## Chemical Kinetics

# Rate of a chemical reaction

**Rate of reaction:**

The change in concentration of a reactant or a product in unit time is called rate of reaction. Its unit is mole L^{−1} sec^{−1} (or) mol dm^{−3} sec^{−1} for solutions and kPa sec^{−1} or Nm^{−2} sec^{−1} for gases.

For example aA → bB

(i) Average rate of reaction = \tt \frac{-1}{a}\frac{\Delta \left[A\right]}{\Delta t}=\frac{1}{b}\frac{\Delta \left[B\right]}{\Delta t}

(ii) \tt -\frac{\Delta \left[A\right]}{\Delta t}\ and\ +\frac{\Delta \left[B\right]}{\Delta t} are average rate of consumption of A and average rate of production of B respectively.

(iii) −Δ[A] is decrease in concentration of A and +Δ[B] is increase in concentration of B in time taken Δt.

Instantaneous rate of reaction is the change in concentration of a reactant or a product at a given time.

It can be identified graphically only

For example w.r.t "A"

Instantaneous rate of reaction

\tt \lim_{\Delta t \rightarrow 0}\frac{\Delta \left[A\right]}{\Delta t}=-\frac{dx}{dt}

dx is very small change of concentration in very small change of time dt.

The kinetics of reaction can be followed (i.e., order, rate constant etc, can be established) by measuring a property which changes with time.

eg: (i) Total pressure in a gaseous reaction.

(ii) Volume of a reagent (Acidic Basic, oxidising or reducing agent)

(iii) Volume of a gaseous mixture (V)

(iv) Optical rotation (r)

For a reaction A_{0} → nB

t = 0 | c | 0 |

t = t | c − x | nx |

t = ∞ | 0 | nc |

For any measurable property X proportional to the concentration of reaction mixture at various times, in terms of

(i) x_{0} and x

\tt k=\frac{1}{t}\ ln\ \frac{x_0}{x_0-x}

(ii) x_{0} and x_{t}

\tt k=\frac{1}{t}\ ln\ \frac{x_0\left(n-1\right)}{nx_0-x_t}

(iii) x_{∞} and x_{t}

\tt k=\frac{1}{t}\ ln\ \frac{\left(n-1\right)x_\infty}{n\left(x_\infty-x_t\right)}

(iv) x_{0}, x_{t} and x_{∞}

\tt k=\frac{1}{t}\ ln\ \left(\frac{x_\infty-x_0}{X_\infty-x_t}\right)

x = amount of reacted in time t.

x_{0} = measured property at t = 0

x_{t} = measured property at t = t

x_{∞} = measured property at t = ∞

### Part1: View the Topic in this Video from 1:10 to 50:09

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1. For the reaction aA + bB → cC + dD

Rate of disappearance of a reactant is negative

\tt -\frac{d\left[A\right]}{dt} = Rate of disappearance of A

\tt -\frac{d\left[B\right]}{dt}= Rate of disappearance of B

Rate of formation of a product is positive

\tt \frac{d\left[C\right]}{dt}= Rate of formation of C

\tt \frac{d\left[D\right]}{dt}= Rate of formation of D

2. In terms of stoichiometric coefficient rate may be expressed as

\tt \frac{dx}{dt}=-\frac{1}{a}\frac{d\left[A\right]}{dt}=-\frac{1}{b}\frac{d\left[B\right]}{dt}=\frac{1}{c}\frac{d\left[C\right]}{dt}=\frac{1}{d}\frac{d\left[D\right]}{dt}

3. Rate in atm time^{-1} = Rate in mole L^{-1} time^{-1} × RT