An aqueous solution contains `10%` ammonia by mass and has a density of `0.09g cm^(-3)`. Calculate hydroxyl and hydrogen ion concentration in this solution. `(K_(a)for NH_(4)^(+)=5.0xx10^(-10)M)`

Explanation

Given, `(wt.of NH_(3))/("wt.of solution")=(10)/(100)`
`.: 100g "solution contains "10 g NH_(3)`
`:. M_(NH_(3))=(10xx1000)//[17xx100//0.99)]=5.82`
`(.: V= "Mass"//"Density")`
Now `{:( NH_(3)+H_(2)Orarr, NH_(4)OH hArr NH_(4)^(+),+OH^(-)),("Before dissociation",1,0,0),("After dissociation",(1-alpha),alpha,alpha):}`
`:. [OH^(-)]=C.alpha=Csqrt((K_(b)//C))=sqrt((K_(b).C))`
`[.: C = 5.82 M and K_(b)=K_(w)//K_(a)=10^(-14)//(5xx10^(-10))=2xx10^(-5)]`
`:. [OH^(-)]=sqrt([2xx10^(-5)xx5.82])=1.07xx10^(-2)M`
`:. [H^(+)]=10^(-14)//1.07xx10^(-2)`
`=.09268xx10^(-12)M`
`:. pH= -log [H^(+)]= - log 0.9268xx10^(-12)`
`=12.0330`