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Chapter 4: Problem 68

(a) How many grams of solute are present in \(15.0 \mathrm{~mL}\) of \(0.736 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} ?\) (b) If \(14.00 \mathrm{~g}\) of \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) is dissolved in enough water to form \(250 \mathrm{~mL}\) of solution, what is the molarity of the solution? (c) How many milliliters of \(0.0455 \mathrm{M} \mathrm{CuSO}_{4}\) contain \(3.65 \mathrm{~g}\) of solute?

Short Answer

Expert verified
(a) There are \(3.25 \mathrm{~g}\) of solute present in \(15.0 \mathrm{~mL}\) of \(0.736 \mathrm{M K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\) solution. (b) The molarity of the solution formed by dissolving \(14.00 \mathrm{~g}\) of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4}\) in \(250 \mathrm{~mL}\) of water is \(0.424 \mathrm{M}\). (c) \(503.1 \mathrm{~mL}\) of \(0.0455 \mathrm{M CuSO}_{4}\) solution contains \(3.65 \mathrm{~g}\) of solute.

Step by step solution

01

Identify the given information

The given information is: - Volume of the solution: \(15.0 \mathrm{~mL}\) - Molarity of the solution: \(0.736 \mathrm{M}\) - Substance: \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\)
02

Determine the molar mass of solute

Use the periodic table to find the molar mass of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7}\): Molar mass of \(\mathrm{K}_{2}\mathrm{Cr}_{2}\mathrm{O}_{7} = 2\times\mathrm{M}_\mathrm{K} + 2\times\mathrm{M}_\mathrm{Cr} + 7\times\mathrm{M}_\mathrm{O} = 2(39.10 \mathrm{~g/mol}) + 2(51.996\mathrm{~g/mol}) + 7(16.00\mathrm{~g/mol}) = 294.2 \mathrm{~g/mol}\)
03

Calculate moles of solute

Use the molarity formula to find moles of solute. Remember that molarity (\(M\)) is the moles of solute per liter of solution: \(0.736 \mathrm{~M} = \frac{\text{moles of solute}}{0.015 \mathrm{~L}}\) \(\text{moles of solute} = 0.736 \mathrm{~M} \times 0.015 \mathrm{~L} = 0.01104 \mathrm{~mol}\)
04

Calculate grams of solute

Multiply the moles of solute by the molar mass of the solute to find the grams of solute present: \(\text{grams of solute} = 0.01104 \mathrm{~mol} \times 294.2 \mathrm{~g/mol} = 3.25 \mathrm{~g}\) (b) Determining the molarity of a solution
05

Identify the given information

The given information is: - Mass of solute: \(14.00 \mathrm{~g}\) - Volume of the solution: \(250 \mathrm{~mL}\) - Substance: \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4} \)
06

Determine the molar mass of solute

Use the periodic table to find the molar mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4} \): Molar mass of \(\left(\mathrm{NH}_{4}\right)_{2}\mathrm{SO}_{4} = 2\times(14.01\mathrm{~g/mol} + 4\times1.008\mathrm{~g/mol}) + 32.07\mathrm{~g/mol} + 4\times16.00\mathrm{~g/mol} = 132.14 \mathrm{~g/mol} \)
07

Calculate moles of solute

Divide the mass of solute by the molar mass of the solute to find the moles of solute present: \(\text{moles of solute} = \frac{14.00 \mathrm{~g}}{132.14 \mathrm{~g/mol}} = 0.10593 \mathrm{~mol}\)
08

Calculate molarity of the solution

Use the molarity formula with the moles of solute and volume of solution: \(M = \frac{\text{moles of solute}}{\text{liters of solution}} = \frac{0.10593 \mathrm{~mol}}{0.250 \mathrm{~L}} = 0.424 \mathrm{M}\) (c) Finding the volume of a solution containing a certain mass
09

Identify the given information

The given information is: - Mass of solute: \(3.65 \mathrm{~g}\) - Molarity of the solution: \(0.0455 \mathrm{M}\) - Substance: \(\mathrm{CuSO}_{4}\)
10

Determine the molar mass of solute

Use the periodic table to find the molar mass of \(\mathrm{CuSO}_{4}\): Molar mass of \(\mathrm{CuSO}_{4} = 63.546\mathrm{~g/mol} + 32.07\mathrm{~g/mol} + 4\times16.00\mathrm{~g/mol} = 159.62 \mathrm{~g/mol}\)
11

Calculate moles of solute

Divide the mass of solute by the molar mass of the solute to find the moles of solute present: \(\text{moles of solute} = \frac{3.65 \mathrm{~g}}{159.62 \mathrm{~g/mol}} = 0.02288 \mathrm{~mol}\)
12

Calculate the volume of the solution

Use the molarity formula with the moles of solute and the molarity of the solution: \(\text{volume of solution} = \frac{\text{moles of solute}}{\text{Molarity}} = \frac{0.02288 \mathrm{~mol}}{0.0455 \mathrm{M}} = 0.5031 \mathrm{L}\)
13

Convert volume to milliliters

Multiply the volume in liters by 1000 to convert it to milliliters: \(\text{volume of solution} = 0.5031 \mathrm{L} \times 1000 = 503.1 \mathrm{~mL}\)

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Most popular questions from this chapter

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]

We have learned in this chapter that many ionic solids dissolve in water as strong electrolytes, that is, as separated ions in solution. What properties of water facilitate this process? Would you expect ionic compounds to be soluble in elemental liquids like bromine or mercury, just as they are in water? Explain.

Write the balanced molecular and net ionic equations for each of the following neutralization reactions: (a) Aqueous acetic acid is neutralized by aqueous barium hydroxide. (b) Solid chromium(III) hydroxide reacts with nitrous acid. (c) Aqueous nitric acid and aqueous ammonia react.

Formic acid, \(\mathrm{HCOOH},\) is a weak electrolyte. What solute particles are present in an aqueous solution of this compound? Write the chemical equation for the ionization of \(\mathrm{HCOOH}\).

(a) By titration, \(15.0 \mathrm{~mL}\) of \(0.1008 \mathrm{M}\) sodium hydroxide is needed to neutralize a \(0.2053-\mathrm{g}\) sample of an organic acid. What is the molar mass of the acid if it is monoprotic? (b) An elemental analysis of the acid indicates that it is composed of \(5.89 \% \mathrm{H}, 70.6 \% \mathrm{C},\) and \(23.5 \% \mathrm{O}\) by mass. What is its molecular formula?
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