Question 6.9: The active ingredient in many commercial antacids is magnesi......
The active ingredient in many commercial antacids is magnesium hydroxide, Mg(OH)_{2}, which reacts with stomach acid (HCl) to produce magnesium chloride (MgCl_{2}) and water. The equation for the reaction is
\quad\quad\quad\quad Mg(OH)_{2} + 2HCl → MgCl_{2} + 2H_{2}O
How many grams of Mg(OH)_{2} are needed to react with 0.30 g of HCl?
Step 1: This problem, like Example 6.8, is a “grams of A” to “grams of B” problem. It differs from the previous problem in that both the given and the desired quantities involve reactants.
\quad\quad\quad\quad0.30 g HCl → ? g Mg(OH)_{2}
Step 2: The pathway used to solve it will be the same as in Example 6.8.
The dimensional-analysis setup is
\quad\quad 0.30 \cancel{g HCl}\times (\frac{1 \cancel{mole HCl}}{36.46 \cancel{g HCl}})\times (\frac{1 \cancel{mole Mg(OH)_{2}}}{2 \cancel{moles HCl}})\times (\frac{58.33 g Mg(OH)_{2}}{1 \cancel{mole Mg(OH)_{2}}})\\ \quad\quad\quad\quad g HCl\longrightarrow moles HCl\longrightarrow moles Mg(OH)_{2}\longrightarrow g Mg(OH)_{2}The balanced chemical equation for the reaction is used as the bridge that enables us to go from HCl to Mg(OH)_{2}. The numbers in the second conversion factor are coefficients from this equation.
Step 3: The solution obtained by combining all of the numbers in the manner indicated in the setup is
\quad\quad\quad\quad(\frac{0.30\times 1\times 1\times 58.33}{36.46\times 2\times 1}) g Mg(OH)_{2}=0.24 g Mg(OH)_{2}To put our answer in perspective, we note that a common brand of antacid tablets has tablets containing 0.10 g of Mg(OH)_{2}.