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**Integrated Rate law Expression:**

Integrated rate law expression provide the predicted temporal evolution in reactant and product concentrations for reactions having an assumed order dependence.

**(1) Zero-order Reaction: **Consider the following elementary reaction

For zero-order reaction, the rate law is

k is rate constant.

â‡’ â€“d[A] = k dt

If at t = 0, the init ial concentration is [A]_{0} and the concentration at t = t, is [A], then integrat ion yields

â‡’ [A]_{0} â€“ [A] = kt

This is integrated rate equation for a zero-order reaction in terms of reactant.

= k d[P] = k dt

at t = 0, [P] = 0

and at t = t, [P] = [P]

then integration yields

[P] = kt

This is integrated rate law equation for a zero-order reaction in terms of product.

i.e. [A]_{0} â€“ [A] = kt = [P]

**Graph representation of zero-order reaction**

[A]_{0} â€“ [A] = kt

[A] = â€“kt + [A]_{0}

y = mx + c

**Graph of reactant vs time.**

[P] = kt

y = mx

**Graph of concentration of product vs time.**

[A]_{0} â€“ [A] = 2kt â€¦(i)

When t = 0 then [P] = 0 and t = t then [P] = [P]

[P] = 3kt â€¦(ii)

â€¦(iii)

**Problem. Find the integrated rate law expression for an elementary zero order reaction given below.**

**Sol.**

The rate law of above elementary reaction is given below

â‡’

â‡’ â€“ [[A] â€“ [A]_{0}] = kt

[A]_{0} â€“ [A] = kt â€¦(i)

â‡’

â€¦(ii)

â‡’

[P] = kt â€¦(iii)

From equation (i), (ii) & (iii) we get

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