Properties of Solutions
A solution is a mixture of materials, one of which is usually a fluid. A fluid is a material that flows, such as a liquid or a gas. The fluid of a solution is usually the solvent. The material other than the solvent is the solute. We say that we dissolve the solute into the solvent.
Some solutions are so common to us that we give them a unique name. A solution of water and sugar is called syrup. A solution of sodium chloride (common table salt) in water is called brine. A sterilized specific concentration (0.15 molar) of sodium chloride in water is called saline. A solution of carbon dioxide in water is called seltzer, and a solution of ammonia gas in water is called ammonia water.
A solution is said to be dilute if there is less of the solute. The process of adding more solvent to a solution or removing some of the solute is called diluting. A solution is said to be concentrated if it has more solute. The process of adding more solute or removing some of the solvent is called concentrating. The concentration of a solution is some measurement of how much solute there is in the solution.
It might initially offend your sensibilities to consider a solution in which the solvent is a gas or a solid. The molecules of a gas do not have much interaction among them, and so do not participate to a large extent in the dissolving process. Solids are difficult to consider as solvents because there is a lack of motion of the particles of a solid relative to each other. There are, however, some good reasons to view some mixtures of these types as solutions. The molecules of a gas do knock against each other, and the motion of a gas can assist in vaporizing material from a liquid or solid state. The fan in a 'frost free' home freezer moves air around inside the freezer to sublimate any exposed ice directly into water vapor, a process clearly akin to dissolving. Solid metals can absorb hydrogen gas in a mixing process in which the metal clearly provides the structure.
True solutions with liquid solvents have the following properties:
PROPERTIES OF SOLUTIONS
These last four of the properties of solutions collectively are called colligative properties. These characteristics are all dependent only on the number of particles of solute rather than the type of particle or the mass of material in solution.
Other Types of Mixtures
Take a spoonful of dirt and vigorously mix it with a glass of water. As soon as you stop mixing, a portion of the dirt drops to the bottom. Any material that is suspended by the fluid motion alone is only in temporary suspension. A portion of the dirt makes a true solution in the water with all of the properties of the above table, but there are some particles, having a diameter roughly between 1 nm and 500 nm, that are suspended in a more lasting fashion. A suspended mixture of particles of this type is called a colloid, or colloidal suspension, or colloidal dispersion.
For colloids or temporary suspensions the phrase dispersed material or the word dispersants describes the material in suspension, analogous to the solute of a solution. The phrase dispersing medium is used for the material of similar function to a solvent in solutions.
As with true solutions, it is a bit of a stretch to consider solids as a dispersing medium or gases as forming a large enough particle to be a colloid, but most texts list some such. A sol is a liquid or solid with a solid dispersed through it, such as milk or gelatin. Foams are liquids or solids with a gas dispersed into them. Emulsions are liquids or solids with liquids dispersed through them, such as butter or gold-tinted glass. Aerosols are colloids with a gas as the dispersing medium and either a solid or liquid dispersant. Fine dust or smoke in the air are good examples of colloidal solid in a gas. Fog and mist are examples of colloidal liquid in a gas.
Liquid dispersion media with solid or liquid dispersants are the most often considered. Homogenized whole milk is a good example of a liquid dispersed into a liquid. The cream does not break down into molecular sized materials to spread through the milk, but collects in small micelles of oily material and proteins with the more ionic or hydrophilic portions on the outside of the globule and the more fatty, or oily, or non-polar, or hydrophobic portions inside the ball-shaped little particle. Blood carries liquid lipids (fats) in small bundles called lipoproteins with specific proteins making a small package with the fat.
Proteins are in a size range to be considered in colloidal suspension in water. Broth or the independent proteins of blood or the casein (an unattached protein) in milk are colloidal. There are many proteins in the cellular fluids of living things that are in colloidal suspension.
Colloidal dispersants in water stay in suspension by having a layer of charge on the outside of the particle that is attractive to one end of water molecules. The common charge of the particles and the water solvation layer keep the particles dispersed. A Cottrell precipitator collects the smoke particles from air by a high voltage charge and collection device. Boiling an egg will denature and coagulate the protein in it. Proteins can be fractionally 'salted out' of blood by adding specific amounts of sodium chloride to make the proteins coagulate. The salt adds ions to the liquid that interfere with the dispersion of the colloidal particles.
Colloids with liquid as a dispersing agent have the following properties:
PROPERTIES OF COLLOIDS
The concentration of a solution is an indication of how much solute there is dissolved into the solvent. There are a number of ways to express concentration of a solution. By far the most used and the most useful of the units of concentration is molarity. You might see '6 M HCl' on a reagent bottle. The 'M' is the symbol for molar. One molar is one mol of solute per liter of solution. The reagent bottle has six mols of HCl per liter of acid solution. Since the unit 'molar' rarely appears in the math of chemistry other than as a concentration, to do the unit analysis correctly, you will have to insert concentrations into the math as 'mols per liter' and change answers of 'mols per liter' into molar.
Molality is concentration in mols of solute per kilogram of solvent. Mol fraction is the number of mols of solute per number of mols of solution. Weight-weight percent (really mass percent) is the number of grams of solute per grams of solution expressed in the form of a percent. Mass-volume concentration is the number of grams of solute per milliliter of solution. There are other older units of concentration, such as Baume (or Baumé), that are still in use, mainly in industrial chemicals.
Normality is the number of mols of effective material per liter. In acid-base titrations, the hydroxide ion of bases and the hydrogen (hydronium) ion of acids is the effective material. Sulfuric acid (H2SO4) has two ionizable hydrogens per formula of acid, or one mol of acid has two mols of ionizable hydrogen. 0.6 M H2SO4 is the same concentration as 1.2 N H2SO4.
We say that sulfuric acid is diprotic because it has two protons (hydrogen ions) per formula available. Hydrochloric acid (HCl) is monoprotic, phosphoric acid (H3PO4) is triprotic, and acids with two or more ionizable hydrogens are called polyprotic. Sodium hydroxide (NaOH) is monobasic, calcium hydroxide (Ca(OH)2) is dibasic, and aluminum hydroxide (Al(OH)3) is tribasic.
Where 'X' is the number of available hydrogen ions or hydroxide ions in an acid or base, N, the normality, is equal to the molarity, M, times X.
The normality system can be used for redox reactions, but the effective material is now available electrons or absorption sites for electrons. Consider the following reaction, #43 in the redox section.
In a sulfuric acid solution potassium permanganate will titrate with oxalic acid to produce manganese II sulfate, carbon dioxide, water, and potassium sulfate in solution.
|5e- + Mn+7 Mn+2 Reduction|
5( C+3 C+4 + e-) Oxidation
|Balanced 2 KMnO4 + 5 H2C2O4 + 3 H2SO4 2 MnSO4 + 10 CO2 + 10 H2O + 2 KCl|
Since the manganese has a place for five electrons and the potassium permanganate contains the manganese, we could say that the normality of the permanganate solution is five times the molarity. The oxalic acid solution contains the carbon that becomes oxidized with only one electron added. The normality of the oxalic acid solution is the same as the molarity.
Where 'X' is the number of electrons either donated or accepted by a material in a redox reaction, the normality, N, is the molarity, M, times X.
In acid-base or redox titrations, the math is made easier by the use of normality. There is no need for a chemical equation because only the net reaction is considered. Where 'C' is the concentration in normality, and 'V' is the volume of solution, the formula is:
C1 V1 = C2 V2
Dissolving Solids Into Liquids
The best way to measure the amount of a solid material is usually to weigh it. The best way to find the amount of a liquid is to find the volume. The formula for solutions is: C V = n, where C is concentration in molar, V is the volume in liters, and n is the number of mols of solute. Further, n = m/Fw , where m is the mass and Fw is the formula weight of the solute. Solving for the mass, m = C V Fw.
C V = n
How do you make the solution of a solid in a liquid. First weigh the solid to get the mass. The concentration you want times the volume of solution times the formula weight of the solute will get you the mass of solute you need to weigh. Place the mass of solute in a volume measuring device such as a volumetric flask or a graduated cylinder. Use a small amount of water to dissolve the solute in the volumetric device. Add water to the volume desired and mix.
The act of dissolving a solid into a liquid is a process that happens on the surface of the particles of the solute. The smaller the particles (the larger the surface area) the faster the solute dissolves. Triple-X sugar, called 'confectioner's sugar,' has smaller particles than regular 'table sugar.' Rock candy is just regular table sugar that has been crystallized in large lumps. When you put each crystal size the chemically identical materials in your mouth, which one dissolves faster? The triple-X sugar tastes sweetest because more of it has dissolved in the same short time. (You can only taste dissolved sugar.)
Expose the surface area of the solid to more solid and the solute will dissolve faster. Mixing helps dissolve the solid. You can try this with sugar. Take two glasses of water at the same temperature and add a spoonful of sugar to each. Mix one, but not the other. In which glass does the sugar dissolve more easily?
Most solid materials will dissolve faster with increased temperature. Since the increased temperature increases the motion of the molecules, you can think of this effect as being similar to mixing. You have seen this effect. Sugar dissolves more quickly in warm tea than iced tea. Table salt dissolves more quickly in hot water than in cold.
HOW TO DISSOLVE A SOLID INTO A LIQUID
- Increase surface area of solid by decreasing the size of particle.
- Increase temperature of the mixture.
Dissolving Gases Into Liquids
Gases are more easily measured by knowing the pressure, volume, and temperature of the gas. Seltzer water and ammonia water are two good examples of solutions of a gas in a liquid. Seltzer, or carbonated water, is the result of pressing carbon dioxide gas into water. Seltzer is used as the base liquid in any carbonated beverage. The bubbles in beer or sparkling wines are also due to carbon dioxide, but the CO2 is a natural product of the fermentation process, so it does not have to be added artificially. Ammonia water, also called ammonium hydroxide solution, is made from ammonia (NH3) being pressed into water. It is used as a weak base and as a cleaning material, particularly for glass.
Because the process is better done under pressure, it is often difficult to directly observe the actual dissolving done in most cases. The notable exception is the addition of dry ice, solid carbon dioxide, to water as described in the section on carbon dioxide.
As with a solid dissolving in a liquid, a gas dissolves in a liquid more easily with agitation or mixing, but that is where the similarity ends. Remove a carbonated beverage from its container and it becomes obvious that pressure is necessary to keep the gas in the liquid. The drink fizzes and bubbles, releasing the gas. As the beverage sits for a few hours, the taste becomes what we describe as 'flat.' Almost all of the carbon dioxide has escaped from the liquid. The only CO2 remaining in the water will produce a partial pressure equal to the partial pressure of the gas in the atmosphere. Water carries dissolved oxygen from the partial pressure of the oxygen in the atmosphere.
As the combination of liquid and gas is NOT the favored (lowest energy) condition, an increase in temperature causes the separation. Lower temperature favors dissolving the gas into the liquid. You can verify this experimentally on your own. Leave one can of carbonated beverage at room temperature. Refrigerate a can of the same carbonated beverage. Gently heat a third can of the same beverage. Open them all and record the results. You are likely to find that the gas stays in solution better in the cooler liquid.
HOW TO DISSOLVE A GAS INTO A LIQUID
- Increase the gas pressure on the liquid.
- Decrease the temperature.
Liquids In Liquids
A solution of two liquids is relatively uncomplicated. For the most part, liquids either mix together or they don't. When liquids will mix together, they usually do so in all proportions and are said to be miscible. If they do not mix, as oil and water, they are said to be immiscible. Using ethyl alcohol and water as examples of miscible liquids, we can have a solution of the two liquids with one drop of alcohol in a bucketful of water or one drop of water in a bucketful of alcohol.
Immiscible liquids can make a mixture of the nature of a colloidal suspension by very finely dividing one of the liquids and dispersing it through the other liquid. Milk fresh from the cow separates into a milk and a cream layer, the cream rising to the top. The cream of milk is a fatty material of a lower density, so it floats. The milk may be homogenized, a process that violently shakes the milk so that the cream forms very small ball-shaped particles. This homogenized milk will remain well mixed with normal treatment.
The stability of homogenized milk as a mixture is helped by the presence of the proteins of milk. Proteins often have areas of large amounts of available electrical charge and areas of very little charge. The areas of higher charge are more soluble in water and the areas of lower charge are more soluble in the fat of the cream. In this way the protein acts as a surface active agent, or surfactant. A surfactant is a large molecule with one area in one liquid and another area in another. Proteins of milk on the surface of the small globules of fat in homogenized milk will keep the globules from attaching back to each other, so the milk stays homogenized. Soaps and detergents are surfactants that help get oily dirt into suspension in water.
Agitation (mixing) is usually the most important factor in making a liquid-liquid mixture. The agitation of milk to homogenize it is a good example for colloids, but many other liquids do not mix without considerable agitation. If you make a highly concentrated syrup and pour it into water, the syrup will drop to the bottom of the water and stay there until it is agitated or (in a much longer time) diffusion mixes the layers.
For the best view of solubility, we will use the examples of a solid solute dissolved into a liquid solvent. This does not mean that other materials do not work in the same fashion.
The solubility of a solution is a measure of how much of the solute can be dissolved into the solvent. The solution reaches a point called the saturation point when no more solute will be accepted by the solvent. Any further addition of solute will result in solid solute mixed in with the saturated solution. Each solvent and solute pair has a characteristic solubility at a given temperature. Usually as you increase the temperature, an increased amount of solute will be able to dissolve.
Take a Pyrex measuring cup and put in exactly a cup of table sugar. Heat water to boiling and pour in a small amount. Notice what happens. The volume of material in the cup appears to shrink! Continue adding boiling water until the level is back up to the 'one cup' mark. Notice the temperature of the solution. It takes heat to dissolve sugar. Stir. You should be able to almost dissolve all the sugar. The solution should be very close to the saturation point at that temperature. The solution should end up at about room temperature. Now add a few heaping tablespoons of sugar. Stir and attempt to dissolve all the sugar. If you succeed, add another few tablespoonsful of sugar. Put the saturated solution with a lot of undissolved sugar into the microwave, and heat until all the sugar is dissolved. If you have a meat thermometer, find the temperature of the boiling mixture. (Be careful. The solution is VERY hot. Handle with something to insulate you from the heat.)
Observe the solution after you take it out of the microwave and put it on the counter. Notice the temperature at which the sugar crystals begin to form again.
If you have done the experiment just right, you may see the crystals appearing at a temperature far below what you might think. If you boil the solution enough in the microwave, you will dissolve all traces of a seed crystal for the saturated solution to deposit sugar onto. At one time your solution will be supersaturated, or beyond the normal amount of solute in the solution. Supersaturation is an unstable condition. If any crystal is presented to a supersaturated solution, the crystallization of the solute onto it will occur fairly rapidly.
At home if you have done this demonstration with only sugar and water in a clean cup, don't waste the sugar solution. A little bit of maple flavoring will make it a fine syrup for pancakes, or you can use it in the frosting of the chocolate cake I have published here on the site. Do not eat any material made at school. Lab materials may contain traces of contaminants. If you eat anything in the school laboratory, the school lawyers will turn green and purple, have a conniption fit, and likely take their discomfort out upon you.
Solubility of salts depends upon the type of ions in the salt. There is a very great range of solubility of salts in water. Even the most insoluble, such as silver chloride, have a very small but detectable solubility. Some salts, called deliquescent salts, are so soluble that they grab water molecules out of the air and can dissolve themselves in this way.
Using the simplification of classifying materials as either soluble or not in water at room temperature, there are some nice easy general rules for predicting whether or not a salt will dissolve in water. These rules are useful not just for predicting how to make solutions, but ion reactions, such as a double displacement reaction, depend upon the insolubility of a salt as a possible product for the reaction to happen. Depending upon what your instructor suggests, it may be a good idea for you to know the following rules:
(a) Almost all simple ionic compounds with Group I elements (lithium and elements below it on the Periodic Table) or ammonium ion, (NH4)+, are soluble.
(b) All nitrates (NO4)-, most sulfates, (SO4)2-, and most chlorides, Cl-, are soluble. ** Notable insoluble exceptions to this rule are: barium sulfate, Ba(SO4), lead II sulfate, Pb(SO4), and silver chloride, AgCl.
(c) Most hydroxides, (OH)-, carbonates, (CO3)2- sulfides, S2-, and phosphates, (PO4)3-, are insoluble except for the compounds of rule (a). Barium hydroxide, Ba(OH)2 is a soluble exception to this rule.
The colligative properties of solutions have already been mentioned in the section on properties of solutions. A colligative property is one that depends only on the number of particles in solution rather than the type of particle. Molecular solutes have only one particle per formula, but ionic materials come apart into their ions and have almost as many particles in the solution as there are ions available. The word 'almost' was included on purpose because there is a small tendency for ions to re-associate with each other, making ion pairs that decrease the number of particles. The ion pair effect depends upon the properties of the species dissolved and the concentration of solute. The more concentrated the solute, the greater percentage of ion pairing takes place.
The colligative properties of solutions are;
- The solution shows an increase in osmotic pressure between it and a reference solution as the amount of solute is increased.
- A solution of a solid non-volatile solute in a liquid solvent shows a decrease in vapor pressure above the solution as the amount of solute is increased.
- The solution shows an increase in boiling point as the amount of solute is increased.
- The solution shows a decrease in melting point as the amount of solute is increased.
Osmotic pressure occurs when a semipermeable membrane divides two solutions, one of which has more solute than the other. A semipermeable membrane is one that lets through water but not some materials in solution or in suspension in the water. Semipermeable membranes are an important part of any living thing. Cell membranes are semipermeable. The membranes on the outside of eggs are semipermeable. Trees pull up water from their roots by osmosis.
Here is an easy way to demonstrate osmotic pressure. Take two similar hen's eggs and keep them in a dilute vinegar solution for a few days. The acid in the vinegar will react with the calcium compounds that are the hardening materials for the shell. There are two semipermeable membranes under the hard shell of the egg. Replace the vinegar solution if the process stops for a few days before all of the shell is removed. When all of the hard shell has gone, compare the size of the eggs. They should be fairly close. Put one egg into pure water (or tap water). Put the other egg into a brine solution (table salt dissolved in water). Observe the eggs over a few days.
Water goes through the semipermeable membrane in a direction to make the particle concentration on either side equal. The egg in just water will absorb water and become very large. The egg in brine will shrivel from water going out of it. The tight skin on the large egg is a demonstration of the pressure provided by osmosis.
Don't eat the eggs. Open them up and see what's inside. Inspect them carefully, particularly the yolk and its size. The membranes of the egg are a pretty good barrier to bacteria, but the stretched membrane particularly may not be able to keep bacteria out. Smell the eggs after you have opened them. Is there an odor that would indicate bacterial contamination? Cook them to see if the proteins react the same way as other eggs, but do not eat them due to the possibility of hidden bacterial contamination.
Red blood corpuscles (in humans) are not much more than semipermeable bags containing oxygen-absorbing protein (hemoglobin) floating in the blood. If you were to pump pure water into a person, the osmotic pressure due to the difference in osmolarity would swell and burst the red corpuscles. If the blood plasma has too many dissolved particles, the red corpuscles would shrivel up or crenate. Saline is a solution that is designed to be the same osmolarity as the cellular and corpuscular contents.
Honey has some moisture in it that is close to saturation in sugar. Take two small shallow dishes and put in an equal (small) amount of honey in one and water in the other. Leave them exposed to the air in the same place, and observe them over a few days. The sugar in the honey will reduce the vapor pressure of the solution.
The boiling point of a liquid is just the point at which the vapor pressure of the liquid equals the surrounding pressure. If the vapor pressure decreases, it will take a greater temperature to boil the liquid.
Put a small amount of honey in the bottom of a glass and about the same level of water in the same kind of glass. Place them both in a microwave oven. Which one boils first? Try the same experiment with various amounts of salt in solution.
It may be that the dissolved materials block the water molecules from attaching on to the rest of the water crystal. Or possibly that the dissolved material holds on to the water molecules more tightly than the water in the crystals.
Whatever the cause, you have seen this in action in the making of homemade barrel ice cream. The barrel on the outside of the ice cream container has ice and salt (sodium chloride) in it. The ice melts (grabs up the heat) at a temperature lower than the usual melting point of water. Just ice in the barrel would not work, because it does not get cold enough to freeze the ice cream inside that has dissolved materials in it itself.
Concentration Math in Stoichiometry
If you are given the concentration and volume of a solution, you know the amount of solute in that solution. ( C V = n ) The concentration times volume can serve as the 'given' and will go directly to the mol ratio on the stoichiometry roadmap.
Since C V = n, and the first thing found from stoichiometry is the number of mols of a material (n), if you need to find the volume of a known concentration of a solution, you must attach (1/C) to the end of the roadmap to get the volume. If you need to find the concentration of a known volume of a solution, you must attach (1/V) to the end of the roadmap DA.
Math Problems on Concentration
1. Explain how to make up five liters of a 0.175 M NaCl solution.
2. What volume of 0.86 M table sugar (C12H23O12) has 50 grams of sugar in it?
3. How many grams of KMnO4 would you get if you evaporated the water from 85.75 mL of 1.27 M solution?
4. To what volume must you dilute 15 grams of silver nitrate to make it 0.05 M?
5. What is the concentration of KCl if five grams of it are in 25.3 L?
6. How many moles of chlorine gas are in 17 L of 1.02 M solution?
7. How many grams of sulfuric acid are in 5 mL of 3.2 M acid?
8. I make up 500 ml of 0.1 M sodium hydroxide solution. Explain how I did it.
9. To what volume must you take 27 g of table salt if you want a physiological saline solution? (Physiological saline is 0.15 M NaCl.)
10. What is the concentration of silver nitrate if 15 grams of it are dissolved into 14.28 liters?
11. How many moles of NaCl are in 68 mL of a 0.15 M NaCl solution?
(That is physiological saline when sterilized.)
12.How many grams of NaCl do you have to put into a 5 liter container to make a physiological saline solution?
13. What volume of physiological saline solution would give you a gram of salt when evaporated?
14. What is the concentration of KCl if ten grams are dissolved in enough water to make 12 liters?
WRITE AND BALANCE THE CHEMICAL EQUATION FOR THOSE PROBLEMS THAT NEED IT.SHOW ALL YOUR WORK. USE W5P OR DA METHOD ACCORDING TO THE ROADMAP.
15. Sodium hydroxide and hydrochloric acid combine to make table salt and water. 14 mL of 0.1 M sodium hydroxide is added to an excess of acid. How many moles of table salt are made? How many grams of salt is that?
16. 50 mL of 0.25 M copper II sulfate evaporates to leave CuSO4 · H2O. (That is the pentahydrate crystal of copper II sulfate.) What is the mass of this beautiful blue crystal from the solution?
17. Chlorine gas is bubbled into 100 mL of 0.25 M potassium bromide solution. This produces potassium chloride and bromine gas. The bromine (which dissolves in water) is taken from the solution and measured at 27°C and 825 mmHg. What is the volume of bromine?
18. 95 mL of 0.55 M sulfuric acid is put on an excess of zinc. This produces zinc sulfate and hydrogen. How many grams of zinc sulfate are made?
19. 27.6 mL of a 0.19 M solution of silver nitrate and 15.4 mL of an unknown (but excess) amount of sodium chloride combine to make a white precipitate silver chloride and some dissolved sodium nitrate. (a) How many moles of silver chloride are made? (b) How many grams of silver chloride is that? (c) How many moles of sodium nitrate are made? (d) What is the concentration of sodium nitrate in the final solution?
20. What mass (how many grams) of potassium permanganate, KMnO4, is needed to make 1.72 liters of 0.29 M solution?
21. By my calculations, a drop of ethyl alcohol, C2H5OH , in an olympic-sized swimming pool produces a 1.2 E-10 M solution of alcohol in water. A drop is a twentieth of a mL. How many molecules of ethyl alcohol are in a drop of the water in the pool?
22. 93 mL of 0.15 M magnesium hydroxide is added to 57 mL of 0.4 M nitric acid. (Magnesium nitrate and water are formed.) What is the concentration of the magnesium nitrate after the reaction?
23. Does concentration ruin your concentration?
ANSWERS TO MATH PROBLEMS
|1. (a) Weigh out 51.2 grams of NaCl. (b) Dissolve the solid in a small amount of water in a suitable volumetric device. (c) Bring the solution to volume by adding water (q.s.) and mix to completely disburse.|
|2. 0.162 L||3. 17.2 g||4. 1.77 L||
|5. 2.65 m mols||6. 17.34 mols||7. 1.57 g||
|8. (a) Weigh out 2.00 grams of NaOH. (b) Dissolve the solid in a small amount of water in a suitable volumetric device. (c) Bring the solution to volume by adding water (q.s.) and mix to completely disburse.||
|9. 3.08 L||10. 6.18 m molar||11. 10.2 millimols||
|12. 43.9 g||13. 0.114 L||14. 0.0112 M||
|15a. 1.4 E-3 mols||15b. 0.0819 g||16. 3.12 g||
|17. 284 ml||18. 8.44 g||19a. 5.24 E-3 mols||
|19b. 0.752 g||19c. 5.24 E-3 mols||19d. 122 mmolar||
|20. 78.8 g||21. 3.61 E9 molecules||22. 0.152 M||