What volume of a solution is needed to dissolve 1.0 mol of KOH to make a solution whose pH is 13.55?
A. 2.82 L
B. 12.43 L
C. 4.77 L
D. 3.35 L

Option A. 2.82 L

Explanation:

Step 1:

Data obtained from the question.

pH = 13.55

Step 2:

Determination of the pOH of the solution.. This is illustrated below:

pH + pOH = 14

pH = 13.55

13.55 + pOH = 14

Collect like terms

pOH = 14 - 13.55

pOH = 0.45

Step 3:

Determination of the concentration of the OH ion.

This is illustrated below:

pOH = - Log [OH-]

pOH = 0.45

0.45 = - Log [OH-]

- 0.45 = Log [OH-]

[OH-] = antilog (- 0.45)

[OH-] = 0.355 M

Step 4:

Determination of the molarity of KOH. This is illustrated below:

First, we'll write the dissociation equation of KOH as follow:

KOH —> K+(aq) + OH-(aq)

From the balanced equation above,

1 mole of KOH produced 1 mole of OH-.

Therefore, 0.355 M of KOH will definitely produce 0.355 M of OH-.

The molarity of KOH is 0.355 M

Step 5:

Determination of the volume of the solution needed to dissolve 1 mole of KOH. This is illustrated below:

Mole of KOH = 1 mole

Molarity of KOH = 0.355 M

Volume =?

Molarity = mole /Volume

Volume = mole /Molarity

Volume = 1/0.355 M

Volume = 2.82L