Rate of a chemical reaction:
The rate of a chemical reaction is a measure of speed with which the reactants are converted into products. It may be defined as the change in any one of the reactants or products per unit time. For example,
A ———-> B
The rate of the reaction may be expressed in either of the following two ways:
1) The rate of disappearance or decrease in concentration of A (reactants).
Rate of reaction = Decrease in concentration of A / Time taken
2) The rate of increase in concentration of B (products).
Rate of reaction =Increase in concentration of B / Time taken
The decrease or increase in the concentration of reactants or products may also be expressed in terms of change in their concentration during the time interval, Δt, as
Rate of reaction (r) =Δ[A] /Δt
Or,
Rate of reaction (r) = Δ[B] / Δt
Where Δ[A] gives the decrease in concentration of A and Δ[B] represents increase in concentration of B. The square brackets [ ] around the substances are used to express the molar concentration (mol/litre). It may be noted that in the case of concentration of reactants minus sign is used. This implies that the concentration of reactants is decreasing with time. Therefore, Rate of reaction(r) = – Δ[A] /Δt = + Δ[B] /Δt
Reaction involving same stoichiometric coefficients of reactants and products:
Let us consider a gaseous reaction between NO2 and CO.
NO2 (g) + CO (g) ———–> NO (g) + CO2 (g)
In the above reaction, as the reactants and products appear in same stoichiometric proportions, therefore, the rate of reaction may be expressed in terms of rate of disappearance of NO2 or CO or alternatively, by the rate of appearance of NO or CO2. Thus, rate of reaction is given by-
Rate of reaction (r) = [rate of disappearance of NO2] = [rate of disappearance of CO]
= [rate of appearance of NO] = [rate of appearance of CO2].
Rate of reaction (r) = – Δ [NO2] / Δt = – Δ [CO]/Δt = + Δ [NO]/ Δt = +Δ [CO2]/Δt
Since, NO2 is a deep radish brown gas; the rate of this reaction can be followed more easily by measuring the change in the intensity of colour of gaseous mixture in a given interval of time.
Reaction involving different stoichiometric coefficients of reactants and products:
Consider the reaction between hydrogen and iodine to give HI.
H2 (g) + I2 (g) ———> 2HI (g)
In this case, one mole of H2 reacts with one mole of I2 to form 2 moles of HI. This means that the rates of disappearance of H2 and I2 are same but the rate of appearance of HI must be twice the rate of disappearance of H2 and I2. Thus,
2 Rate of disappearance of H2 = 2 Rate of disappearance of I2 = Rate of appearance of HI
To get unique value of the reaction rate (independent of the concentration terms chosen), we divide the rate of reaction defined with any of the reactants or products by the stoichiometric coefficient of that reactant or product involved in the reaction. Thus, for the above reaction,
Rate of reaction (r) = -Δ[H2] / Δt = – Δ [I2] /Δt = +1Δ [HI] / 2Δt
Similarly, for a general reaction,
aA+ bB ——–> cC + dD
Rate of reaction (r) = 1Δ [A] / a Δt = –1Δ [B]/ b Δt = +1Δ [C] /cΔt =+1 Δ [D / d Δt
Average Rate and Instantaneous Rate:
Average rate of a reaction is defined as the rate of change of concentration per unit time. It is calculated by dividing the total change in concentration of any one of the reactant or products by the total time taken to complete the reaction. Therefore,
Average Rate (ravg) = Total change in concentration / Time Intervals= ΔX / Δt
The concept of mechanical speed cannot be applied in measuring the rates of reactions as the rate depends upon the concentration of the reactants. As the reaction proceeds, the concentration of the reactants keeps on decreasing. Thus, the rate cannot be determined simply by dividing the total change in concentration by the time taken as in case of mechanical speed.
On the other hand, the rate of reaction may be expressed at a particular instant of time. Therefore, rate of reaction may be defined as the rate of change of concentration of any one of the reactants or products at a particular instant of time for a given temperature.
Such a reaction rate is also known as instantaneous rate. For this purpose the time interval At is made as small as possible so that rate of reaction remains almost constant during that time interval. Therefore, instantaneous rate may be expressed by dx/dt instant of Δx/Δt.
