Kinetics and Solutions
Molarity (M)
Molarity tells you how many moles of solute are present in one litre of solution.
M = moles of solute / volume of solution in litres
Think of molarity as "concentration per litre." If you dissolve more solute in the same volume, molarity increases. But if the volume changes, molarity changes too—even if the amount of solute stays the same.
The important thing to remember here is that molarity depends on temperature.
Temperature affects volume. When a solution is heated, it expands. Since molarity depends on volume, any expansion or contraction directly changes its value.
note : if temperature increases, the solution expands, volume increases, and molarity decreases.
Molality (m)
m = moles of solute / mass of solvent in kg
Molality focuses on mass instead of volume. Since mass does not change with temperature, molality remains constant even if the solution is heated or cooled.
Unlike molarity, molality is temperature-independent, because mass does not change with temperature.
molality is often used in colligative properties, so don’t confuse it with molarity.
In many numerical problems (especially freezing and boiling point), molality is preferred because it avoids complications caused by temperature changes.
Mole Fraction (χ)
χA = nA / (nA + nB)
Mole fraction simply tells you the proportion of one component compared to the total number of moles present. It is a ratio, not an absolute quantity.
- Mole fraction has no unit
- The sum of mole fractions in a solution is always equal to 1
Because it's a ratio, all mole fractions together must add up to 1. This makes it very useful in vapor pressure and gas-related problems.
Parts Per Million (ppm)
ppm = (mass of solute / mass of solution) × 10⁶
ppm is used when the concentration is extremely small. For example, pollutants in water or air are measured in ppm because normal units would give very tiny decimals.
Henry’s Law
P = KH · χ
This law tells us how gases dissolve in liquids. It says that the amount of gas dissolved is directly proportional to the pressure applied on it.
- Higher value of KH means the gas is less soluble
- Gas solubility decreases with increase in temperature
If KH is high, the gas does not dissolve easily. Also, since dissolving gas releases heat (exothermic), increasing temperature pushes the gas out of the solution.
Raoult’s Law
Ptotal = PA⁰χA + PB⁰χB
Raoult’s Law explains how vapor pressure behaves in liquid mixtures. Each component contributes to the total pressure based on its mole fraction.
Ideal Solutions
- Intermolecular forces are similar
- ΔHmix = 0
- ΔVmix = 0
In ideal solutions, molecules behave as if they are surrounded by similar molecules. So mixing does not release or absorb energy.
Non-Ideal Solutions
Positive Deviation
When interactions between different molecules are weaker, they escape easily into vapor phase. That’s why vapor pressure becomes higher than expected.
Negative Deviation
Here, molecules attract each other strongly, so fewer molecules escape into vapor. This lowers the vapor pressure.
Colligative Properties
These properties depend only on the number of solute particles, not their nature.
It doesn’t matter whether the solute is sugar or salt—only the number of particles matters. More particles = stronger effect.
(P⁰ - P)/P⁰ = χsolute
Adding solute reduces vapor pressure because it blocks solvent molecules from escaping.
ΔTb = i · Kb · m
Boiling point increases because solute makes it harder for liquid to vaporize.
ΔTf = i · Kf · m
Freezing point decreases because solute disrupts crystal formation.
π = i · C R T
Osmotic pressure measures the tendency of solvent to move into the solution. This is widely used to find molar mass of large molecules like proteins.
Van’t Hoff Factor (i)
This factor corrects the number of particles in solution. Some solutes break into multiple ions, while others combine.
- Non-electrolytes: i = 1
- Electrolytes: i > 1
- Association: i < 1
i = 1 + (n - 1)α
Here, α tells how much of the solute actually dissociates. This formula helps calculate real particle count in solution.
Rate of Reaction
Rate = -(1/a)d[A]/dt = (1/c)d[C]/dt
This equation shows how concentration changes with time. Reactants decrease (negative sign), products increase (positive sign).
Order vs Molecularity
Order is determined from experiments and can be anything—even fractional. Molecularity is theoretical and always a whole number because it counts actual collisions.
Integrated Rate Laws
Zero Order
[A]t = [A]0 - kt
t½ = [A]0 / 2k
Rate is constant here, so concentration decreases linearly. Half-life depends on initial concentration.
First Order
k = (2.303/t) log([A]0/[A]t)
t½ = 0.693/k
Rate depends on concentration. As concentration decreases, reaction slows down. Half-life stays constant.
Arrhenius Equation
k = A e^(-Ea/RT)
This equation connects temperature with reaction rate. Higher temperature means more molecules have enough energy to react.
log(k2/k1) = Ea/(2.303R) × (T2 - T1)/(T1T2)
Used in numerical problems to compare rate constants at two different temperatures.
Catalysis
A catalyst provides an easier path for the reaction, reducing the energy barrier. It speeds up both forward and backward reactions equally.
- Lowers activation energy
- Does not change equilibrium
Quick Tips
- Always check units
- Azeotropes: min → positive, max → negative
- Graphs help identify order
- Pseudo-first order reactions are common in exams