Caustic soda will add hydroxide ions to the water and thus increase its pH. Remember that pH + pOH = 14 and pH = `-log_10[H^+]` . We can use these two equations to solve the numerical.

Since, we are adding hydroxide ions, it is much easier to solve for hydroxide ions.

If we write a mass balance in terms of hydroxide ions, it will be something like:

M1V1 + M2V2 = M3 (V1 + V2)

where, M1, M2 and M3 are concentrations of hydroxide ions in caustic soda, water sample initially and finally, respectively. V1 and V2 are volumes of caustic soda and water.

Here, V1 is unknown, V2 = 2 l.

M1 = `10^-2` M (since pH = 12, pOH = 2), M2 = `10^-7` M and M3 = `10^-6.4` M` `

Substituting all the values and solving, we get

V1 = 59.6 `mul` .

We can similarly solve for the second case, when pH of caustic soda is 13.5 (or pOH = 0.5). Solving similarly, we get, V1 = 1.88 `mul` .

We can see that very small quantities of caustic soda are required since the concentrations are so high.

Hope this helps.

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