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Chapter 4: Problem 89

A \(0.5895-\mathrm{g}\) 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 percent by mass of magnesium hydroxide in the sample, assuming that it is the only substance reacting with the HCl solution.

Short Answer

Expert verified
The percent by mass of magnesium hydroxide in the sample is approximately 91.33%.

Step by step solution

01

Write the balanced equations for the reactions

We need the balanced equations for the reactions: 1. Between magnesium hydroxide and HCl: \(Mg(OH)_2(aq) + 2HCl(aq) \rightarrow MgCl_2(aq) + 2H_2O(l)\) 2. Between excess HCl and NaOH: \(HCl(aq) + NaOH(aq) \rightarrow NaCl(aq) + H_2O(l)\)
02

Calculate the moles of HCl used in both reactions

Moles of HCl reacted with the impure sample = Volume of HCl solution × Molarity of HCl solution \(= 100.0 \, \text{mL} \times 0.2050 \, \text{M} = 0.2050 \times 10^2 \, \mathrm{mmol} = 20.50 \, \mathrm{mmol}\) Moles of excess HCl = Volume of NaOH needed for titration × Molarity of NaOH \(= 19.85 \, \text{mL} \times 0.1020 \, \text{M} = 0.1020 \times 19.85 \, \mathrm{mmol} = 2.0257 \, \mathrm{mmol}\)
03

Calculate the moles of HCl that reacted with magnesium hydroxide

Moles of HCl that reacted with magnesium hydroxide = Total moles of HCl - Moles of excess HCl \(= 20.50 \, \mathrm{mmol} - 2.0257 \, \mathrm{mmol} = 18.4743 \, \mathrm{mmol}\)
04

Calculate the moles of magnesium hydroxide

Using the balanced equation of reaction between magnesium hydroxide and HCl, we know that 1 mole of magnesium hydroxide reacts with 2 moles of HCl. Thus: Moles of magnesium hydroxide = Moles of HCl reacting with magnesium hydroxide / 2 \(= 18.4743 \, \mathrm{mmol} / 2 = 9.23715 \, \mathrm{mmol}\)
05

Calculate the mass of magnesium hydroxide

Now, calculate the mass of magnesium hydroxide: Mass of magnesium hydroxide = Moles of magnesium hydroxide × Molar mass of magnesium hydroxide \(= 9.23715 \, \mathrm{mmol} \times 58.32 \, \mathrm{g\,mol^{-1}} = 538.383 \, \mathrm{mg}\)
06

Calculate the percentage of magnesium hydroxide in the sample

Finally, calculate the percent by mass of magnesium hydroxide in the sample: Percentage of magnesium hydroxide = (Mass of magnesium hydroxide / Mass of the sample) × 100% \(= (538.383 \, \mathrm{mg} / 589.5 \, \mathrm{mg}) \times 100\% = 91.33\%\) The percent by mass of magnesium hydroxide in the sample is approximately 91.33%.

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Most popular questions from this chapter

Acetone, \(\mathrm{CH}_{3} \mathrm{COCH}_{3},\) is a nonelectrolyte; hypochlorous acid, \(\mathrm{HClO},\) is a weak electrolyte; and ammonium chloride, \(\mathrm{NH}_{4} \mathrm{Cl},\) is a strong electrolyte. (a) What are the solute particles present in aqueous solutions of each compound? (b) If \(0.1 \mathrm{~mol}\) of each compound is dissolved in solution, which one contains \(0.2 \mathrm{~mol}\) of solute particles, which contains \(0.1 \mathrm{~mol}\) of solute particles, and which contains somewhere between 0.1 and 0.2 mol of solute particles?

The labels have fallen off three bottles containing powdered samples of metals; one contains zinc, one lead, and the other platinum. You have three solutions at your disposal: \(1 \mathrm{M}\) sodium nitrate, \(1 \mathrm{M}\) nitric acid, and \(1 \mathrm{M}\) nickel nitrate. How could you use these solutions to determine the identities of each metal powder? [Section 4.4]

Which element is oxidized and which is reduced in the follow- ing reactions? $$ \begin{array}{l} \text { (a) } \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) \\ \text { (b) } 3 \mathrm{Fe}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{Al}(s) \longrightarrow \\ \text { (c) } \mathrm{Cl}_{2}(a q)+2 \mathrm{NaI}(a q) \longrightarrow \mathrm{I}_{2}(a q)+2 \mathrm{NaCl}(a q) \\ \text { (d) } \mathrm{PbS}(s)+4 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow \mathrm{PbSO}_{4}(s)+4 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$

(a) Is the concentration of a solution an intensive or an extensive property? (b) What is the difference between \(0.50 \mathrm{~mol}\) \(\mathrm{HCl}\) and \(0.50 \mathrm{M} \mathrm{HCl} ?\)

(a) Calculate the molarity of a solution made by dissolving 12.5 grams of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in enough water to form exactly \(550 \mathrm{~mL}\) of solution. (b) How many moles of KBr are present in \(150 \mathrm{~mL}\) of a \(0.275 \mathrm{M}\) solution? (c) How many milliliters of 6. \(1 \mathrm{M}\) HCl solution are needed to obtain \(0.100 \mathrm{~mol}\) of \(\mathrm{HCl} ?\)
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