Question

Suppose that the stomach contains \(0.200 \mathrm{~L}\) of \(0.05 M\) \(\mathrm{HCl}\). What mass of the antacid \(\mathrm{Mg}(\mathrm{OH})_{2}\) is required to completely neutralize all of the \(\mathrm{HCl}\) ?

Short answer

0.4617 grams of Mg(OH)2 is required to neutralize all of the HCl.

Step-by-step solution

Write down the neutralization reaction

The neutralization reaction between hydrochloric acid (HCl) and magnesium hydroxide (Mg(OH)2) can be written as follows: \[\text{2HCl}(aq) + \text{Mg}(\text{OH})_2(s) \rightarrow \text{MgCl}_2(aq) + \text{2H}_2\text{O}(l)\]This shows that 2 moles of HCl react with 1 mole of Mg(OH)2.

Calculate moles of HCl

Calculate the moles of HCl present in 0.200 L of a 0.05 M solution using the formula:\[\text{moles of HCl} = \text{molarity} \times \text{volume in liters}\]\[\text{moles of HCl} = 0.05\ M \times 0.200\ L = 0.010\ moles\]

Calculate moles of Mg(OH)2 needed

Using the stoichiometry of the chemical reaction, calculate the moles of Mg(OH)2 needed to neutralize the moles of HCl. Since it takes 1 mole of Mg(OH)2 to neutralize 2 moles of HCl, divide the moles of HCl by 2:\[\text{moles of Mg(OH)2} = \frac{\text{moles of HCl}}{2} = \frac{0.010\ moles}{2} = 0.005\ moles\]

Calculate mass of Mg(OH)2

Calculate the mass of Mg(OH)2 required using its molar mass (58.32 g/mol for Mg and 17.01 g/mol for each OH, totaling 58.32 + 2(17.01) = 92.34 g/mol):\[\text{mass of Mg(OH)2} = \text{moles of Mg(OH)2} \times \text{molar mass of Mg(OH)2}\]\[\text{mass of Mg(OH)2} = 0.005\ moles \times 92.34 \frac{g}{mol}= 0.4617\ g\]

Key concepts

Stoichiometry

Stoichiometry is a division of chemistry that deals with the ratios of reactants and products in chemical reactions. In essence, it is a balancing act, ensuring that atoms are conserved in the transformation from reactants to products. For example, in the neutralization reaction provided, the stoichiometry shows that 2 moles of hydrochloric acid react with 1 mole of magnesium hydroxide.

To understand stoichiometry, imagine it as a recipe. Just as a recipe outlines the exact amounts of each ingredient needed to bake a cake, stoichiometry provides the precise proportions of reactants required to complete a chemical reaction without any excess. This understanding is essential for tasks ranging from laboratory experiments to the manufacture of pharmaceuticals, where precise chemical composition is crucial.

Molar Mass Calculation

Molar mass is the weight of one mole of a substance, typically expressed in grams per mole (g/mol). In calculations, it plays a vital role, since it allows us to convert between the mass of a substance and the number of moles, facilitating the use of stoichiometry in practical problems.

When you're calculating molar mass, you are essentially adding up the atomic weights of each element in a compound as listed on the periodic table. For magnesium hydroxide, \(\mathrm{Mg}(\mathrm{OH})_2\), you would calculate the molar mass by adding the atomic weight of magnesium (Mg, 24.31 g/mol) to twice the atomic weight of oxygen (O, 16.00 g/mol) and hydrogen (H, 1.01 g/mol), the components of the hydroxide group. It's a simple yet fundamental part of solving chemistry problems accurately, as it ensures that the proportions of reactants used are based on their actual mass ratios.

Acid-Base Neutralization

Acid-base neutralization is a specific type of chemical reaction where an acid and a base react to form water and a salt. This reaction is important for many processes, from industrial manufacturing to biological systems like the neutralizing of stomach acid. The general formula is \(\text{HA} + \text{BOH} \rightarrow \text{BA} + \text{H}_2\text{O}\), where \(\text{HA}\) is the acid, and \(\text{BOH}\) is the base.

In the exercise, stomach acid, hydrochloric acid (HCl), reacts with the antacid, magnesium hydroxide (Mg(OH)2), to produce magnesium chloride (MgCl2) and water (H2O). Understanding neutralization reactions is beneficial not only in chemistry but also in everyday life, as it underpins the mechanisms behind antacids, the treatment of acidic waste, and the maintenance of the pH balance in our environment.