...............
#H_2N-NH_2(aq) + H_2O(l)rightleftharpoonsH_3N^(+)-NH_2 +HO^-#
#K_"eq"=([N_2H_5^+][HO^-])/([N_2H_4])=1.0xx10^-6#, and if #x*mol# of hydrazine associate, we can put in the numbers........
#K_"eq"=1.0xx10^-6=((x)xx(x))/(0.15-x)=x^2/(0.15-x)#
This is a quadratic in #x# that we could solve exactly. However, because #K_"eq"# is so small, we are justified in making the approx. #0.15">>"x#, and we write.........
#1.0xx10^-6~=x^2/0.15#
#x_1=sqrt(1.0xx10^-6xx0.15)=3.87xx10^-4#, this is indeed small compared to #0.15*mol*L^-1#, but now we have an approximation for #x# we can plug this value back into the equation to get #x^2#...
#x_2=3.87xx10^-4*mol*L^-1#, and given the convergence of #x_1# and #x_2# we are satisfied that these values are as good as if we used the quadratic equation............
But we are not finished there.....we know that ..............
#[N_2H_5^+]=[HO^-]=3.87xx10^-4*mol*L^-1#...
We DO NOT KNOW #pH#.
But in aqueous solution, #14=pH+pOH#
#pOH=-log_10[HO^-]=-log_10(3.87xx10^-4)=3.41#
#pH=14-3.41=10.6#
