Question

A \(0.5895-\mathrm{g}\) sample of impure magnesium hydroxide is dissolved in \(100.0 \mathrm{~mL}\) of \(0.2050 \mathrm{MHCl}\) solution. The excess acid then needs \(19.85 \mathrm{~mL}\) of \(0.1020 \mathrm{M} \mathrm{NaOH}\) for neutralization. Calculate the percentage by mass of magnesium hydroxide in the sample, assuming that it is the only substance reacting with the HCl solution.

Short answer

The percentage by mass of magnesium hydroxide in the impure sample is approximately 91.31%.

Step-by-step solution

Determine the moles of HCl reacted with Mg(OH)₂

To determine the moles of HCl consumed in the reaction with Mg(OH)₂, first find out how many moles of HCl reacted with the excess NaOH. The balanced reaction between NaOH and HCl is: NaOH + HCl → NaCl + H₂O The stoichiometry of this reaction is 1:1, which means that one mole of NaOH reacts with one mole of HCl. Use the formula: moles = Molarity * Volume (in L) Find the moles of NaOH used to neutralize excess HCl: moles(NaOH) = 0.1020 * (19.85/1000) L = 0.0020257 mol Since the stoichiometry is 1:1, the same amount of HCl reacted with this NaOH: moles(HCl reacted with NaOH) = moles(NaOH) = 0.0020257 mol Now find the moles of HCl initially present in the solution: moles(HCl initially) = 0.2050 * (100/1000) L = 0.0205 mol Now find the moles of HCl that reacted with magnesium hydroxide in the sample: moles(HCl reacted with Mg(OH)₂) = moles(HCl initially) - moles(HCl reacted with NaOH) moles(HCl reacted with Mg(OH)₂) = 0.0205 - 0.0020257 = 0.0184743 mol

Determine the moles of magnesium hydroxide in the sample

Next, we need to find out how many moles of magnesium hydroxide reacted with the HCl. The balanced equation for the reaction between Mg(OH)₂ and HCl is: Mg(OH)₂ + 2HCl → MgCl₂ + 2H₂O The stoichiometry of this reaction is 1:2, meaning one mole of Mg(OH)₂ reacts with two moles of HCl. Use the stoichiometry to calculate the moles of Mg(OH)₂ in the sample: moles(Mg(OH)₂) = moles(HCl reacted with Mg(OH)₂) / 2 moles(Mg(OH)₂) = 0.0184743 / 2 = 0.00923715 mol

Calculate the mass of magnesium hydroxide in the sample

To find the mass of magnesium hydroxide, multiply the moles of Mg(OH)₂ with its molar mass. First, find the molar mass of Mg(OH)₂: Molar mass(Mg(OH)₂) = 24.31 (Mg) + 2(16.00 + 1.01) (2OH) = 58.32 g/mol Now, calculate the mass of Mg(OH)₂ in the sample: mass(Mg(OH)₂) = moles(Mg(OH)₂) * molar mass(Mg(OH)₂) mass(Mg(OH)₂) = 0.00923715 * 58.32 g/mol = 0.538288 g

Calculate the percentage by mass of magnesium hydroxide in the sample

Finally, calculate the percentage by mass of magnesium hydroxide in the impure sample using the formula: percentage by mass = (mass of Mg(OH)₂ / mass of impure sample) * 100 percentage by mass = (0.538288 / 0.5895) * 100 = 91.31% The percentage by mass of magnesium hydroxide in the impure sample is approximately 91.31%.

Key concepts

Magnesium Hydroxide

Magnesium hydroxide is a chemical compound often encountered in various applications, including medicine and industry. Its chemical formula is Mg(OH)₂, indicating that each molecule contains one magnesium atom and two hydroxide groups. This compound is depicted as a white solid and can be found naturally or produced synthetically.

In real-world usage, magnesium hydroxide is widely known for its antacid properties. It's the active ingredient in milk of magnesia, a common over-the-counter medication used to neutralize stomach acid and relieve indigestion.

In the context of chemistry, particularly in stoichiometry and reactions, understanding the interactions and amounts of magnesium hydroxide is crucial. Its reactions, such as those with hydrochloric acid, are key to calculating mass percentages and understanding chemical equilibria.

Stoichiometry

Stoichiometry is a core concept in chemistry that allows you to calculate the quantities of reactants or products involved in a chemical reaction. It involves using balanced chemical equations to interpret the relationships between substances.

The principle behind stoichiometry is the conservation of mass, which states that the mass of reactants must equal the mass of products in a chemical reaction. To use stoichiometry effectively, you need to understand the molar ratios from a balanced chemical equation. These ratios help you convert between moles of different substances.

In our exercise, stoichiometry helps in calculating how much magnesium hydroxide reacts with hydrochloric acid. The balanced reaction: \[ \text{Mg(OH)}_2 + 2\text{HCl} \rightarrow \text{MgCl}_2 + 2\text{H}_2\text{O} \] shows that one mole of magnesium hydroxide reacts with two moles of hydrochloric acid. This relationship is critical in computing the mass percentage of magnesium hydroxide in a sample.

Molarity

Molarity is a term used to describe the concentration of a solution. It is expressed as the number of moles of solute per liter of solution, with units \( ext{M} \) (molar). Understanding molarity is essential for preparing solutions and conducting accurate chemical experiments.

To determine molarity, use the formula: \[ ext{Molarity (M)} = \frac{\text{Moles of Solute}}{\text{Liters of Solution}} \]This allows chemists to measure and adjust the concentration of substances precisely.

In the given problem, molarity plays a key role. The hydrochloric acid solution has a known molarity of 0.2050 M, and this information is used to calculate how much HCl the magnesium hydroxide reacts with. Similarly, the molarity of sodium hydroxide (0.1020 M) is vital for determining the excess HCl after the initial reaction with magnesium hydroxide.

Neutralization Reaction

Neutralization reactions are a type of chemical reaction in which an acid and a base react to form a salt and water. These reactions are significant in many areas, such as chemistry labs, industrial processes, and even in everyday life scenarios.

The general formula for a neutralization reaction is: \[ \text{Acid} + \text{Base} \rightarrow \text{Salt} + \text{Water} \] This reaction is important for stoichiometry calculations and for understanding how different substances interact together in solution.

In the exercise, the excess hydrochloric acid not used by magnesium hydroxide was neutralized by sodium hydroxide. The reaction between NaOH and HCl is 1:1, forming NaCl and H₂O. This process indicates that an equal amount of moles of the acid and base are consumed, allowing the determination of how much acid was in excess and how much reacted with magnesium hydroxide.