Question

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 \(0.10 \mathrm{M} \mathrm{HCl}\) per gram?

Short answer

The balanced chemical equations for the neutralization of hydrochloric acid by MgO, Mg(OH)2, and Al(OH)3 are: a. MgO + 2HCl → MgCl2 + H2O b. Mg(OH)2 + 2HCl → MgCl2 + 2H2O c. Al(OH)3 + 3HCl → AlCl3 + 3H2O To neutralize 0.10 moles of HCl, the required mass of each substance is: a. MgO: 2.02 g b. Mg(OH)2: 2.92 g c. Al(OH)3: 2.60 g MgO is the most effective antacid, as it requires the least mass (2.02 g) to neutralize the same amount of HCl (0.10 moles) compared to the other two substances.

Step-by-step solution

Write balanced chemical equations

Write the balanced chemical equations for the neutralization reactions: a. MgO + 2HCl → MgCl2 + H2O b. Mg(OH)2 + 2HCl → MgCl2 + 2H2O c. Al(OH)3 + 3HCl → AlCl3 + 3H2O

Calculate moles of HCl neutralized by 1 mole of each substance

Determine the stoichiometric ratio of each substance reacting with HCl from the balanced chemical equations: a. 1 mole of MgO neutralizes 2 moles of HCl b. 1 mole of Mg(OH)2 neutralizes 2 moles of HCl c. 1 mole of Al(OH)3 neutralizes 3 moles of HCl

Calculate the mass of each substance to neutralize 0.10 moles of HCl

Determine the mass of each substance needed to neutralize 0.10 moles of HCl using the molar mass of each substance and the stoichiometric ratios calculated in Step 2: a. MgO: \( (1 \ mol\ of\ MgO) \cdot \frac{40.31\ g}{1\ mol} \cdot \frac{0.10\ mol\ of\ HCl}{2\ mol\ of\ HCl} \approx 2.02\ g \) b. Mg(OH)2: \( (1 \ mol\ of\ Mg(OH)_2) \cdot \frac{58.33\ g}{1\ mol} \cdot \frac{0.10\ mol\ HCl}{2\ mol\ HCl} \approx 2.92\ g \) c. Al(OH)3: \( (1 \ mol\ of\ Al(OH)_3) \cdot \frac{78.00\ g}{1\ mol} \cdot \frac{0.10\ mol\ HCl}{3\ mol\ HCl} \approx 2.60\ g \)

Compare masses of substances to determine the most effective antacid

Compare the masses of the substances required to neutralize 0.10 moles of HCl: a. MgO: 2.02 g b. Mg(OH)2: 2.92 g c. Al(OH)3: 2.60 g From the comparison, we can see that MgO requires the least mass (2.02 g) to neutralize the same amount of HCl (0.10 moles) compared to the other two substances. Therefore, MgO will neutralize the greatest amount of 0.10 M HCl per gram.

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a critical skill in chemistry that ensures the law of conservation of mass is upheld. This law states that matter cannot be created or destroyed in a chemical reaction. Therefore, it is essential that the number of each type of atom on the reactant side of the equation is equal to the number of each type of atom on the product side.
To balance an equation, one must carefully add coefficients in front of chemical formulas to achieve this balance. For example:

• For the reaction involving MgO and hydrochloric acid (HCl), the balanced equation is: \( \text{MgO} + 2 \text{HCl} \rightarrow \text{MgCl}_2 + \text{H}_2\text{O} \)
• With Mg(OH)\(_2\), the equation is: \( \text{Mg(OH)}_2 + 2 \text{HCl} \rightarrow \text{MgCl}_2 + 2 \text{H}_2\text{O} \)
• For Al(OH)\(_3\), it is: \( \text{Al(OH)}_3 + 3 \text{HCl} \rightarrow \text{AlCl}_3 + 3 \text{H}_2\text{O} \)

These coefficients show how many molecules or moles of each substance participate in the reaction, ensuring that all atoms are accounted for on both sides of the equation.

Stoichiometry

Stoichiometry is the study of the quantitative relationships between the amounts of reactants and products in a chemical reaction. It allows chemists to predict how much of a substance will be consumed or produced in a given reaction.
Using the balanced chemical equations from the previous section, we can explore stoichiometric relationships as follows:

• 1 mole of MgO neutralizes 2 moles of HCl.
• 1 mole of Mg(OH)\(_2\) also neutralizes 2 moles of HCl.
• 1 mole of Al(OH)\(_3\) neutralizes 3 moles of HCl.

This indicates that for every 1 mole of MgO needed, 2 moles of HCl will be consumed. Similarly, Al(OH)\(_3\) is more efficient in terms of moles, as it neutralizes 3 moles of HCl for every 1 mole used. Understanding these ratios is crucial to figuring out how much of each substance is needed for a reaction.

Molar Mass Calculations

Molar mass is a measure of the mass of a given substance (chemical element or chemical compound) divided by its amount of substance in moles. It is typically expressed in units of grams per mole ( ext{g/mol}).
Molar masses are helpful for converting between the mass of a substance and the number of moles of that substance. Here are the molar masses of the substances in our exercise:

• MgO has a molar mass of approximately 40.31 ext{g/mol}
• Mg(OH)\(_2\) has a molar mass of about 58.33 ext{g/mol}
• Al(OH)\(_3\) has a molar mass of roughly 78.00 ext{g/mol}

To calculate the quantity of each substance needed to neutralize 0.10 moles of HCl, we utilize these molar masses alongside stoichiometry. By doing so, we determine how much of each substance, in grams, is required to completely react with the specified amount of HCl.

Antacid Effectiveness

In evaluating antacid effectiveness, it's important to consider how much acid can be neutralized by a given mass of an antacid substance. This is often determined by calculating the smallest mass of each substance required to neutralize a fixed amount of hydrochloric acid (HCl).
Using our previous calculations:

• MgO: 2.02 grams are needed to neutralize 0.10 moles of HCl.
• Mg(OH)\(_2\): Requires 2.92 grams to do the same.
• Al(OH)\(_3\): Needs 2.60 grams for neutralization.

Hence, per gram, MgO is the most effective at neutralizing HCl, requiring the least mass compared to Mg(OH)\(_2\) and Al(OH)\(_3\). Understanding the effectiveness of antacids helps in choosing the right one for addressing conditions like heartburn or acid indigestion, providing relief by efficiently neutralizing excess stomach acid.