Question

A 0.5895-g sample of impure magnesium hydroxide is dissolved in \(100.0 \mathrm{~mL}\) of \(0.2050 \mathrm{M} \mathrm{HCl}\) 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 \(\mathrm{HCl}\) solution.

Short answer

The percentage by mass of magnesium hydroxide in the impure sample is approximately 91.26%.

Step-by-step solution

Determine moles of HCl reacted with impure magnesium hydroxide

We have 100.0 mL of 0.2050 M HCl solution. To find the moles of HCl, we will use the formula: Moles of HCl = volume (in liters) × molarity Moles of HCl = \(100.0 \times 10^{-3}\) L × 0.2050 mol/L Moles of HCl = 0.020500 mol

Determine moles of excess HCl neutralized by NaOH

To find the moles of HCl neutralized by the 19.85 mL of 0.1020 M NaOH solution, we use the same formula as in step 1: Moles of HCl = volume (in liters) × molarity Moles of HCl = \(19.85 \times 10^{-3}\) L × 0.1020 mol/L Moles of HCl = 0.0020237 mol

Determine moles of HCl that reacted with the impure magnesium hydroxide

Subtract the moles of HCl neutralized by NaOH from the total moles of HCl to find the moles of HCl that reacted with the impure magnesium hydroxide: Moles of HCl with Mg(OH)2 = total moles of HCl - moles of HCl neutralized by NaOH Moles of HCl with Mg(OH)2 = 0.020500 - 0.0020237 = 0.0184763 mol

Determine moles of magnesium hydroxide

The balanced chemical equation for the reaction between magnesium hydroxide and HCl is: Mg(OH)2 + 2HCl → MgCl2 + 2H2O The stoichiometry of the reaction shows that 1 mole of Mg(OH)2 reacts with 2 moles of HCl. Using the moles of HCl that reacted with the magnesium hydroxide, we can find the moles of Mg(OH)2: Moles of Mg(OH)2 = moles of HCl with Mg(OH)2 / 2 Moles of Mg(OH)2 = 0.0184763 mol / 2 = 0.00923815 mol

Determine mass of magnesium hydroxide

To find the mass of Mg(OH)2, we multiply the moles by the molar mass of Mg(OH)2 (which is 58.32 g/mol): Mass of Mg(OH)2 = moles of Mg(OH)2 × molar mass of Mg(OH)2 Mass of Mg(OH)2 = 0.00923815 mol × 58.32 g/mol = 0.538 g (approx.)

Calculate the percentage by mass of magnesium hydroxide

Finally, we calculate the percentage by mass of magnesium hydroxide in the sample: Percentage of Mg(OH)2 = (mass of Mg(OH)2 / mass of sample) × 100% Percentage of Mg(OH)2 = (0.538 g / 0.5895 g) × 100% = 91.26% Thus, the impure magnesium hydroxide sample contains approximately 91.26% by mass of magnesium hydroxide.

Key concepts

Molarity Calculation

Understanding molarity is crucial when working with chemical solutions. Molarity, denoted as M, is a measure of the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. When calculating molarity, the formula to use is:
\[ \text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}} \]
For example, as seen in the exercise, if you have a volume of 100.0 mL (0.1 L) of a solution containing hydrochloric acid with the known concentration of 0.2050 M, the number of moles can be found by rearranging the above formula:
\( \text{Moles of HCl} = \text{volume (in liters)} \times \text{molarity} \)
It's crucial to ensure that the volume is in liters to match the molarity units adequately.

Acid-Base Neutralization

Acid-base neutralization is a chemical reaction where an acid and a base react to form water and a salt. This is an important reaction in chemistry, often seen in titration experiments where an acid's unknown concentration is determined by reacting it with a base of known concentration, or vice versa.
In the context of our exercise, hydrochloric acid (HCl) is neutralized by sodium hydroxide (NaOH), following this reaction:
\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \]
Using stoichiometry, we can understand the mole-to-mole relationship. For every mole of HCl, there is one mole of NaOH reacting. Therefore, by knowing the moles of NaOH used, we also find the moles of excess HCl neutralized.

Percent Composition

Percent composition is a way of representing the concentration of an element or compound in a sample as a percentage of the sample's total mass. The calculation is simple but essential in determining the purity of a sample.
\[ \text{Percent Composition} = \left(\frac{\text{mass of component}}{\text{total mass of sample}}\right) \times 100\% \]
In our problem, the final step involved calculating the mass percent of magnesium hydroxide in the given impure sample. Starting with the mass of pure magnesium hydroxide obtained from the stoichiometry of the reaction and then dividing it by the mass of the initial impure sample, we multiply by 100% to get the percent composition. This concept is not only significant in lab analyses but is also extensively used in various industries like pharmaceuticals and nutrition to determine the composition of a product.