Question

Milk of magnesia is often taken to reduce the discomfort associated with acid stomach or heartburn. The recommended dose is 1 teaspoon, which contains 4.00×10²mg of Mg(OH)². What volume of an HCl solution with a pH of 1.4 can be neutralized by one dose of milk of magnesia?

Answer 1

Answer:

8.61 mL of the HCl solution

Explanation:

The reaction that takes place is:

• 2HCl + Mg(OH)₂ → MgCl₂ + 2H₂O

From the given mass of Mg(OH)₂, we can calculate the moles of HCl that are neutralized:

• 4x10² mg = 400 mg = 0.400g

• 0.400g Mg(OH)₂ ÷ 58.32g/1mol = 6.859*10⁻³ mol Mg(OH)₂

• 6.859*10⁻³ mol Mg(OH)₂ * $\frac{1molHCl}{1molMg(OH)_{2}} =$ 3.429x10⁻³ mol HCl

Finally, to calculate the volume of an HCl solution, we need both the moles and the concentration. We can calculate the concentration using the pH value:

• pH = -log[H⁺]

• 1.4 =  -log[H⁺]

• $10^{-1.4}$ = [H⁺]

• 0.0398 M = [H⁺] = [HCl]  *Because HCl is a strong acid*

Thus, the volume is:

• 0.0398 M = 3.429x10⁻³mol HCl / Volume

• Volume = 8.616x10⁻³ L = 8.62 mL

Answer 2

Explanation:

The reaction equation will be as follows.

           $Mg(OH)_{2} + 2HCl \rightarrow MgCl_{2} + 2H_{2}O$

It is given that mass of magnesium hydroxide is 400 mg or 0.4 g (as 1 g = 1000 g). Molar mass of $Mg(OH)_{2}$ is 58.31 g/mol.

Therefore, calculate the number of moles of $Mg(OH)_{2}$ as follows.

             No. of moles = $\frac{mass}{\text{molar mass}}$

                                   = $\frac{0.4 g}{58.31 g/mol}$

                                   = $6.85 \times 10^{-3}$ mol

                                   = 0.00685 mol

Now, moles of HCl = 2 × moles of $Mg(OH)_{2}$

                               = 2 × 0.00685 mol

                               = 0.0137 mol

Concentration of HCl = $10^{-pH}$ = $10^{-1.4}$ = 0.0398 M

Now, we will calculate the volume of HCl as follows.

       Volume of HCl = $\frac{moles}{\text{concentration of HCl}}$

                                 = $\frac{0.0137}{0.0398}$

                                 = 0.344 L

or,                             = 344 ml     (as 1 L = 1000 ml)

Thus, we can conclude that 344 ml of an HCl solution with a pH of 1.4 can be neutralized by one dose of milk of magnesia.