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Determine the forms of the integrated and the differential rate laws for the decomposition of benzene diazonium chloride C6H5N2Cl(aq)C6H5Cl(l)+N2(g)

from the following data, which were collected at50.0oCand1.00atm:

Time (s)N2Evolved (ml)
619.3
926.0
1436.0
2245.0
3050.4

58.3

The total solution volume was 40.0ml.

Short Answer

Expert verified

Differential rate law is -dC6H5N2Cldt=Rate=KC6H5N2Cl.

Integrated rate law is lnC6H5N2Cl=-Kt+lnC6H5N2Cl.

Step by step solution

01

Find the initial concentration of C6H5N2Cl.

It can be calculated from the amount ofN2evolved after t=.

n=PVRT=1.00atm58.3×10-3L0.08LatmKmol×323K=2.20×10-3molN2

localid="1663831195780" 1moleC6H5N2Cl1moleN2

Initial concentration of C6H5N2Cl=2.20×10-3mol40.0×10-3L

=0.0550M

02

Check for the order of the reaction.

The quantity V-Vtwill be proportional to the moles remaining C6H5N2Cl. It will also be proportional to the C6H5N2Clconcentration. For first-order reaction, lnV-Vtvs graph would be linear. We can obtain the following data:

Time(s)N2Evolvedml
619.3
926.0
1436.0
2245.0
3050.4

58.3
03

Plot the graph and find the order of the reaction.

lnV-Vt

t(s)

We can see that the plot betweenlnV-Vtvs t is linear, so it is a first order reaction.

So, the differential rate law will be:

role="math" localid="1663919967834" -dC6H5N2Cldt=Rate=KC6H5N2Cl

Integrated rate law will be:

lnC6H5N2Cl=-Kt+lnC6H5N2Cl

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