The concentration of hydrogen ion is a measure of acidity or alkalinity of a solution. A convenient way of expressing the hydrogen ion concentration of a solution is, in terms of the pH scale devised by Sorenson's . The pH of a solution is defined as the negative logarithm of active concentration of `H^(+)` ions to the base 10 i.e.,
`pH =- log_(10)[HI^(+)]` or `[H^(+)]=10^(-pH)`
At `25^(@)C`
`(i)` if `pH lt1` , then solution is acidic
(ii) if `pH=7`, then solution is neutral
(iii) if `pH gt 7`, then the solution is basic
Total `[H^(+)]` and `[OH^(-)]` in a mixture of strong acids or bases are represented in terms normality, which is equal to final number of milliequivalents of `H^(+)` or `OH^(-)` present in millilitre of solution Since `H_(2)O` ionizes as
`H_(2)O hArr H^(+)+OH^(-)`
Ionic product of water , `K_(w)=[H^(+)][OH^(-)] ...(i)`
Taking log on both sides in equation (i), we find `pH +pOH=pK_(w)`
For neutral solution, `pH =pOH:. 2pH =pK_(w)`
`:. pH =1.2pK_(w)`
Since dissociation of water is an endothermic process, so temperature will have great effect on `K_(w)` as well as on the pH of solution i.e., the nature of the soluiton . `K_(w)` at different temperature are related as under.
ln `(K_(w2))/(K_(w1))=(DeltaH)/(R)[(1)/(T_(1))-(1)/(T_(2))]`
At `T_(1)K=T_(2)K, K_(w_(2))=K_(w1)`
`(i)` pH mixture of monoprotic weak acid is calculated as under `:` pH of monoprotic weak acid `i.e., CH_(3)COOH`
`{:(,CH_(3)COOH,hArr,CH_(3)COO^(-),+,H^(+)),("at " t=0,C,,0,,0),("at "t=t,C-alpha,,C alpha,,Calpha):}`
`:. K_(a)=(C alpha xx C alpha)/(C-Calpha)=(alpha^(2)C)/(1-alpha)`
When `a le0.1 , 100 alpha =1-alpha=1`
`:. K_(a)=(alpha^(2)C)/(1)` [When `(1-alpha)=1]`
`alpha=sqrt((K_(a))/(C)):. [H^(+)]=alphaC=sqrt(K_(a)xxC)`
(ii) pH of a mixture of monoprotic weak acids is calculated as follows
`[H^(+)]=sqrt(K_(a1)C_(1)+K_(a2)C_(2))`.
where `K_(a1)` and `K_(a2)` are dissociation constants of monoprotic weak acids HA and HB acid `C_(1)` and `C_(2)` are their concentrations respectively.
(ii) pH of polyprotic weak acid, say `H_(3)A-a` triprotic weak acid having dissociation constants `K_(a1).K_(a2)` and `K_(a3)` where `K_(a1) gt gt K_(a2) gt gt K_(a3)`. Then in that case , maximum `[H^(+)]` will be contributed from step I, and neglibily small from concentration of species producing from step III will be negligible with respect to steop II and similarly concentration of species producig from step II will be negligible with respect to step I. Based upon the above discussion, answer the following questions.
What is the sulphide ion concentration of a dilute solution that has been saturated with 0.1 M of `H_(2)S`, If pH of the solution is 3 ?
`(K_(a1)= 1.0 xx 10^(-7) , K_(a2) =1.3 xx 10^(-13))`

Options

A. `1.25 xx 10^(-17)`
B. `1.3 xx 10^(-13)`
C. `1.45 xx 10^(19)`
D. `1.30 xx 10^(-15)`

Answer

A