Determine the degree of ionization and `pH` of `0.05M` of ammonia solution. The ionization constant of ammonia can be taken from Table `7.7`. Also, calculate the ionization constant of the conjugate acid of ammonia.

Explanation

The ionization of `NH_(3)` in water is represented by equation.
`NH_(3)+H_(2)O hArr NH_(4)^(+)+OH^(-)`
We use equation (7.33) to calculate hydroxyl ion concentration,
`pOH^(-)C alpha=0.05 alpha`
`K_(b)=0.5 alpha^(2)//(1-alpha)`
The value of `alpha` is small, therefore, the quadratic eqution can be simplified by neglecing `alpha` in comparison to 1 in the denominator on right hand side of the equation,
Thus,
`K_(b)=C alpha^(2) or alpha= sqrt((1.77x10^(-5)//0.05))`
`=0.018`
`[OH^(-)]=C alpha=0.05xx0.018=9.4xx10^(-4)M`
`[H^(+)]=K_(w)//[OH^(-)]=10^(-14)//(9.4xx10^(-4))`
`=1.06xx10^(-11)`
`pH=-log(1.06xx10^(-11))=10.97`
Now using the relation for conjugate acid base pair,
`K_(a)xx K_(b) = K_(w)`
using the value of `K_(b) of NH_(3)` from Tabel 7.7. We can determine te concentration of conjugate acid `NH_(4)^(+)`
`K_(a)xxK_(w)//K_(b)=10^(-14)//1.77xx10^(-5)`
`=5.64xx10^(-10)`