Private: Chapter Six
Key Terms, Key Equations, Summaries and Exercises (Chapter 6)
Key Terms
aqueous solution solution for which water is the solvent
Avogadro’s number (NA) experimentally determined value of the number of entities comprising 1 mole of substance, equal to 6.022 × 1023 mol−1
concentrated qualitative term for a solution containing solute at a relatively high concentration
concentration quantitative measure of the relative amounts of solute and solvent present in a solution
dilute qualitative term for a solution containing solute at a relatively low concentration
dilution process of adding solvent to a solution in order to lower the concentration of solutes
dissolved describes the process by which solute components are dispersed in a solvent
empirical formula mass sum of average atomic masses for all atoms represented in an empirical formula
formula mass sum of the average masses for all atoms represented in a chemical formula; for covalent compounds, this is also the molecular mass
mass percentage ratio of solute-to-solution mass expressed as a percentage
mass-volume percent ratio of solute mass to solution volume, expressed as a percentage
molar mass mass in grams of 1 mole of a substance
molarity (M) unit of concentration, defined as the number of moles of solute dissolved in 1 liter of solution
mole amount of substance containing the same number of atoms, molecules, ions, or other entities as the number of atoms in exactly 12 grams of 12C
parts per billion (ppb) ratio of solute-to-solution mass multiplied by 109
parts per million (ppm) ratio of solute-to-solution mass multiplied by 106
percent composition percentage by mass of the various elements in a compound
solute solution component present in a concentration less than that of the solvent
solvent solution component present in a concentration that is higher relative to other components
volume percentage ratio of solute-to-solution volume expressed as a percentage
% X =× 100%•
Key Equations
mass X mass compound
molecular or molar mass ⎛amu or g ⎞
- ⎝mol⎠
= n formula units/molecule
empirical formula mass ⎛amu or g ⎞
⎝
- (AxBy)n = AnxBny
M =
mol solute L solution
- C1V1 = C2V2
mol⎠
- mass of solution
Percent by mass = mass of solute × 100
ppm =× 10 ppm
mass solute6
mass solution
ppb =× 10 ppb
mass solute9
mass solution
Summary
The formula mass of a substance is the sum of the average atomic masses of each atom represented in the chemical formula and is expressed in atomic mass units. The formula mass of a covalent compound is also called the molecular mass. Due to the use of the same reference substance in defining the atomic mass unit and the mole, the formula mass (amu) and molar mass (g/mol) for any substance are numerically equivalent (for example, one H2O molecule weighs approximately18 amu and 1 mole of H2O molecules weighs approximately 18 g).
Determining Empirical and Molecular Formulas
The chemical identity of a substance is defined by the types and relative numbers of atoms composing its fundamental entities (molecules in the case of covalent compounds, ions in the case of ionic compounds). A compound’s percent composition provides the mass percentage of each element in the compound, and it is often experimentally determined and used to derive the compound’s empirical formula. The empirical formula mass of a covalent compound may be compared to the compound’s molecular or molar mass to derive a molecular formula.
Solutions are homogeneous mixtures. Many solutions contain one component, called the solvent, in which other components, called solutes, are dissolved. An aqueous solution is one for which the solvent is water. The concentration of a solution is a measure of the relative amount of solute in a given amount of solution. Concentrations may be measured using various units, with one very useful unit being molarity, defined as the number of moles of solute per liter of solution. The solute concentration of a solution may be decreased by adding solvent, a process referred to as dilution. The dilution equation is a simple relation between concentrations and volumes of a solution before and after dilution.
Other Units for Solution Concentrations
In addition to molarity, a number of other solution concentration units are used in various applications. Percentage concentrations based on the solution components’ masses, volumes, or both are useful for expressing relatively high concentrations, whereas lower concentrations are conveniently expressed using ppm or ppb units. These units are popular in environmental, medical, and other fields where mole-based units such as molarity are not as commonly used.
Exercises
1.
What is the total mass (amu) of carbon in each of the following molecules?
(a) CH4
(b) CHCl3
(c) C12H10O6
(d) CH3CH2CH2CH2CH3
2.
What is the total mass of hydrogen in each of the molecules?
(a) CH4
(b) CHCl3
(c) C12H10O6
(d) CH3CH2CH2CH2CH3
3.
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)
4.
Determine the molecular mass of the following compounds:
(a)
(b)
(c)
(d)
5.
Determine the molecular mass of the following compounds:
(a)
(b)
(c)
(d)
6.
Which molecule has a molecular mass of 28.05 amu?
(a)
(b)
(c)
6.2 Determining Empirical and Molecular Formulas
7.
What information is needed to determine the molecular formula of a compound from the empirical formula?
8.
Calculate the following to four significant figures:
(a) the percent composition of ammonia, NH3
(b) the percent composition of photographic fixer solution “hypo,” Na2S2O3
(c) the percent of calcium ion in Ca3(PO4)2
9.
Determine the following to four significant figures:
(a) the percent composition of hydrazoic acid, HN3
(b) the percent composition of TNT, C6H2(CH3)(NO2)3
(c) the percent of SO42– in Al2(SO4)3
10.
Determine the percent ammonia, NH3, in Co(NH3)6Cl3, to three significant figures.
11.
Determine the percent water in CuSO4∙5H2O to three significant figures.
12.
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
13.
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
14.
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?
15.
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?
16.
Determine the empirical and molecular formula for chrysotile asbestos. Chrysotile has the following percent composition: 28.03% Mg, 21.60% Si, 1.16% H, and 49.21% O. The molar mass for chrysotile is 520.8 g/mol.
17.
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:
(a) Lucite (Plexiglas); 59.9% C, 8.06% H, 32.0% O
(b) Saran; 24.8% C, 2.0% H, 73.1% Cl
(c) polyethylene; 86% C, 14% H
(d) polystyrene; 92.3% C, 7.7% H
(e) Orlon; 67.9% C, 5.70% H, 26.4% N
18.
A major textile dye manufacturer developed a new yellow dye. The dye has a percent composition of 75.95% C, 17.72% N, and 6.33% H by mass with a molar mass of about 240 g/mol. Determine the molecular formula of the dye.
6.3 Molarity
19.
Explain what changes and what stays the same when 1.00 L of a solution of NaCl is diluted to 1.80 L.
20.
What information is needed to calculate the molarity of a sulfuric acid solution?
21.
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?
22.
Determine the molarity for each of the following solutions:
(a) 0.444 mol of CoCl2 in 0.654 L of solution
(b) 98.0 g of phosphoric acid, H3PO4, in 1.00 L of solution
(c) 0.2074 g of calcium hydroxide, Ca(OH)2, in 40.00 mL of solution
(d) 10.5 kg of Na2SO4·10H2O in 18.60 L of solution
(e) 7.0 ×
10−3 mol of I2 in 100.0 mL of solution
(f) 1.8 ×
104 mg of HCl in 0.075 L of solution
23.
Determine the molarity of each of the following solutions:
(a) 1.457 mol KCl in 1.500 L of solution
(b) 0.515 g of H2SO4 in 1.00 L of solution
(c) 20.54 g of Al(NO3)3 in 1575 mL of solution
(d) 2.76 kg of CuSO4·5H2O in 1.45 L of solution
(e) 0.005653 mol of Br2 in 10.00 mL of solution
(f) 0.000889 g of glycine, C2H5NO2, in 1.05 mL of solution
24.
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.
25.
Consider this question: What is the mass of solute in 200.0 L of a 1.556-M solution of KBr?
(a) Outline the steps necessary to answer the question.
(b) Answer the question.
26.
Calculate the number of moles and the mass of the solute in each of the following solutions:
(a) 2.00 L of 18.5 M H2SO4, concentrated sulfuric acid
(b) 100.0 mL of 3.8 ×
10−6 M NaCN, the minimum lethal concentration of sodium cyanide in blood serum
(c) 5.50 L of 13.3 M H2CO, the formaldehyde used to “fix” tissue samples
(d) 325 mL of 1.8 ×
10−6 M FeSO4, the minimum concentration of iron sulfate detectable by taste in drinking water
27.
Calculate the number of moles and the mass of the solute in each of the following solutions:
(a) 325 mL of 8.23 ×
10−5 M KI, a source of iodine in the diet
(b) 75.0 mL of 2.2 ×
10−5 M H2SO4, a sample of acid rain
(c) 0.2500 L of 0.1135 M K2CrO4, an analytical reagent used in iron assays
(d) 10.5 L of 3.716 M (NH4)2SO4, a liquid fertilizer
28.
Consider this question: What is the molarity of KMnO4 in a solution of 0.0908 g of KMnO4 in 0.500 L of solution?
(a) Outline the steps necessary to answer the question.
(b) Answer the question.
29.
Consider this question: What is the molarity of HCl if 35.23 mL of a solution of HCl contain 0.3366 g of HCl?
(a) Outline the steps necessary to answer the question.
(b) Answer the question.
30.
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
31.
Calculate the molarity of each of the following solutions:
(a) 293 g HCl in 666 mL of solution, a concentrated HCl solution
(b) 2.026 g FeCl3 in 0.1250 L of a solution used as an unknown in general chemistry laboratories
(c) 0.001 mg Cd2+ in 0.100 L, the maximum permissible concentration of cadmium in drinking water
(d) 0.0079 g C7H5SNO3 in one ounce (29.6 mL), the concentration of saccharin in a diet soft drink.
32.
There is about 1.0 g of calcium, as Ca2+, in 1.0 L of milk. What is the molarity of Ca2+ in milk?
33.
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?
34.
If 0.1718 L of a 0.3556-M C3H7OH solution is diluted to a concentration of 0.1222 M, what is the volume of the resulting solution?
35.
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 of the resulting solution?
36.
What volume of a 0.33-M C12H22O11 solution can be diluted to prepare 25 mL of a solution with a concentration of 0.025 M?
37.
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?
38.
What is the molarity of the diluted solution when each of the following solutions is diluted to the given final volume?
(a) 1.00 L of a 0.250-M solution of Fe(NO3)3 is diluted to a final volume of 2.00 L
(b) 0.5000 L of a 0.1222-M solution of C3H7OH is diluted to a final volume of 1.250 L
(c) 2.35 L of a 0.350-M solution of H3PO4 is diluted to a final volume of 4.00 L
(d) 22.50 mL of a 0.025-M solution of C12H22O11 is diluted to 100.0 mL
39.
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?
40.
A 2.00-L bottle of a solution of concentrated HCl was purchased for the general chemistry laboratory. The solution contained 868.8 g of HCl. What is the molarity of the solution?
41.
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?
42.
What volume of a 0.20-M K2SO4 solution contains 57 g of K2SO4?
43.
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?
6.4 Other Units for Solution Concentrations
44.
Consider this question: What mass of a concentrated solution of nitric acid (68.0% HNO3 by mass) is needed to prepare 400.0 g of a 10.0% solution of HNO3 by mass?
(a) Outline the steps necessary to answer the question.
(b) Answer the question.
45.
What mass of a 4.00% NaOH solution by mass contains 15.0 g of NaOH?
46.
What mass of solid NaOH (97.0% NaOH by mass) is required to prepare 1.00 L of a 10.0% solution of NaOH by mass? The density of the 10.0% solution is 1.109 g/mL.
47.
What mass of HCl is contained in 45.0 mL of an aqueous HCl solution that has a density of 1.19 g cm–3 and contains 37.21% HCl by mass?
48.
The hardness of water (hardness count) is usually expressed in parts per million (by mass) of CaCO3, which is equivalent to milligrams of CaCO3 per liter of water. What is the molar concentration of Ca2+ ions in a water sample with a hardness count of 175 mg CaCO3/L?
49.
The level of mercury in a stream was suspected to be above the minimum considered safe (1 part per billion by weight). An analysis indicated that the concentration was 0.68 parts per billion. Assume a density of 1.0 g/mL and calculate the molarity of mercury in the stream.
50.
In Canada and the United Kingdom, devices that measure blood glucose levels provide a reading in millimoles per liter. If a measurement of 5.3 mM is observed, what is the concentration of glucose (C6H12O6) in mg/dL?
51.
A throat spray is 1.40% by mass phenol, C6H5OH, in water. If the solution has a density of 0.9956 g/mL, calculate the molarity of the solution.
52.
Copper(I) iodide (CuI) is often added to table salt as a dietary source of iodine. How many moles of CuI are contained in 1.00 lb (454 g) of table salt containing 0.0100% CuI by mass?
53.
A cough syrup contains 5.0% ethyl alcohol, C2H5OH, by mass. If the density of the solution is 0.9928 g/mL, determine the molarity of the alcohol in the cough syrup.
54.
D5W is a solution used as an intravenous fluid. It is a 5.0% by mass solution of dextrose (C6H12O6) in water. If the density of D5W is 1.029 g/mL, calculate the molarity of dextrose in the solution.
55.
Find the molarity of a 40.0% by mass aqueous solution of sulfuric acid, H2SO4, for which the density is 1.3057 g/mL.