We know that is aqueous solution the following equilibrium operates......
#H_2O(l) rightleftharpoonsH^(+) + HO^-#
#H^+# and #HO^-# are the characteristic cation, and characteristic anion of the water solvent. Sometimes, we write #H^+# as #H_3O^+#, i.e. the #"hydronium ion"#. As far as anyone knows this is a cluster of 3-4 (or more) water molecules, with an extra PROTON, #H^+# to give #H_7O_3^+#, or #H_9O_4^+#, we use #H^+# and #H_3O^+# as convenient shorthands.
As with any equilibrium we can quantify it......
#K=([H^+][HO^-])/[[H_2O(l)]]#
Because #[H_2O]# is so large, it can be removed from the equation, and we get
#K_w=[H^+][HO^-]=[H_3O^+][HO^-]=10^(-14)# at #298*K#. Now back in the day before the advent of electronic calculators, scientists used log tables to the #"base e"# or #"base 10"# to simplify products and quotients of very large and very small numbers.
We DEFINE #pH=-log_10[H_3O^+]#, and #pOH=-log_10[HO^-]#, and thus if we take #log_10# of
#K_w=[H^+][HO^-]=[H_3O^+][HO^-]=10^(-14)#.....
..............we gets.................
#log_10K_w=log_10[H_3O^+]+log_10[HO^-]=log_10(10^-14)#
And on rearrangement,
#-14=log_10[H_3O^+]+log_10[HO^-]#, and multiplying thru by #-1#..
#14=underbrace(-log_10[H_3O^+])_(pH)underbrace(-log_10[HO^-])_(pOH)#
And finally our defining relationship......#pH+pOH=14#. Wheww!
And so we can at last address your question. I will do the first row in the table. I suggest that you have a go at the rest yourself.
#"Solution A"#, #[H^+]=3.7xx10^-8*mol*L^-1#; #pH=-log_10(3.7xx10^-8)=7.43#; #pOH=14-7.43=6.57#. And #[HO^-]=10^(-6.57)=2.70xx10^-7*mol*L^-1#.
Over to you for #B# and #C# and #D# hoss............
One final caveat: I stress that #H^+# is equivalent to #H_3O^+#; which expression you use is a matter of personal preference, but be consistent.
