1. Let us say that initially there was 1 mol of a substrate.

    For a 1st order reaction     ln(a/a-x) = kt

    Here a=1(no. of moles present initially), x= no. of moles released and t= time

    Now plotting a linear fitted graph between ln(a/a-x) vs t (for each pH value) and measuring the slope of each graph , we will get rate constant corresponding to each pH(slope=rate constant). Here unit of rate constant is (hr)-1

2. For 1st order reaction

         Half life= 0.693/rate constant

    So

pH

Half life(hr)

7

165

6

63.8

5

56.3

4

57

3

61.6

3.   Rate at any instant of time= rate constant × no. Of moles present at any instant of time

        [no. Of moles present at any instant of time = 1- moles released at that instant of time]

Lets say after 0.1 hr,

pH

Rate(moles.hr-1)

7

0.011

6

0.0042

5

0.012

4

0.0121

3

0.0112

So after 0.1 hr the graph is –

      

pH

Half life(hr)

7

165

6

63.8

5

56.3

4

57

3

61.6

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