Comprehensive Study Notes: Solution Concentration, Solubility, and Chemical Reactions

Solution Concentration and Percentage-Based Units

Fundamentals of Concentration

Concentration is defined as the strength of a solution, representing the ratio of the amount of solute to the total amount of solution: $\text{Concentration} = \frac{\text{Amount of Solute}}{\text{Amount of Solution}}$

The amount of solute can be expressed in terms of mass, volume, or the number of molecules.

Percent Concentrations

A percent concentration is a unit equal to the number of grams or milliliters of solute per 100 mL of solution.

Weight per Volume (w/v)

This represents the number of grams of solute per $100\,mL$ of solution, expressed as a percentage. It is primarily used when the solute is a solid.

• Example: $5.0\%\,(\text{w/v})$ glucose solution means there are $5.0\,g$ of glucose in every $100\,mL$ of solution.

• Formula: $\text{P.C. (w/v)} = \frac{\text{Amount of solute (g)}}{\text{Volume of solution (mL)}} \times 100$

Volume Percentage (v/v)

This represents the number of milliliters of solute per $100\,mL$ of solution, expressed as a percentage. It is used when the solute is a liquid.

• Example: $5.0\%\,(\text{v/v})$ Alcohol means there are $5.0\,mL$ of alcohol in every $100\,mL$ of solution.

Sample Problems

• Problem 5.1: A solution contains $15\,g$ of $NaCl$ in a total volume of $360\,mL$.   $\frac{15\,g\,NaCl}{360\,mL} \times 100 = 4.17\%\,(\text{w/v})$

• Problem 5.2: Calculating mass from percentage. For a $5\%\,(\text{w/v})$ urea solution, how much urea is in $600\,mL$?   $600\,mL\,\text{solution} \times \frac{5\,g\,\text{urea}}{100\,mL\,\text{solution}} = 30\,g\,\text{urea}$

Very Low Concentrations and Clinical Units

In medical contexts, mass units like milligrams ($mg = 1/1000\,g$), micrograms ($\mu g = 1/1,000,000\,g$), or nanograms ($ng = 1/1,000,000,000\,g$) are often measured per deciliter ($dL$).

Relationships to Percentage (w/v)

• $1\,mg/dL = 0.001\%$

• $1\,\mu g/dL = 0.000001\%$

• $1\,ng/dL = 0.000000001\%$

Clinical Examples

• Blood Glucose: $90\,mg/dL$

• Iron: $100\,\mu g/dL$

• Thyroxine in plasma: $11\,ng/dL$

Parts Per Million and Billion

• Parts per million (ppm): Equivalent to $1\,\mu g$ in $1\,mL$ of solution.

• Parts per billion (ppb): Equivalent to $1\,ng$ in $1\,mL$ of solution.

Sample Problem 5.3

Calculate concentration in $mg/dL$ and $ppm$ for $0.25\,mg$ of niacin in $5\,dL$ of solution.

1. $C = \frac{0.25\,mg}{5\,dL} = 0.05\,mg/dL$

2. Converting to $ppm$: $0.05\,mg/dL \times \frac{1\,dL}{100\,mL} \times \frac{1000\,\mu g}{1\,mg} = 0.5\,\mu g/mL = 0.5\,ppm$

Solubility and Molecular Structure

Defining Solubility

Solubility is the maximum possible concentration of a solute in a specific solvent.

• Example: The solubility of $NaCl$ in water is $360\,g/L$.

• Unsaturated Solution: Contains less than the maximum possible concentration of solute.

• Saturated Solution: Contains exactly the maximum possible concentration of solute.

• Insoluble Compounds: These actually dissolve in water, but only to a very small extent.

Effects of Temperature and Pressure

Temperature

• Solids: The solubility of a solid in water generally increases as the temperature increases (e.g., sugar in water).

• Gases: Gases dissolve better in cold water than in hot water. The solubility of a gas decreases as temperature increases (e.g., $O_2$ solubility in warm water is too low for some aquatic life).

Pressure (Henry's Law)

• Solids and Liquids: Solubility does not depend on pressure.

• Gases: The solubility of any gas increases as the pressure of the gas increases.

Molecular Structure: Hydrophilic vs. Hydrophobic

• Hydrophilic (water-loving): These regions are attracted to and able to mix with water. They are typically ionized or have the ability to participate in hydrogen bonding.

• Hydrophobic (water-fearing): These regions are unable to mix with water. They are not ionized and cannot participate in hydrogen bonds.

• Lauric Acid Example: Contains a hydrophobic region (no atoms for H-bonding) and a hydrophilic region (contains atoms that can form H-bonds).

• Solubility Rule: The more hydrogen bonds a molecule can form, the higher its solubility. Conversely, the more Carbon and Hydrogen atoms it contains (hydrophobic C-H bonds), the lower its solubility.

Vitamins

• Water-soluble vitamins: Organic nutrients required in small amounts that dissolve well in water (e.g., Vitamin C and all B-vitamins). Because they dissolve in water, the body cannot store them easily.

• Fat-soluble vitamins: Organic compounds required in small amounts that dissolve in nonpolar liquids but not in water (e.g., Vitamins A, D, E, K).

Molarity and Equivalents

Molarity (M)

Molarity, or molar concentration, is the number of moles of solute per liter of solution. $\text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} = mol/L$

Sample Problem 5.8: Calculating Molarity

$6.82\,g$ of glycine ($C_2H_5NO_2$) in $75\,mL$ of solution.

1. Molar Mass: $(2 \times 12.01) + (5 \times 1.01) + (1 \times 14.01) + (2 \times 16.00) = 75.08\,g/mol$

2. Moles: $\frac{6.82\,g}{75.08\,g/mol} = 0.0908\,mol$

3. Volume: $75\,mL = 0.075\,L$

4. Molarity: $\frac{0.0908\,mol}{0.075\,L} = 1.21\,M$

Equivalents (Eq)

Equivalents measure the amount of charge in a solution containing dissolved ions.

• $1\,mol$ of $K^+ = 1\,Eq$

• $1\,mol$ of $Mg^{2+} = 2\,Eq$

• $1\,mol$ of $Fe^{3+} = 3\,Eq$

• For negative ions, ignore the sign: $1\,mol$ of $S^{2-} = 2\,Eq$

Sample Problem 5.15

$3.75\,g$ of $Fe^{3+}$ in $250\,mL$ of solution; find $mEq/L$.

1. Moles: $\frac{3.75\,g}{55.85\,g/mol} = 0.0671\,mol$

2. Equivalents: $0.0671\,mol \times 3\,Eq/mol = 0.2014\,Eq$

3. Concentration: $\frac{0.2014\,Eq}{0.250\,L} = 0.8057\,Eq/L = 805.7\,mEq/L$

Osmosis, Dialysis, and Tonicity

Definitions

• Semipermeable Membrane: A barrier that allows only certain small molecules or ions (like water) to pass, but blocks large molecules.

• Osmosis: The net movement of solvent (water) molecules through a semipermeable membrane from the side with lower solute molarity to the side with higher solute molarity.

• Diffusion: The spontaneous mixing of liquids or gases by random molecular motion to achieve even distribution.

• Osmotic Pressure: The pressure required to prevent osmosis; also the pressure exerted on the membrane at equilibrium.

• Dialysis: The movement of solute particles across a semipermeable membrane. Dialysis and osmosis often move in opposite directions.

Tonicity and Red Blood Cells

• Tonicity: The relationship between solute concentration in a solution and the concentration inside a cell.

• Isotonic: Equal solute concentration to intracellular fluid. No effect on the cell ($0.28\,M$ glucose is isotonic).

• Hypertonic: Higher solute concentration than the cell. The cell loses water, shrivels, and dies (Crenation).

• Hypotonic: Lower solute concentration than the cell. The cell absorbs water, swells, and bursts (Hemolysis).

Electrolytes and Ion Concentration

When an electrolyte dissolves, individual ions contribute to the total particle concentration.

• Example: $0.1\,M\,NaCl_{(s)} \rightarrow 0.1\,M\,Na^+<em>{(aq)} + 0.1\,M\,Cl^-</em>{(aq)}$, totaling $0.2\,mol$ of ions per liter.

• Sample Problem 5.11: A solution with $0.07\,M$ glucose and $0.07\,M\,Na_2CO_3$.   $Na_2CO_3 \rightarrow 2Na^+ + CO_3^{2-}$ (3 ions). Total particles = $0.07\,M$ (glucose) + $(3 \times 0.07\,M)$ (ions) = $0.28\,M$.

Chemical Reactions and Equations

Physical vs. Chemical Changes

• Physical Change: A process that changes properties (like state) without changing the chemical formula (e.g., boiling water: $H_2O_{(l)} \rightarrow H_2O_{(g)}$).

• Chemical Reaction: Involves changes in the chemical formulas of the substances involved (e.g., combustion or rusting).

• Law of Mass Conservation: The total mass of chemicals does not change in either a physical or chemical change.

Chemical Equations

Equations use formulas and coefficients to represent reactions.

• Reactants: Starting substances.

• Product: Substance formed.

• Coefficient: Number in front of a formula showing how many molecules/moles are required. If no number is shown, it is assumed to be 1.

Balancing Equations

Equations must have the same number of each type of atom on both sides.

• Example: $2H_2 + O_2 \rightarrow 2H_2O$

• Problem 6.4: $2Al + 6HCl \rightarrow 2AlCl_3 + 3H_2$

Thermodynamics and Kinetics

Heat of Reaction

The amount of heat absorbed or given off during a reaction.

• Exothermic Reaction: Gives off energy (heat) to surroundings. Heat is a product ($\Delta H$ is negative). Examples: burning fuels, rusting, batteries.

• Endothermic Reaction: Absorbs energy from surroundings; surroundings become colder ($\Delta H$ is positive). Heat is a reactant.

Nutritive Value of Food

The number of calories obtained from nutrients:

• Carbohydrates: $4\,Cal/g$

• Protein: $4\,Cal/g$

• Fat: $9\,Cal/g$

Reaction Rates and Activation Energy

• Rate: Amount of reactant converted to product in a specific time. High concentration increases rate due to more frequent molecular collisions.

• Activation Energy ($E_a$): The minimum energy reactant molecules must have to react during collision.

• Factors affecting rate:   1. Frequency of collisions.   2. Energy of molecules when they collide.   3. The amount of energy needed to react ($E_a$).

• Catalyst: A substance that speeds up a reaction by lowering the activation energy but is not consumed/changed (e.g., Platinum in catalytic converters).

Combustion and the Carbon Cycle

Equilibrium and Cycles

• Combustion: Compound reacts with $O_2$ to form oxides (usually $CO_2$ and $H_2O$).

• Photosynthesis: Plants convert $CO_2$, $H_2O$, and sunlight into glucose and $O_2$.   $6CO_2 + 6H_2O + 686\,kcal \rightarrow C_6H_{12}O_6 + 6O_2$

• Respiration: Organisms oxidize glucose for energy, producing $CO_2$ and $H_2O$.

• Carbon Cycle: The biological and chemical series of reactions converting inorganic carbon to organic molecules and back.

Chemical Equilibrium

In a reversible reaction, the forward and backward reactions occur at the same rate, resulting in a stable equilibrium mixture of reactants and products.

• Example: $CO_2 + H_2O \rightleftharpoons H_2CO_3$ (Carbonic acid).