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Chapter 4: Problem 118

A mixture contains only sodium chloride and potassium chloride. A \(0.1586-\mathrm{g}\) sample of the mixture was dissolved in water. It took \(22.90 \mathrm{~mL}\) of \(0.1000 \mathrm{M} \mathrm{AgNO}_{3}\) to completely precipitate all the chloride present. What is the composition (by mass percent) of the mixture?

Short Answer

Expert verified
The composition of the mixture is approximately 21.4% sodium chloride (\(NaCl\)) and 78.6% potassium chloride (\(KCl\)).

Step by step solution

01

Calculate the mols of silver nitrate

Find the moles of silver nitrate that reacted with the chloride mixture using the given volume and concentration: Moles of AgNO3 = (volume) 脳 (concentration) Moles of AgNO3 = (22.90 ml) 脳 (0.1000 mol/L) Note that we need to convert the volume from ml to L: Moles of AgNO3 = (0.0229 L) 脳 (0.1000 mol/L) Moles of AgNO3 = 0.00229 mol
02

Calculate the mols of chloride ions

Calculate the moles of both chloride ions, as silver nitrate reacts equally with chloride ions from sodium chloride and potassium chloride. Moles of chloride ions = moles of AgNO3 = 0.00229 mol
03

Assign variables and write an equation

Assign variable x to moles of NaCl and y to moles of KCl in the mixture. Then, write an equation for total mass of the mixture sample. 0.1586 g = (x 脳 58.44 g/mol) + (y 脳 74.55 g/mol) We also know that the total moles of chloride equal the moles of AgNO鈧�: x + y = 0.00229
04

Solve the equations

Solve the two equations in step 3 simultaneously: x = 0.00229 - y Substitute x in the first equation: 0.1586 = ((0.00229 - y) 脳 58.44) + (y 脳 74.55) Now, solve for y: y 鈮� 0.00171 mol Substitute y in the equation x = 0.00229 - y to find x: x 鈮� 0.00058 mol
05

Calculate mass of NaCl and KCl

Use the molar masses of NaCl and KCl to find their masses in the 0.1586 g mixture: Mass of NaCl = x 脳 molar mass of NaCl = 0.00058 mol 脳 58.44 g/mol 鈮� 0.0339 g Mass of KCl = y 脳 molar mass of KCl = 0.00171 mol 脳 74.55 g/mol 鈮� 0.127 g
06

Calculate the mass percent of each compound

Now, calculate the mass percent of NaCl and KCl in the mixture: Mass percent of NaCl = (mass of NaCl / total mass) 脳 100 Mass percent of NaCl = (0.0339 g / 0.1586 g) 脳 100 鈮� 21.4% Mass percent of KCl = (mass of KCl / total mass) 脳 100 Mass percent of KCl = (0.127 g / 0.1586 g) 脳 100 鈮� 78.6% The composition of the mixture is approximately 21.4% sodium chloride and 78.6% potassium chloride.

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Most popular questions from this chapter

A stream flows at a rate of \(5.00 \times 10^{4}\) liters per second \((\mathrm{L} / \mathrm{s})\) upstream of a manufacturing plant. The plant discharges \(3.50 \times\) \(10^{3} \mathrm{~L} / \mathrm{s}\) of water that contains \(65.0 \mathrm{ppm} \mathrm{HCl}\) into the stream. (See Exercise 113 for definitions.) a. Calculate the stream's total flow rate downstream from this plant. b. Calculate the concentration of \(\mathrm{HCl}\) in ppm downstream from this plant. c. Further downstream, another manufacturing plant diverts \(1.80 \times 10^{4} \mathrm{~L} / \mathrm{s}\) of water from the stream for its own use. This plant must first neutralize the acid and does so by adding lime: $$ \mathrm{CaO}(s)+2 \mathrm{H}^{+}(a q) \longrightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{H}_{2} \mathrm{O}(l) $$ What mass of \(\mathrm{CaO}\) is consumed in an \(8.00-\mathrm{h}\) work day by this plant? d. The original stream water contained \(10.2 \mathrm{ppm} \mathrm{Ca}^{2+}\). Although no calcium was in the waste water from the first plant, the waste water of the second plant contains \(\mathrm{Ca}^{2+}\) from the neutralization process. If \(90.0 \%\) of the water used by the second plant is returned to the stream, calculate the concentration of \(\mathrm{Ca}^{2+}\) in ppm downstream of the second plant.

Write the balanced formula, complete ionic, and net ionic equations for each of the following acid-base reactions. a. \(\mathrm{HClO}_{4}(a q)+\mathrm{Mg}(\mathrm{OH})_{2}(s) \rightarrow\) b. \(\mathrm{HCN}(a q)+\mathrm{NaOH}(a q) \rightarrow\) c. \(\mathrm{HCl}(a q)+\mathrm{NaOH}(a q) \rightarrow\)

Calculate the concentration of all ions present in each of the following solutions of strong electrolytes. a. \(0.0200 \mathrm{~mol}\) of sodium phosphate in \(10.0 \mathrm{~mL}\) of solution b. \(0.300 \mathrm{~mol}\) of barium nitrate in \(600.0 \mathrm{~mL}\) of solution c. \(1.00 \mathrm{~g}\) of potassium chloride in \(0.500 \mathrm{~L}\) of solution d. \(132 \mathrm{~g}\) of ammonium sulfate in \(1.50 \mathrm{~L}\) of solution

A student titrates an unknown amount of potassium hydrogen phthalate \(\left(\mathrm{KHC}_{8} \mathrm{H}_{4} \mathrm{O}_{4}\right.\), often abbreviated \(\mathrm{KHP}\) ) with \(20.46 \mathrm{~mL}\) of a \(0.1000 M\) NaOH solution. KHP (molar mass \(=204.22\) \(\mathrm{g} / \mathrm{mol}\) ) has one acidic hydrogen. What mass of KHP was titrated (reacted completely) by the sodium hydroxide solution?

Give an example how each of the following insoluble ionic compounds could be produced using a precipitation reaction. Write the balanced formula equation for each reaction. a. \(\mathrm{Fe}(\mathrm{OH})_{3}(s)\) b. \(\mathrm{Hg}_{2} \mathrm{Cl}_{2}(s)\) c. \(\mathrm{PbSO}_{4}(s)\) d. \(\mathrm{BaCrO}_{4}(s)\)
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