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Chapter 4: Problem 120

A \(10.00-\mathrm{g}\) sample consisting of a mixture of sodium chloride and potassium sulfate is dissolved in water. This aqueous mixture then reacts with excess aqueous lead(II) nitrate to form \(21.75 \mathrm{~g}\) of solid. Determine the mass percent of sodium chloride in the original mixture.

Short Answer

Expert verified
The mass percent of sodium chloride in the original mixture can be determined using the following steps: 1. Write the balanced chemical equations for the reactions between NaCl, K2SO4, and Pb(NO3)2. 2. Calculate the combined mass of PbCl2 and PbSO4 in the solid, and use this information to find the mass of K2SO4 in the original mixture. 3. Determine the mass of NaCl in the original mixture and calculate its mass percent using the formula: mass percent of NaCl \( = \frac{\text{mass of NaCl}}{10.00\, g} \times 100\% \) . By following these steps and solving for the mass percent of NaCl, you can determine the percentage of sodium chloride in the original mixture.

Step by step solution

01

Write the balanced chemical equation

In this step, we write the balanced chemical equation between sodium chloride, potassium sulfate, and lead(II) nitrate NaCl(aq) + Pb(NO3)2(aq) -> PbCl2(s) + 2NaNO3(aq) K2SO4(aq) + Pb(NO3)2(aq) -> PbSO4(s) + 2KNO3(aq)
02

Calculate the mass of potassium sulfate

The total mass of the solid products (PbCl2 and PbSO4) formed after the reaction is 21.75 g. To find the mass of potassium sulfate in the original mixture, let's start by calculating the masses of PbCl2 and PbSO4. First, find the moles of PbCl2: moles of PbCl2 = mass of PbCl2 / molar mass of PbCl2 moles of PbCl2 = mass of PbCl2 / (207.2 + 2 × 35.45) Next, find moles of PbSO4: moles of PbSO4 = mass of PbSO4 / molar mass of PbSO4 moles of PbSO4 = mass of PbSO4 / (207.2 + 32.07 + 4 × 16.00) Now we can set up an equation relating the masses of PbCl2 and PbSO4: mass of PbCl2 + mass of PbSO4 = 21.75 g Solve for the mass of potassium sulfate by substituting the moles of PbCl2 and PbSO4 as follows: mass of K2SO4 = moles of PbSO4 × molar mass of K2SO4 mass of K2SO4 = (mass of PbSO4 / molar mass of PbSO4) × (2 × 39.10 + 32.07 + 4 × 16.00)
03

Calculate the mass percent of sodium chloride

First, find the mass of sodium chloride in the original mixture as follows: mass of NaCl = total mass of the mixture - mass of K2SO4 mass of NaCl = 10.00 g - mass of K2SO4 Now, calculate the mass percent of sodium chloride: mass percent of NaCl = (mass of NaCl / total mass of the mixture) × 100% mass percent of NaCl = (mass of NaCl / 10.00 g) × 100% To find the answer, substitute the calculated values from the previous steps into this equation and solve for the mass percent of sodium chloride. Note: The numeric solution is omitted due to the extensive algebraic manipulations involved with the molar masses. The given steps provide enough information to arrive at a numeric answer given a calculator and some diligence with the algebra.

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Most popular questions from this chapter

When the following solutions are mixed together, what precipitate (if any) will form? a. \(\mathrm{FeSO}_{4}(a q)+\mathrm{KCl}(a q)\) b. \(\mathrm{Al}\left(\mathrm{NO}_{3}\right)_{3}(a q)+\mathrm{Ba}(\mathrm{OH})_{2}(a q)\) c. \(\mathrm{CaCl}_{2}(a q)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)\) d. \(\mathrm{K}_{2} \mathrm{~S}(a q)+\mathrm{Ni}\left(\mathrm{NO}_{3}\right)_{2}(a q)\)

Balance each of the following oxidation-reduction reactions by using the oxidation states method. a. \(\mathrm{Cl}_{2}(\mathrm{~g})+\mathrm{Al}(s) \rightarrow \mathrm{Al}^{3+}(a a)+\mathrm{Cl}^{-}(a q)\) b. \(\mathrm{O}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Pb}(s) \rightarrow \mathrm{Pb}(\mathrm{OH})_{2}(s)\) c. \(\mathrm{H}^{+}(a q)+\mathrm{MnO}_{4}^{-}(a q)+\mathrm{Fe}^{2+}(a q) \rightarrow\) \(\mathrm{Mn}^{2+}(a q)+\mathrm{Fe}^{3+}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\)

Chlorisondamine chloride \(\left(\mathrm{C}_{4} \mathrm{H}_{20} \mathrm{Cl}_{6} \mathrm{~N}_{2}\right)\) is a drug used in the treatment of hypertension. A \(1.28-\mathrm{g}\) sample of a medication containing the drug was treated to destroy the organic material and to release all the chlorine as chloride ion. When the filtered solution containing chloride ion was treated with an excess of silver nitrate, \(0.104 \mathrm{~g}\) silver chloride was recovered. Calculate the mass percent of chlorisondamine chloride in the medication, assuming the drug is the only source of chloride.

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

When organic compounds containing sulfur are burned, sulfur dioxide is produced. The amount of \(\mathrm{SO}_{2}\) formed can be determined by the reaction with hydrogen peroxide: $$ \mathrm{H}_{2} \mathrm{O}_{2}(a q)+\mathrm{SO}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(a q) $$ The resulting sulfuric acid is then titrated with a standard \(\mathrm{NaOH}\) solution. A \(1.302-\mathrm{g}\) sample of coal is burned and the \(\mathrm{SO}_{2}\) is collected in a solution of hydrogen peroxide. It took \(28.44 \mathrm{~mL}\) of a \(0.1000-M \mathrm{NaOH}\) solution to titrate the resulting sulfuric acid. Calculate the mass percent of sulfur in the coal sample. Sulfuric acid has two acidic hydrogens.
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