Variation of  $pH,pOH$  or  $p{K}_w$  with temperature is shown for $H_{2}O$  .
 
Variation is shown by line
 

Following equilibrium in set up on mixing.  $P{O}_4^{3-}$  is a proton acceptor and  $H_{3}P{O}_4$  is a proton donor.  $P{O}_4^{3-}+H_{3}P{O}_4\stackrel{ }{\rightleftharpoons }H{P}_4^{2-}+H_{2}P{O}_4^{-}$   
Mixture formed is a buffer of 0.05 M  $HP{O}_4^{2-}$ and  $0.05M{H}_{2}P{O}_4^{-}$    $H_{2}P{O}_4^{-}\underset{ }{\rightleftharpoons }HP{O}_4^{2-}+H^{+}$Second ionization constant of  $H_{3}P{O}_4\left(K_{a_2}\right)$   is involved. Thus,  $pH=p{K}_{a_2}+\log \frac{\left[HP{O}_4^{2-}\right]}{\left[H_{2}P{O}_4^{-}\right]}=p{K}_{a_2}$