# 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 A0 → 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) x0 and x
\tt k=\frac{1}{t}\ ln\ \frac{x_0}{x_0-x}
(ii) x0 and xt
\tt k=\frac{1}{t}\ ln\ \frac{x_0\left(n-1\right)}{nx_0-x_t}
(iii) x and xt
\tt k=\frac{1}{t}\ ln\ \frac{\left(n-1\right)x_\infty}{n\left(x_\infty-x_t\right)}
(iv) x0, xt 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.
x0 = measured property at t = 0
xt = measured property at t = t
x = measured property at t = ∞

### Part2: View the Topic in this Video from 33:00 to 39:06

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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