Chemistry FIRST ORDER REACTIONS

Concentration Terms Replaced by Other Terms in `1^(st)` Order Kinetics :

In order to follow the progress of reaction, the concentration of any of the reactants or products which ever is convenient may be determined at various time intervals using some suitable chemical method. At each time interval the progress of the reaction is arrested by immersing the reaction vessel in freezing mixture. The temperature of the freezing mixture being very low (less than `0 ^(o)C`), the rate of reaction is reduced to almost nothing. It is not necessary to determine always the concentration but one can determine any other parameter that changes during the reaction with time and which directly proportional to the concentration of the reactant or product. These facts are illustrated below by some examples.

As we have to generally deal with only first order reactions, we examine some of these reactions from the point of calculating the rate constant based on different experimental data. Now we present several problems in which we shall learn how to calculate the rate constant of reactions based on the variety of data given.

Concentration Terms replaced by Titer Reading :

`tt((H_2O_2 -> , H_2O , + 1/2O_2, ),(a,0,0,t=0),(a-x,x,x,t=t))`

Since `H_2O_ 2` acts as a reducing agent towards `KMnO_4`, so concentrations of `H_2O_2` at various time intervals may be determined by the titration of the reaction mixture against standard `KMnO_4` solution. The titre value will go on decreasing with time.

If `V_0` and `V_t` be the titre values at zero time and any time `t` then `V_0 prop a` and `V_t prop a - x` The above reaction being first- order, its rate constant may be expressed as

`k=2.303/t log (V_0/V_t)`

Concentration Terms replaced by Optical Rotation Terms :

Now we shall see how to find the rate constant of a reaction using a very different set of data. There are some organic compounds which have a property of rotating a plane polarized light in a particular direction by a particular value. The compounds are called optically active compounds. One reaction in which an optically active substance converts to some other optically active substance is,

`text(Sucrose) overset(H^(+)) -> text(Glucose + Fructose)`

Sucrose, Glucose and Fructose are all optically active and while the first two compounds are dextro rotatory (rotating the plane polarized light in the right hand direction and the last is laevo rotatory (rotating the plane polarized light in the left hand direction). All the three compounds rotate the plane polarized light by different angles and their rotation is directly proportional to concentration.

Let's consider a example. `S->G+F` and the data is

`text( Time ) quad quad 0 quad quad t`
`text(Rotation of sucrose)quad r_0 quad t`

Let the rotation of Sucrose be `r_1 ^o` per mole and the initial moles of Sucrose be `a`.

`r_0=a r_1^0`

Let the moles of Sucrose that is converted to Glucose and Fructose be `x`.

`r_t=(a-x) t_1^0 `

`a/(a-x) =r_0/r_t`

`k=1/t ln (a/(a-x)) =1/t ln (r_0/r_t)`

Concentration Terms replaced by Pressure Change :

We are given a first order reaction `A->B+C` where we assume that `A`, `B` and `C` are gases. The data given to us is

`text( Time ) quad quad quad 0 quad quad quad t`
`text(Partial pressure of A) quad P_1 quad quad P_2`

And we have to find the rate constant of the reaction.

Since `A` is a gas and assuming it to be ideal, we can state that `P_A = [A] RT`

[From `PV = nRT`]. At `t = 0`, `P_1 = [A]_0 RT` and at `t= t`, `P_2 = [A]_tRT`. Thus the ratio of the concentration of `A` at two different time intervals is equal to the ratio of its partial pressure at those same time intervals.

`([A]_0)/([A]_t) =P_1/P_2` `K=1/t ln (P_1/P_2)`