General Chemistry/Properties of Solutions

Concentration

The concentration of a solution is the measure of how much solute and solvent there is. A solution is concentrated if it contains a large amount of solute, or dilute if contains a small amount.

Molarity

Molarity is the number of moles of solute per liter of solution. It is abbreviated with the symbol M, and is sometimes used as a unit of measurement, e.g. a 0.3 molar solution of HCl. In that example, there would be 0.3 moles of HCl for every liter of water (or whatever the solvent was).

Molality

Molality is the number of moles of solute per kilogram of solvent. It is abbreviated with the symbol m (lowercase), and is sometimes used as a unit of measurement, e.g. a 0.3 molal solution of HBr. In that example, there would be 0.3 moles of HBr for every kilogram of water (or whatever the solvent was).

Mole Fraction

The mole fraction is simply the moles of solute per moles of solution. As an example, you dissolve one mole of NaCl into three moles of water. Remember that the NaCl will dissociate into its ions, so there are now five moles of particles: one mole Na⁺, one mole Cl^-, and three moles water. The mole fraction of sodium is 0.2, the mole fraction of chloride is 0.2, and the mole fraction of water is 0.6.

The mole fraction is symbolized with the Greek letter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \chi} (chi), which is often written simply as an X.

Dilution

Dilution is adding solvent to a solution to obtain a less concentrated solution. Perhaps you have used dilution when running a lemonade stand. To cut costs, you could take a half-full jug of rich, concentrated lemonade and fill it up with water. The resulting solution would have the same total amount of sugar and lemon juice, but double the total volume. Its flavor would be weaker due to the added water.

Chemists often keep highly concentrated solutions of useful chemicals. They can quickly obtain more dilute solutions of known concentration by this method.

The key concept is that the amount of solute is constant before and after the dilution process. The concentration is decreased (and volume increased) only by adding solvent.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle moles_1 = moles_2}	Thus, the number of moles of solute before and after dilution are equal.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M \times V = moles}	By definition of molarity, you can find the moles of solvent.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle M_1 \times V_1 = M_2 \times V_2}	Substituting the second equation into the first gives the dilution equation.

To determine the amount of solvent (usually water) that must be added, you must know the initial volume and concentration, and the desired concentration. Solving for Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_2} in the above equation will give you the total volume of the diluted solution. Subtracting the initial volume from the total volume will determine the amount of pure solvent that must be added.

Ionic Solutes

When ionic compounds dissolve in water, they separate into ions. This process is called dissociation. Note that because of dissociation, there are more moles of particles in the solution containing ions than there would be with the solute and solvent separated.

If you have two glasses of water, and you dissolve salt into one and sugar into the other, there will be a big difference in concentration. The salt will dissociate into its ions, but sugar (a molecule) will not dissociate. If the salt were NaCl, the concentration would be double that of the sugar. If the salt were MgCl₂, the concentration would be triple (there are three ions).

Solubility Rules

Not all ionic compounds are soluble. Some ionic compounds have so much attractive force between their anions and cations that they will not dissociate. These substances are insoluble and will not dissolve. Instead, they clump together as a solid in the bottom of solution. Many ionic compounds, however, will dissociate in water and dissolve. In these cases, the attractive force between ion and water is greater than that between cation and anion. There are several rules to help you determine which compounds will dissolve and which will not.

Solubility Rules

1. All compounds with Group 1 ions or ammonium ions are soluble.
2. Nitrates, acetates, and chlorates are soluble.
3. Compounds containing a halogen are soluble, except those with fluorine, silver, or mercury. If they have lead, they are soluble only in hot water.
4. Sulfates are soluble, except when combined with silver, lead, calcium, barium, or strontium.
5. Carbonates, sulfides, oxides, silicates, and phosphates are insoluble, except for rule #1.
6. Hydroxides are insoluble except when combined with calcium, barium, strontium, or rule #1.

Sometimes, when two different ionic compounds are dissolved, they react, forming a precipitate that is insoluble. Predicting these reactions requires knowledge of the activity series and solubility rules. These reactions can be written with all ions, or without the spectator ions (the ion that don't react, present on both sides of the reaction), a format known as the net ionic equation.

For example, silver nitrate is soluble, but silver chloride is not soluble (see the above rules). Mixing silver nitrate into sodium chloride would cause a cloudy white precipitate to form. This happens because of a double replacement reaction.

Electrolytes

When solutes dissociate (or if a molecule ionizes), the solution can conduct electricity. Compounds that readily form ions, thus being good conductors, are known as strong electrolytes. If only a small amount of ions are formed, electricity is poorly conducted, meaning the compound is a weak electrolyte.

Colligative Properties

Some properties are the same for all solute particles regardless of what kind. These are known as the colligative properties. These properties apply to ideal solutions, so in reality, the properties may not be exactly as calculated. In an ideal solution, there are no forces acting between the solute particles, which is generally not the case.

Vapor Pressure

All liquids have a tendency for their surface molecules to escape and evaporate, even if the liquid is not at its boiling point. This is because the average energy of the molecules is too small for evaporation, but some molecules could gain above average energy and escape. Vapor pressure is the measure of the pressure of the evaporated vapor, and it depends on the temperature of the solution and the quantities of solute. More solute will decrease vapor pressure.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle P_{solution} = P_{pure~solvent} \times \chi_{solvent}}

The vapor pressure is given by Rauolt's Law, where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \chi} is the mole fraction of the solvent. Notice that the vapor pressure equals that of the pure solvent when there is no solute (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \chi = 1} ). If Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \chi = 0} , there would be no vapor pressure at all. This could only happen if there were no solvent, only solute. A solid solute has no vapor pressure.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle P_{solution} = P_{1} \times \chi_{1} + P_{2} \times \chi_{2}}

If two volatile substances (both have vapor pressures) are in solution, Rauolt's Law is still used. In this case, Rauolt's Law is essentially a linear combination of the vapor pressures of the substances. Two liquids in solution both have vapor pressures, so this equation must be used.

The second equation shows the relationship between the solvents. If two liquids were mixed exactly half-and-half, the vapor pressure of the resulting solution would be exactly halfway between the vapor pressures of the two solvents.

Another relation is Henry's Law, which shows the relationship between gas and pressure. It is given by C_g = k P_g , where C is concentration and P is pressure. As the pressure goes up, the concentration of gas in solution must also increase. This is why soda cans release gas when they are opened - The decrease in pressure results in a decrease in concentration of CO₂ in the soda.

Exercise for the reader

At 50 °C the vapor pressure of water is 11 kPa and the vapor pressure of ethanol is 30 kPa. Determine the resulting vapor pressure if a solution contains 75% water and 25% ethanol (by moles, not mass).

Boiling Point Elevation

A liquid reaches its boiling point when its vapor pressure is equal to the atmosphere around it. Because the presence of solute lowers the vapor pressure, the boiling point is raised. The boiling point increase is given by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Delta T_{solution} = K_b \times m_{solute}}

The reduced vapor pressure increases the boiling point of the liquid only if the solute itself is non-volatile, meaning it doesn't have a tendency to evaporate. For every mole of non-volatile solute per kilogram of solvent, the boiling point increases by a constant amount, known as the molal boiling-point constant (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_b} ). Because this is a colligative property, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_b} is not affected by the kind of solute.

Freezing Point Depression

This explains why roads are salted in the winter.

A liquid reaches its freezing temperature when its vapor pressure is equal to that of its solid form. Because the presence of the solute lowers the vapor pressure, the freezing point is lowered. The freezing point depression is given by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \Delta T_{solution} = K_f \times m_{solute}}

Again, this equation works only for non-volatile solutes. The temperature of the freezing point decreases by a constant amount for every one mole of solute added per kilogram solvent. This constant (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle K_f} ) is known as the molar freezing-point constant.

Osmosis

Osmosis results from the tendency for concentration to distribute itself evenly.

If you studied biology, you would know that osmosis is the movement of water through a membrane. If two solutions of different molarity are placed on opposite sides of a semipermeable membrane, then water will travel through the membrane to the side with higher molarity. This happens because the water molecules are "attached" to the solvent molecules, so they cannot travel through the membrane. As a result, the water on the side with lower molarity can more easily travel through the membrane than the water on the other side.

The pressure of this osmosis is given in the equation

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \pi = MRT}

Where pi is the pressure, M is molarity, R is the gas constant, and T is temperature in Kelvin.

Electrolytes and Colligative Properties

When one mole of table salt is added to water, the colligative effects are double those that would have occurred if sugar were added instead. This is because the salt dissociates, forming twice as many particles as sugar would. This dissociation, called the Van't Hoff Factor describes how many particles that are dissociated into the solution and must be multiplied into the Boiling Point Elevation or Vapor Pressure Lowering equations.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1~mol~\hbox{C}_6\hbox{H}_{12}\hbox{O}_{2(s)} \to 1~mol~\hbox{C}_6\hbox{H}_{12}\hbox{O}_{2(aq)}}	Sugar is a covalent molecule. No dissociation occurs when dissolved.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1~mol~\hbox{NaCl}_{(s)} \to 1~mol~\hbox{Na}^+_{(aq)} + 1~mol~\hbox{Cl}^-_{(aq)} = 2~mol~particles}	Table salt is an ionic compound and a strong electrolyte. Total dissociation occurs when dissolved, doubling the effects of colligative properties.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle 1~mol~\hbox{MgBr}_{2(s)} \to 1~mol~\hbox{Mg}^{2+}_{(aq)} + 2~mol~\hbox{Br}^-_{(aq)} = 3~mol~particles}	Magnesium bromide is also ionic. The colligative effects will be tripled.

Though extremely useful for calculating the general Van't Hoff Factor, this system of calculation is slightly inaccurate when considering ions. This is because when ions are in solution, they may interact and clump together, lessening the effect of the Van't Hoff factor. In addition, more strongly charged ions may have a smaller effect. For example, CaO would be less effective as an electrolyte than NaCl.