`=>` Average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated.
`=>` So, to express the rate at a particular moment of time we determine the instantaneous rate.
`=>` It is obtained when we consider the average rate at the smallest time interval say `dt` (i.e. when `Δt` approaches zero).
`=>` Hence, mathematically for an infinitesimally small `dt` instantaneous rate is given by
`r_(av) = (- Delta [R])/(Delta t) = (Delta [P])/(Delta t)` ........(3).
As `Deltat → 0` or `r_text(inst) = (- d [R])/(dt) = ( d [P])/(dt)`
`=>` Now consider a reaction
`Hg (l) + Cl_2 (g) → Hg Cl_2 (s)` .
● Where stoichiometric coefficients of the reactants and products are same, then rate of the reaction is given as
● Rate of reaction `= (- Delta [Hg])/(Delta t) = ( - Delta [Cl_2])/(Delta t) = (Delta [HgCl_2])/(Delta t)`
i.e., rate of disappearance of any of the reactants is same as the rate of appearance of the products.
`=>` But in the following reaction, two moles of `HI` decompose to produce one mole each of `H_2` and `I_2`,
`2HI (g) → H_2 (g) +I_2(g)`
● For expressing the rate of such a reaction where stoichiometric coefficients of reactants or products are not equal to one, rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. Since rate of consumption of `HI` is twice the rate of formation of `H_2` or `I_2`, to make them equal, the term `Δ[HI]` is divided by 2.
● The rate of this reaction is given by
Rate of reaction ` = -1/2 (Delta [HI])/(Deltat) = ( Delta [H_2])/(Delta t) = (Delta [I_2])/(Deltat)`
`=>` Similarly, for the reaction
`5 Br^(-) (aq) +BrO_3^(-) (aq) + 6 H^+ (aq) → 3 Br_2 (aq) +3H_2O (l)`
● Rate ` = -1/5 ( Delta [Br^-])/(Delta t) = - (Delta [BrO_3^-])/(Deltat t) = - 1/6 (Delta [H^+])/(Deltat) = 1/3 (Delta [Br_2])/(Deltat) = 1/3 (Delta [H_2O])/(Deltat)`
`color { maroon} ® color{maroon} ul (" REMEMBER")`
Symbol △ is used for larger change,i.e., for average rate whereas symbol "d" is used for small change,i.e., for instantaneous rate.
`=>` For a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence, rate can also be expressed as rate of change in partial pressure of the reactant or the product.
`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
The instantaneous rate of reaction,i.e., the rate of reaction at any instant of time is the rate of change of concentration of any one of the reactants or products at that particular instant of time.
`=>` Average rate cannot be used to predict the rate of a reaction at a particular instant as it would be constant for the time interval for which it is calculated.
`=>` So, to express the rate at a particular moment of time we determine the instantaneous rate.
`=>` It is obtained when we consider the average rate at the smallest time interval say `dt` (i.e. when `Δt` approaches zero).
`=>` Hence, mathematically for an infinitesimally small `dt` instantaneous rate is given by
`r_(av) = (- Delta [R])/(Delta t) = (Delta [P])/(Delta t)` ........(3).
As `Deltat → 0` or `r_text(inst) = (- d [R])/(dt) = ( d [P])/(dt)`
`=>` Now consider a reaction
`Hg (l) + Cl_2 (g) → Hg Cl_2 (s)` .
● Where stoichiometric coefficients of the reactants and products are same, then rate of the reaction is given as
● Rate of reaction `= (- Delta [Hg])/(Delta t) = ( - Delta [Cl_2])/(Delta t) = (Delta [HgCl_2])/(Delta t)`
i.e., rate of disappearance of any of the reactants is same as the rate of appearance of the products.
`=>` But in the following reaction, two moles of `HI` decompose to produce one mole each of `H_2` and `I_2`,
`2HI (g) → H_2 (g) +I_2(g)`
● For expressing the rate of such a reaction where stoichiometric coefficients of reactants or products are not equal to one, rate of disappearance of any of the reactants or the rate of appearance of products is divided by their respective stoichiometric coefficients. Since rate of consumption of `HI` is twice the rate of formation of `H_2` or `I_2`, to make them equal, the term `Δ[HI]` is divided by 2.
● The rate of this reaction is given by
Rate of reaction ` = -1/2 (Delta [HI])/(Deltat) = ( Delta [H_2])/(Delta t) = (Delta [I_2])/(Deltat)`
`=>` Similarly, for the reaction
`5 Br^(-) (aq) +BrO_3^(-) (aq) + 6 H^+ (aq) → 3 Br_2 (aq) +3H_2O (l)`
● Rate ` = -1/5 ( Delta [Br^-])/(Delta t) = - (Delta [BrO_3^-])/(Deltat t) = - 1/6 (Delta [H^+])/(Deltat) = 1/3 (Delta [Br_2])/(Deltat) = 1/3 (Delta [H_2O])/(Deltat)`
`color { maroon} ® color{maroon} ul (" REMEMBER")`
Symbol △ is used for larger change,i.e., for average rate whereas symbol "d" is used for small change,i.e., for instantaneous rate.
`=>` For a gaseous reaction at constant temperature, concentration is directly proportional to the partial pressure of a species and hence, rate can also be expressed as rate of change in partial pressure of the reactant or the product.
`color{purple}(✓✓)color{purple} " DEFINITION ALERT"`
The instantaneous rate of reaction,i.e., the rate of reaction at any instant of time is the rate of change of concentration of any one of the reactants or products at that particular instant of time.