1.3.E: Composition of Substances and Solutions (Exercises)

Formula Mass and the Mole Concept

What is the total mass of hydrogen in each of the molecules?

1. (a) CH₄
2. (b) CHCl₃
3. (c) C₁₂H₁₀O₆
4. (d) CH₃CH₂CH₂CH₂CH₃

Calculate the molecular or formula mass of each of the following:

(a) P₄

(b) H₂O

(c) Ca(NO₃)₂

(d) CH₃CO₂H (acetic acid)

(e) C₁₂H₂₂O₁₁ (sucrose, cane sugar).

Determine the molecular mass of the following compounds:

(a)

(b)

(c)

(d)

Determine the molecular mass of the following compounds:

(a)

(b)

(c)

(d)

Which molecule has a molecular mass of 28.05 amu?

(a)

(b)

(c)

Write a sentence that describes how to determine the number of moles of a compound in a known mass of the compound if we know its molecular formula.

Compare 1 mole of H₂, 1 mole of O₂, and 1 mole of F₂.

1. (a) Which has the largest number of molecules? Explain why.
2. (b) Which has the greatest mass? Explain why.

Which contains the greatest number of moles of oxygen atoms: 1 mol of ethanol (C₂H₅OH), 1 mol of formic acid (HCO₂H), or 1 mol of water (H₂O)? Explain why.

How are the molecular mass and the molar mass of a compound similar and how are they different?

Calculate the molar mass of each of the following compounds:

1. (a) hydrogen fluoride, HF
2. (b) ammonia, NH₃
3. (c) nitric acid, HNO₃
4. (d) silver sulfate, Ag₂SO₄
5. (e) boric acid, B(OH)₃

Calculate the molar mass of each of the following:

1. (a) S₈
2. (b) C₅H₁₂
3. (c) Sc₂(SO₄)₃
4. (d) CH₃COCH₃ (acetone)
5. (e) C₆H₁₂O₆ (glucose)

Calculate the empirical or molecular formula mass and the molar mass of each of the following minerals:

1. (a) limestone, CaCO₃
2. (b) halite, NaCl
3. (c) beryl, Be₃Al₂Si₆O₁₈
4. (d) malachite, Cu₂(OH)₂CO₃
5. (e) turquoise, CuAl₆(PO₄)₄(OH)₈(H₂O)₄

Calculate the molar mass of each of the following:

1. (a) the anesthetic halothane, C₂HBrClF₃
2. (b) the herbicide paraquat, C₁₂H₁₄N₂Cl₂
3. (c) caffeine, C₈H₁₀N₄O₂
4. (d) urea, CO(NH₂)₂
5. (e) a typical soap, C₁₇H₃₅CO₂Na

Determine the number of moles of compound and the number of moles of each type of atom in each of the following:

1. (a) 25.0 g of propylene, C₃H₆
2. (b) 3.06 × 10⁻³ g of the amino acid glycine, C₂H₅NO₂
3. (c) 25 lb of the herbicide Treflan, C₁₃H₁₆N₂O₄F (1 lb = 454 g)
4. (d) 0.125 kg of the insecticide Paris Green, Cu₄(AsO₃)₂(CH₃CO₂)₂
5. (e) 325 mg of aspirin, C₆H₄(CO₂H)(CO₂CH₃)

Determine the number of moles of the compound and determine the number of moles of each type of atom in each of the following:

1. (a) 2.12 g of potassium bromide, KBr
2. (b) 0.1488 g of phosphoric acid, H₃PO₄
3. (c) 23 kg of calcium carbonate, CaCO₃
4. (d) 78.452 g of aluminum sulfate, Al₂(SO₄)₃
5. (e) 0.1250 mg of caffeine, C₈H₁₀N₄O₂

Determine the mass of each of the following:

1. (a) 2.345 mol LiCl
2. (b) 0.0872 mol acetylene, C₂H₂
3. (c) 3.3 × 10⁻² mol Na₂ CO₃
4. (d) 1.23 × 10³ mol fructose, C₆ H₁₂ O₆
5. (e) 0.5758 mol FeSO₄(H₂O)₇

The approximate minimum daily dietary requirement of the amino acid leucine, C₆H₁₃NO₂, is 1.1 g. What is this requirement in moles?

Determine the mass in grams of each of the following:

1. (a) 0.600 mol of oxygen atoms
2. (b) 0.600 mol of oxygen molecules, O₂
3. (c) 0.600 mol of ozone molecules, O₃

A 55-kg woman has 7.5 × 10⁻³ mol of hemoglobin (molar mass = 64,456 g/mol) in her blood. How many hemoglobin molecules is this? What is this quantity in grams?

Determine the number of atoms and the mass of zirconium, silicon, and oxygen found in 0.3384 mol of zircon, ZrSiO₄, a semiprecious stone.

Determine which of the following contains the greatest mass of hydrogen: 1 mol of CH₄, 0.6 mol of C₆H₆, or 0.4 mol of C₃H₈.

Determine which of the following contains the greatest mass of aluminum: 122 g of AlPO₄, 266 g of Al₂Cl₆, or 225 g of Al₂S₃.

Diamond is one form of elemental carbon. An engagement ring contains a diamond weighing 1.25 carats (1 carat = 200 mg). How many atoms are present in the diamond?

The Cullinan diamond was the largest natural diamond ever found (January 25, 1905). It weighed 3104 carats (1 carat = 200 mg). How many carbon atoms were present in the stone?

One 55-gram serving of a particular cereal supplies 270 mg of sodium, 11% of the recommended daily allowance. How many moles and atoms of sodium are in the recommended daily allowance?

A certain nut crunch cereal contains 11.0 grams of sugar (sucrose, C₁₂H₂₂O₁₁) per serving size of 60.0 grams. How many servings of this cereal must be eaten to consume 0.0278 moles of sugar?

A tube of toothpaste contains 0.76 g of sodium monofluorophosphate (Na₂PO₃F) in 100 mL.

1. What mass of fluorine atoms in mg was present?
2. How many fluorine atoms were present?

Which of the following represents the least number of molecules?

1. 20.0 g of H₂O (18.02 g/mol)
2. 77.0 g of CH₄ (16.06 g/mol)
3. 68.0 g of CaH₂ (42.09 g/mol)
4. 100.0 g of N₂O (44.02 g/mol)
5. 84.0 g of HF (20.01 g/mol)

Determining Empirical and Molecular Formulas

Calculate the following to four significant figures:

1. (a) the percent composition of ammonia, NH₃
2. (b) the percent composition of photographic “hypo,” Na₂S₂O₃
3. (c) the percent of calcium ion in Ca₃(PO₄)₂

Determine the following to four significant figures:

1. the percent composition of hydrazoic acid, HN₃
2. the percent composition of TNT, C₆H₂(CH₃)(NO₂)₃
3. the percent of SO₄^2– in Al₂(SO₄)₃

Determine the percent ammonia, NH₃, in Co(NH₃)₆Cl₃, to three significant figures.

Determine the percent water in CuSO₄∙5H₂O to three significant figures.

Determine the empirical formulas for compounds with the following percent compositions:

(a) 15.8% carbon and 84.2% sulfur

(b) 40.0% carbon, 6.7% hydrogen, and 53.3% oxygen

Determine the empirical formulas for compounds with the following percent compositions:

(a) 43.6% phosphorus and 56.4% oxygen

(b) 28.7% K, 1.5% H, 22.8% P, and 47.0% O

A compound of carbon and hydrogen contains 92.3% C and has a molar mass of 78.1 g/mol. What is its molecular formula?

Dichloroethane, a compound that is often used for dry cleaning, contains carbon, hydrogen, and chlorine. It has a molar mass of 99 g/mol. Analysis of a sample shows that it contains 24.3% carbon and 4.1% hydrogen. What is its molecular formula?

Polymers are large molecules composed of simple units repeated many times. Thus, they often have relatively simple empirical formulas. Calculate the empirical formulas of the following polymers:

1. Lucite (Plexiglas); 59.9% C, 8.06% H, 32.0% O
2. Saran; 24.8% C, 2.0% H, 73.1% Cl
3. polyethylene; 86% C, 14% H
4. polystyrene; 92.3% C, 7.7% H
5. Orlon; 67.9% C, 5.70% H, 26.4% N

Molarity

What information do we need to calculate the molarity of a sulfuric acid solution?

What does it mean when we say that a 200-mL sample and a 400-mL sample of a solution of salt have the same molarity? In what ways are the two samples identical? In what ways are these two samples different?

Determine the molarity for each of the following solutions:

1. 0.444 mol of CoCl₂ in 0.654 L of solution
2. 98.0 g of phosphoric acid, H₃PO₄, in 1.00 L of solution
3. 0.2074 g of calcium hydroxide, Ca(OH)₂, in 40.00 mL of solution
4. 10.5 kg of Na₂SO₄·10H₂O in 18.60 L of solution
5. 7.0 × 10⁻³ mol of I₂ in 100.0 mL of solution
6. 1.8 × 10⁴ mg of HCl in 0.075 L of solution

Consider this question: What is the mass of the solute in 0.500 L of 0.30 M glucose, C₆H₁₂O₆, used for intravenous injection?

(a) Outline the steps necessary to answer the question.

(b) Answer the question.

(a) determine the number of moles of glucose in 0.500 L of solution; determine the molar mass of glucose; determine the mass of glucose from the number of moles and its molar mass; (b) 27 g

Consider this question: What is the mass of solute in 200.0 L of a 1.556-M solution of KBr?

1. (a) Outline the steps necessary to answer the question.
2. (b) Answer the question.

Answer:

(a)

1. Calculate to moles of KBr by multiplying the Molarity by the amount of solution (200.0 L)
2. Find the Molar Mass of KBr and convert moles of solute to grams

(b)

[latex]\dfrac{1.556\:moles\:\ce{KBr}}{1\:\cancel{L}}\times 200.0\:\cancel{L}=311.2\:moles\:\ce{KBr}[/latex]
[latex]311.2\:\cancel{moles}\:\ce{KBr}\times\dfrac{119.0\:g\:\ce{KBr}}{1\:\cancel{mole}\:\ce{KBr}}=37,030\:g[/latex]

37,030g; 37.03 kg

Calculate the number of moles and the mass of the solute in each of the following solutions:

1. 325 mL of 8.23 × 10⁻⁵ M KI, a source of iodine in the diet
2. 75.0 mL of 2.2 × 10⁻⁵ M H₂SO₄, a sample of acid rain
3. 0.2500 L of 0.1135 M K₂CrO₄, an analytical reagent used in iron assays
4. 10.5 L of 3.716 M (NH₄)₂SO₄, a liquid fertilizer

Answers:

a. 2.67×10^-5 moles KI; 4.44×10^-3g KI

b. 1.7×10^-6 moles H₂SO₄ ; 1.6×10^-4 g H₂SO₄

c. 2.838×10^-2 moles K₂CrO₄ ; 5.510g K₂CrO₄

d. 39.0 moles (NH₄)₂SO₄ ; 5,160 g (NH₄)₂SO₄

Consider this question: What is the molarity of KMnO₄ in a solution of 0.0908 g of KMnO₄ in 0.500 L of solution?

1. (a) Outline the steps necessary to answer the question.
2. (b) Answer the question.

Consider this question: What is the molarity of HCl if 35.23 mL of a solution of HCl contain 0.3366 g of HCl?

1. (a) Outline the steps necessary to answer the question.
2. (b) Answer the question.

Answer:

(a)

1. Convert g of HCl to moles of HCl and convert mL of solution to L of solution
2. Divide moles of HCl by L of solution

(b)

[latex]0.3366\:\cancel{g}\:\ce{HCl}\times\dfrac{1\:mole\:\ce{HCl}}{36.46\:\cancel{g}\:\ce{HCl}}=9.232\times10^{-3}\:moles\:\ce{HCl}[/latex]
[latex]35.23\:mL = 0.03523\:L[/latex]
[latex]\dfrac{9.232\times10^{-3}\:moles\:\ce{HCl}}{0.03523\:L}=0.2621\:M\:\ce{HCl}[/latex]

0.2621 M ;

Calculate the molarity of each of the following solutions:

(a) 0.195 g of cholesterol, C₂₇H₄₆O, in 0.100 L of serum, the average concentration of cholesterol in human serum

(b) 4.25 g of NH₃ in 0.500 L of solution, the concentration of NH₃ in household ammonia

(c) 1.49 kg of isopropyl alcohol, C₃H₇OH, in 2.50 L of solution, the concentration of isopropyl alcohol in rubbing alcohol

(d) 0.029 g of I₂ in 0.100 L of solution, the solubility of I₂ in water at 20 °C

Calculate the molarity of each of the following solutions:

1. 293 g HCl in 666 mL of solution, a concentrated HCl solution
2. 2.026 g FeCl₃ in 0.1250 L of a solution used as an unknown in general chemistry laboratories
3. 0.001 mg Cd²⁺ in 0.100 L, the maximum permissible concentration of cadmium in drinking water
4. 0.0079 g C₇H₅SNO₃ in one ounce (29.6 mL), the concentration of saccharin in a diet soft drink.

There is about 1.0 g of calcium, as Ca²⁺, in 1.0 L of milk. What is the molarity of Ca²⁺ in milk?

What volume of a 1.00-M Fe(NO₃)₃ solution can be diluted to prepare 1.00 L of a solution with a concentration of 0.250 M?

If 4.12 L of a 0.850 M-H₃PO₄ solution is be diluted to a volume of 10.00 L, what is the concentration the resulting solution?

What is the concentration of the NaCl solution that results when 0.150 L of a 0.556-M solution is allowed to evaporate until the volume is reduced to 0.105 L?

What is the molarity of the diluted solution when each of the following solutions is diluted to the given final volume?

1. (a) 1.00 L of a 0.250-M solution of Fe(NO₃)₃ is diluted to a final volume of 2.00 L
2. (b) 0.5000 L of a 0.1222-M solution of C₃H₇OH is diluted to a final volume of 1.250 L
3. (c) 2.35 L of a 0.350-M solution of H₃PO₄ is diluted to a final volume of 4.00 L
4. (d) 22.50 mL of a 0.025-M solution of C₁₂H₂₂O₁₁ is diluted to 100.0 mL

What is the final concentration of the solution produced when 225.5 mL of a 0.09988-M solution of Na₂CO₃ is allowed to evaporate until the solution volume is reduced to 45.00 mL?

An experiment in a general chemistry laboratory calls for a 2.00-M solution of HCl. How many mL of 11.9 M HCl would be required to make 250 mL of 2.00 M HCl?

What volume of a 0.20-M K₂SO₄ solution contains 57 g of K₂SO₄?

The US Environmental Protection Agency (EPA) places limits on the quantities of toxic substances that may be discharged into the sewer system. Limits have been established for a variety of substances, including hexavalent chromium, which is limited to 0.50 mg/L. If an industry is discharging hexavalent chromium as potassium dichromate (K₂Cr₂O₇), what is the maximum permissible molarity of that substance?

3.4: Other Units for Solution Concentrations