Some of the substances commonly used in stomach antacids are \(\mathrm{MgO}, \mathrm{Mg}(\mathrm{OH})_{2},\) and \(\mathrm{Al}(\mathrm{OH})_{3}\) a. Write a balanced equation for the neutralization of hydrochloric acid by each of these substances. b. Which of these substances will neutralize the greatest amount of 0.10 \(M\) HCl per gram?

To write the balanced equations, we need to combine each antacid substance with hydrochloric acid (HCl) and balance the resulting equation. a. The reactions are: 1. Magnesium oxide (MgO) + hydrochloric acid (HCl): MgO + 2HCl → MgCl₂ + H₂O 2. Magnesium hydroxide (Mg(OH)₂) + hydrochloric acid (HCl): Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O 3. Aluminum hydroxide (Al(OH)₃) + hydrochloric acid (HCl): Al(OH)₃ + 3HCl → AlCl₃ + 3H₂O

To do this, we need to analyze the previously balanced equations and find out the ratio of moles of HCl neutralized to the moles of each antacid substance. Then, we will find the molar mass of each substance and calculate the moles of HCl neutralized per gram of the substance. 1. MgO: - The balanced equation shows that 1 mole of MgO neutralizes 2 moles of HCl. - Molar mass of MgO = (24.31 g/mol for Mg) + (16.00 g/mol for O) = 40.31 g/mol - Moles of HCl neutralized per gram of MgO = (2 moles HCl)/(40.31 g MgO) = 0.0496 mol HCl/g 2. Mg(OH)₂: - The balanced equation shows that 1 mole of Mg(OH)₂ neutralizes 2 moles of HCl. - Molar mass of Mg(OH)₂ = (24.31 g/mol for Mg) + (2 x 17.01 g/mol for OH) = 58.33 g/mol - Moles of HCl neutralize per gram of Mg(OH)₂ = (2 moles HCl)/(58.33 g Mg(OH)₂) = 0.0343 mol HCl/g 3. Al(OH)₃: - The balanced equation shows that 1 mole of Al(OH)₃ neutralizes 3 moles of HCl. - Molar mass of Al(OH)₃ = (26.98 g/mol for Al) + (3 x 17.01 g/mol for OH) = 78.00 g/mol - Moles of HCl neutralize per gram of Al(OH)₃ = (3 moles HCl)/(78.00 g Al(OH)₃) = 0.0385 mol HCl/g

Now that we have the moles of HCl neutralized per gram of each substance, we can compare the values and determine the most effective antacid. Moles of HCl neutralized per gram: - MgO: 0.0496 mol HCl/g - Mg(OH)₂: 0.0343 mol HCl/g - Al(OH)₃: 0.0385 mol HCl/g MgO neutralizes the greatest amount of 0.10 M HCl per gram. Therefore, MgO is the most effective antacid among the three substances.