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Chapter 4: Problem 117

(a) Describe a preparation for magnesium hydroxide \(\left[\mathrm{Mg}(\mathrm{OH})_{2}\right]\) and predict its solubility. (b) Milk of magnesia contains mostly \(\mathrm{Mg}(\mathrm{OH})_{2}\) and is effective in treating acid (mostly hydrochloric acid) indigestion. Calculate the volume of a \(0.035 \mathrm{M} \mathrm{HCl}\) solution (a typical acid concentration in an upset stomach) needed to react with two spoonfuls (approximately \(10 \mathrm{~mL}\) ) of milk of magnesia [at \(0.080 \mathrm{~g}\) \(\left.\mathrm{Mg}(\mathrm{OH})_{2} / \mathrm{mL}\right]\).

Short Answer

Expert verified
Magnesium hydroxide can be prepared by the reaction of magnesium chloride with sodium hydroxide and it is sparingly soluble in water but dissolves in acidic solution. About 784 mL of 0.035M HCl solution is needed to react with two spoonfuls of milk of magnesia.

Step by step solution

01

Preparation and Solubility of magnesium hydroxide [Mg(OH)2]

Magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_{2}\), can be prepared by the reaction of magnesium chloride with sodium hydroxide. The equation for the reaction is given as follows: \(\mathrm{MgCl_2} + 2\mathrm{NaOH} \rightarrow \mathrm{Mg(OH)_2} + 2\mathrm{NaCl}\) Regarding the solubility, magnesium hydroxide is sparingly soluble in water, but it does dissolve in acidic solution due to the reaction with the acid.
02

Calculation of the mass of magnesium hydroxide

The concentration of magnesium hydroxide in the milk of magnesia is given as \(0.080 \mathrm{~g}\) \(\mathrm{Mg}(\mathrm{OH})_{2} / \mathrm{mL}\). Using this information, the mass of magnesium hydroxide in two spoonfuls can be calculated. Since one spoonful is approximately \(5 \mathrm{~mL}\), two spoonfuls result in \(10 \mathrm{~mL}\). Therefore, by multiplying the volume in mL by the concentration in g/mL, the mass of magnesium hydroxide can be calculated: \(10 \mathrm{ mL} \cdot 0.080 \mathrm{g/mL} = 0.800 \mathrm{g}\).
03

Calculation of the number of moles of magnesium hydroxide

The number of moles of magnesium hydroxide can be calculated by dividing the mass in grams by the molar mass. The molar mass of magnesium hydroxide is given by \(\mathrm{M}(\mathrm{Mg(OH)_2})=58.319 \mathrm{~g/mol}\). Therefore, the number of moles can be calculated by \(\frac{0.800 \mathrm{g}}{58.319 \mathrm{g/mol}} \approx 0.0137 \mathrm{mol}\).
04

Calculation of the volume of the hydrochloric acid solution

We can use the balanced chemical equation for the reaction of magnesium hydroxide with hydrochloric acid to find the ratio in which they react, i.e., \(\mathrm{Mg(OH)_2 + 2 HCl} \rightarrow 2H_2O + \mathrm{MgCl_2}\). Therefore, we see that one mole of Mg(OH)2 reacts with two moles of HCl. We have already calculated the moles of Mg(OH)2, so we can say that the moles of HCl will be double of this. Hence, moles of HCl= \(0.0137 \times 2 =0.0274 \mathrm{mol}\). We also know that Molarity= Moles/Volume (in liters), therefore Volume= Moles/Molarity. Hence, Volume= \(0.0274 mol / 0.035 M=0.784 L\), or approximately \(784 mL\).

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Most popular questions from this chapter

How many moles of \(\mathrm{MgCl}_{2}\) are present in \(60.0 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{MgCl}_{2}\) solution?

Explain how you would prepare potassium iodide (KI) by means of (a) an acid- base reaction and (b) a reaction between an acid and a carbonate compound.

Determine how many grams of each of the following solutes would be needed to make \(2.50 \times 10^{2} \mathrm{~mL}\) of a \(0.100 M\) solution: (a) cesium iodide (CsI), (b) sulfuric acid \(\left(\mathrm{H}_{2} \mathrm{SO}_{4}\right),\) (c) sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right),\) (d) potassium dichromate \(\left(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\right)\) (e) potassium permanganate \(\left(\mathrm{KMnO}_{4}\right)\).

The molar mass of a certain metal carbonate, \(\mathrm{MCO}_{3}\), can be determined by adding an excess of \(\mathrm{HCl}\) acid to react with all the carbonate and then "back titrating" the remaining acid with a \(\mathrm{NaOH}\) solution. (a) Write an equation for these reactions. (b) In a certain experiment, \(20.00 \mathrm{~mL}\) of \(0.0800 \mathrm{M} \mathrm{HCl}\) were added to a 0.1022 -g sample of \(\mathrm{MCO}_{3}\). The excess HCl required \(5.64 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{NaOH}\) for neutralization. Calculate the molar mass of the carbonate and identify \(\mathrm{M}\).

A quantitative definition of solubility is the maximum number of grams of a solute that will dissolve in a given volume of water at a particular temperature. Describe an experiment that would enable you to determine the solubility of a soluble compound.
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