In water, we invoke the following equilibrium...
2H_2O(l) rightleftharpoonsH_3O^+ + HO^-
And we can write an equilibrium expression, to quantify this dissociation.......
underbrace(K_w=[HO^-][H_3O^+]=10^-14)_"specified under standard conditions of 298 K and near 1 atm"
And we take log_10 OF BOTH SIDES....
log_10K_w=log_10[HO^-]+log_10[H_3O^+]=log_(10)10^-14
But log_(10)10^-14=-14
And so +14=underbrace(-log_10[H_3O^+])_"pH by definition"underbrace(-log_10[HO^-])_"pOH by definition"
And thus our working relationship...14=pH+pOH
And thus if we gots 0.5*mol*L^-1 HCl(aq), we gots [H_3O^+]=0.50*mol*L^-1...pH=-log_10(0.50)=-(-0.301)=+0.301..
And so pOH=14-0.301=13.7...
Conc. HCl(aq) is 10.6*mol*L^-1 out of the bottle. What is pH here?