Calculate the weight of solid NaOH required to prepare (a) 5 liters of a 2 M solution, (b) 2 liters of a solution of pH 11.5? i need full solution not just result please

A. 400g of NaOH.

B. 0.253g of NaOH.

Explanation:

A. The following data were obtained from the question:

Volume = 5 L

Molarity = 2 M

Mass =..?

Next, we shall determine the number of mole of NaOH. This can be obtain as follow:

Molarity = mole /Volume

2 = mole/5

Cross multiply

Mole = 2 x 5

Mole of NaOH = 10 moles

Finally, we shall convert 10 moles of NaOH to grams. This is illustrated below:

Mole of NaOH = 10 moles

Molar mass of NaOH = 23 + 16 + 1 = 40g/mol

Mass of NaOH =?

Mole = mass /molar mass

10 = mass of NaOH /40

Cross multiply

Mass of NaOH = 10 x 40

Mass of NaOH = 400g

Therefore, 400g of NaOH is needed to prepare the solution.

B. The following data were obtained from the question:

pH = 11.5

Volume = 2 L

Next, we shall determine the pOH of the solution. This can be obtain as shown below:

pH + pOH = 14

pH = 11.5

11.5 + pOH = 14

Collect like terms

pOH = 14 – 11.5

pOH = 2.5

Next, we shall determine the concentration of the hydroxide ion, [OH-] in the solution.

This is illustrated below:

pOH = - Log [OH-]

pOH = 2.5

2.5 = - Log [OH-]

-2.5 = Log [OH-]

Take the antilog of both side

[OH-] = antilog (-2.5)

[OH-] = 3.16×10¯³ M

Next, we shall determine the concentration of NaOH. This is illustrated below:

NaOH —> Na+ + OH-

From the balanced equation above,

1 mole of NaOH produced 1 mole of OH-.

Therefore, 3.16×10¯³ M NaOH will also produce 3.16×10¯³ M OH-.

Therefore, the concentration of NaOH is 3.16×10¯³ M

Next, we shall determine the number of mole of NaOH in the solution. This can be obtain as follow:

Molarity = 3.16×10¯³ M

Volume = 2 L

Mole of NaOH =?

Molarity = mole /Volume

3.16×10¯³ = mole of NaOH / 2

Cross multiply

Mole of NaOH = 3.16×10¯³ x 2

Mole of NaOH = 6.32×10¯³ mole

Finally, we shall convert 6.32×10¯³ mole of NaOH to grams

Mole of NaOH = 6.32×10¯³ mole

Molar mass of NaOH = 23 + 16 + 1 = 40g/mol

Mass of NaOH =?

Mole = mass /molar mass

6.32×10¯³ = mass of NaOH /40

Cross multiply

Mass of NaOH = 6.32×10¯³ x 40

Mass of NaOH =0.253 g

Therefore, 0.253g of NaOH is needed to prepare the solution.

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