Question

What is the pH of a 2500. ml solution that contains 10.4 g of calcium hydroxide. Show all work and round answers to significant figures.

Answer 1

The pH of the solution is 12.75

EXPLANATION;

Given that;

The volume of the solution is 2500mL

The mass of calcium hydroxide is 10.4g

Follow the steps below to find pH of the solution

Step 1; Convert the volume to L

Recall, that 1mL is equivalent to 0.001L

Let the volume of the solution be x

`\begin{gathered} \text{ 1mL }\rightarrow\text{ 0.001L} \\ \text{ 2500mL }\rightarrow\text{ xL} \\ \text{ cross multiply} \\ \text{ 1mL }*\text{ xL }=0.001L\text{ }*\text{ 2500mL} \\ \text{ isolate x} \\ \text{ x = }\frac{0.001L*2500\cancel{mL}}{1\cancel{mL}} \\ \text{ x = 0.001 }*\text{ 2500} \\ \text{ x = 2.5L} \end{gathered}`

Step 2; Find the mole of calcium hydroxide using the formula below

`\text{ mole }=\text{ }\frac{\text{ mass}}{\text{ molar mass}}`

Recall, that the molar mass of calcium hydroxide is 74.093 g/mol

`\begin{gathered} \text{ mole }=\text{ }\frac{\text{ mass}}{\text{ molar mass}} \\ \\ \text{ mole }=\text{ }\frac{\text{ 10.4}}{\text{ 74.093}} \\ \text{ mole = 0.140 mol} \end{gathered}`

Step 3; Find the molarity of calcium hydroxide

`\begin{gathered} \text{ molarity = }\frac{\text{ mole }}{\text{ volume}} \\ \\ \text{ molarity = }(0.140)/(2.5) \\ \text{ molarity = 0.056M} \end{gathered}`

Since calcium hydroxide is a base, then calculate the pOH of calcium hydroxide

`\text{ pOH = - log \lbrack OH}^-\text{ \rbrack}`

`\begin{gathered} \text{ \lbrack OH}^-\text{ \rbrack = 0.056M} \\ \text{ pOH = -log 0.056} \\ \text{ pOH = 1.25} \end{gathered}`

Step 5; Find the pH of the solution

Recall, that pOH + pH = 14

`\begin{gathered} \text{ pOH }+\text{ pH }=\text{ 14} \\ \text{ 1.25 }+\text{ pH }=\text{ 14} \\ \text{ subtract 1.25 from both sides of the equation} \\ \text{ 1.25 - 1.25 + pH = 14 - 1.25} \\ \text{ pH = 12.75} \end{gathered}`

Therefore, the pH of the solution is 12.75