Q.Considering the formation, breaking and strength of hydrogen bond, predict which of the following mixtures will show a positive deviation from Raoult's law?
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Molality: The Concentration That Ignores Temperature
Imagine you're making a cup of sweet tea. You add sugar to hot water, stir, and taste. If you let the tea cool to room temperature, the amount of sugar hasn't changed — but the volume of the liquid has shrunk slightly. If you measured concentration as "grams of sugar per litre of solution," that number would change just because the temperature changed. That's annoying if you're a chemist who needs a reliable, temperature-independent way to describe how much solute is present.
Molality was invented to solve exactly this problem.
The Intuition
Instead of measuring the volume of the solution (which expands and contracts with temperature), molality measures the mass of the solvent. Mass doesn't change with temperature. So molality gives you a concentration that stays the same whether your solution is hot or cold.
Think of it this way:
- Molarity = moles of solute per litre of solution (temperature-sensitive)
- Molality = moles of solute per kilogram of solvent (temperature-independent)
The solvent is the substance doing the dissolving — usually water. The solute is what gets dissolved — sugar, salt, etc.
The Precise Definition
Molality (m)=kilograms of solventmoles of solute
The symbol for molality is a lowercase m (not to be confused with M for molarity).
Key points to remember:
- The denominator is solvent mass, not solution mass
- The unit is mol/kg (often written as simply "m")
- It is independent of temperature because mass doesn't change with temperature
Worked Example
Problem: 36 g of glucose (C6H12O6, molar mass = 180 g/mol) is dissolved in 500 g of water. Calculate the molality of the solution.
Step 1: Find moles of solute
Moles of glucose=180 g/mol36 g=0.2 mol
Step 2: Convert solvent mass to kilograms
500 g=0.5 kg
Step 3: Apply the formula
m=0.5 kg0.2 mol=0.4 m
The answer is 0.4 m (or 0.4 mol/kg). Notice we used the mass of water (500 g), not the mass of the solution (which would be 536 g).
Common Mistake to Avoid
Do not use the mass of the solution in the denominator. The formula specifically asks for the mass of the solvent alone. If the problem gives you the total mass of the solution, subtract the mass of the solute to find the solvent mass.
When Do You Use Molality?
Molality is the star in two important situations: …
Why this formula?
Molality Calculation: Why the Formula Works
Molality is a measure of concentration that is temperature-independent — this is its key advantage over molarity. Let's understand why the formula takes the form it does.
The Definition First
Molality (m) is defined as:
m=mass of solvent in kgmoles of solute
The unit is mol/kg, often written as m (e.g., 0.5 m glucose solution).
Why Mass of Solvent, Not Solution?
This is the critical conceptual point.
The Reasoning
- Molarity uses volume of solution → volume changes with temperature (expansion/contraction). So molarity changes with temperature.
- Molality uses mass of solvent → mass is invariant with temperature. So molality remains constant regardless of temperature changes.
Key insight: By using the solvent's mass (not the solution's volume), we eliminate temperature dependence. This is why molality is preferred for colligative properties (boiling point elevation, freezing point depression) — these properties depend on the number of solute particles, not on temperature.
Deriving the Formula Step-by-Step
Step 1: Moles of Solute
If you have wsolute grams of solute with molar mass Msolute (g/mol):
moles of solute=Msolutewsolute
Step 2: Mass of Solvent in kg
If the solvent mass is Wsolvent grams:
mass of solvent in kg=1000Wsolvent
Step 3: Putting It Together
m=1000WsolventMsolutewsolute
Simplifying:
m=Msolute×Wsolventwsolute×1000
The Final Formula (Exam-Ready)
m=Msolute×Wsolventwsolute×1000
Where:
- wsolute = mass of solute in grams
- Msolute = molar mass of solute in g/mol
- Wsolvent = mass of solvent in grams
Why the ×1000 Factor? …
The key idea is that positive deviation from Raoult’s law occurs when the A–B interactions in the mixture are weaker than the A–A and B–B interactions in the pure components. This makes the vapour pressure higher than ideal.
Step 1 – Analyse pure components:
Methanol (CH₃OH) forms strong hydrogen bonds with itself. Acetone (CH₃COCH₃) has a polar carbonyl group but no –OH group; its self-interactions are weaker dipole–dipole forces.
Step 2 – Compare mixture interactions: …
Positive deviation from Raoult’s law occurs when A-B interactions are weaker than A-A and B-B interactions. In the given options, only methanol and acetone form weaker cross hydrogen bonds than the self-association in pure methanol, leading to higher vapour pressure. The correct option is (i).
Why This Approach Works
Raoult’s law states that the partial vapour pressure of each component in an ideal solution is proportional to its mole fraction. Real solutions deviate from this depending on how A-B interactions compare with A-A and B-B interactions.
Positive deviation: A-B interactions weaker than A-A/B-B - higher vapour pressure than ideal.
Negative deviation: A-B interactions stronger - lower vapour pressure than ideal.
Step-by-Step Reasoning
- (i) Methanol and acetone - Pure methanol has strong O-H...O self-association. The cross hydrogen bond with acetone's carbonyl oxygen is weaker than methanol-methanol bonds. A-B < A-A -> positive deviation. …
Concept: Deviation from Raoult’s Law and Hydrogen Bonding
Method: Intermolecular Force Comparison Method
Why this method works
Raoult’s law assumes ideal behaviour — the intermolecular forces between A–A, B–B, and A–B are all equal.
- Positive deviation occurs when A–B interactions are weaker than A–A and B–B.
- This makes the vapour pressure higher than predicted, because molecules escape more easily.
Steps to apply
- Identify the dominant intermolecular force in each pure component (usually hydrogen bonding here).
- Compare the strength of A–B hydrogen bonds with the pure component hydrogen bonds.
- If A–B bonds are weaker → positive deviation. If A–B bonds are stronger → negative deviation.
Applying to the options
(i) Methanol and acetone ✓
- Pure methanol: strong O–H···O hydrogen bonding.
- Pure acetone: only weak dipole-dipole (C=O is polar, but no –OH or –NH).
- In mixture: Methanol’s –OH can form H-bonds with acetone’s C=O, but acetone disrupts the strong methanol–methanol network.
- Result: A–B bonds are weaker than A–A bonds → positive deviation.
(ii) Chloroform and acetone ✗
- Chloroform (CHCl₃) has a slightly acidic H (C–H···O type H-bond possible).
- Acetone’s C=O accepts H-bonds.
- Result: A–B H-bonds are stronger than pure component interactions → negative deviation.
(iii) Nitric acid and water ✗ …
Common Mistakes & How to Avoid Them
This question tests your understanding of Raoult's law deviations in liquid-liquid solutions, specifically linked to hydrogen bonding between components.
✗ Mistake 1: Confusing "positive deviation" with "stronger intermolecular forces"
The error:
Students think that if a mixture forms strong hydrogen bonds, it will show positive deviation.
Actually, positive deviation occurs when A–B interactions are weaker than A–A and B–B interactions. This makes the mixture easier to vaporise (higher vapour pressure than ideal).
How to avoid:
Remember the rule:
Positive deviation → weaker A–B forces → vapour pressure higher than ideal
Negative deviation → stronger A–B forces → vapour pressure lower than ideal
So for positive deviation, the mixture must break strong self-association (like in pure methanol or water) and form weaker cross hydrogen bonds.
✗ Mistake 2: Assuming all hydrogen-bonding mixtures show negative deviation
The error:
Many students think "hydrogen bond = negative deviation". But that’s only true if the cross hydrogen bond is stronger than the self-hydrogen bonds in the pure components.
Example:
- Methanol + acetone: Methanol has strong self-association. Acetone can only accept H-bonds (C=O). The cross bond is weaker than methanol–methanol bonds → positive deviation.
- Chloroform + acetone: Chloroform’s H is acidic, acetone’s O is basic → stronger cross bond → negative deviation.
How to avoid:
Compare the strength of the cross bond vs. the self bonds. If the pure component has strong self-association (like alcohols, water, carboxylic acids), and the other component is a weak H-bond acceptor (like acetone, ether), expect positive deviation.
✗ Mistake 3: Not recognising when both components form strong self-association
The error:
Students sometimes pick options like (iii) Nitric acid + water or (iv) Phenol + aniline, thinking they show positive deviation because both have H-bonding.
Correction:
- Nitric acid + water: Both form very strong self-association, but the cross H-bond (acid–water) is even stronger → negative deviation.
- Phenol + aniline: Both have strong self-association, but phenol (acidic H) and aniline (basic N) form a very strong cross H-bond → negative deviation.
How to avoid: …
- GUJCET 2024Set 131 markMCQQ.Calculate the mass of Glucose (C6H12O6) required in making 2.5 kg of 0.25 molal aqueous solution. [Atomic wt : H = 1, O = 16, C = 12 amu] (A) 135.0 g (B) 107.65 g (C) 90.0 g (D) 112.5 g
›Reveal solutionSolution
Molality is moles solute per kg solvent; set up the equation with (solution − solute) as solvent mass and solve for the solute mass.
Concept: Molar mass of glucose C6H12O6=6(12)+12(1)+6(16)=180 g/mol. Molality m=kg solventmoles solute.
Let mass of glucose =w g. Solvent mass =(2500−w) g =10002500−w kg.
0.25=(2500−w)/1000w/180
0.25×10002500−w=180w …
- GSEB Higher Secondary Certificate (HSC) Examination 2022Set ANNUAL1 markMCQQ.What is the molality of a 10% w/w aqueous solution of NaOH? (Molecular mass of NaOH = 40 g mol-1)(a) 2.78 m(b) 2.87 m(c) 2.5 m(d) 2.05 m
›Reveal solutionSolution
Molality = moles of solute / mass of solvent in kg; for 10% w/w NaOH, take 100 g solution = 10 g NaOH + 90 g water.
Moles of NaOH = 10 g / 40 g mol-1 = 0.25 mol. …
- GUJCET 2021Set 151 markMCQQ.3.0 gram ethanoic acid in 50 gram benzene having ___ molality? (Atomic weights : H = 1, C = 12, O = 16). (A) 0.1 (B) 1.0 (C) 0.6 (D) 0.06
›Reveal solutionSolution
m=kg solventmol solute=0.0500.05=1.0.
Concept: Molality = moles of solute per kg of solvent.
Moles of CH3COOH (M = 60): 603.0=0.05 mol. …
- GSEB Higher Secondary Certificate (HSC) Examination 2020Set ANNUAL1 markMCQQ.Molality of 30% w/w aqueous solution of NaOH is -(a) 7.5 m(b) 8.32 m(c) 10.71 m(d) 9.17 m
›Reveal solutionSolution
Taking a 100 g basis for a 30% w/w solution gives 30 g NaOH in 70 g water; converting to moles and dividing by the mass of water in kg gives the molality.
Basis: 100 g of solution contains 30 g NaOH and (100-30) = 70 g water = 0.070 kg. …
- GUJCET 2019Set 131 markMCQQ.The value of which of the following unit of concentration will not change with the change in temperature? (A) Formality (B) Normality (C) Molality (D) Molarity
›Reveal solutionSolution
Molality uses mass, not volume, so it is independent of temperature.
Concept: Concentration units defined using volume (molarity, normality, formality expressed per litre) change with temperature because volume expands or contracts. Molality is defined per kilogram of solvent (mass), and mass does not vary with temperature, so molality is temperature-independent.
Steps: …
- GUJCET 2014Set A1 markMCQQ.What will be the value of molality for an aqueous solution of 10% w/w NaOH. (Na = 23, O = 16, H = 1) (A) 2.778 (B) 5 (C) 10 (D) 2.5
›Reveal solutionSolution
[!TLDR]
Molality =2.778 mol kg−1.
Concept
Molality m=mass of solvent (kg)moles of solute. For a w/w percentage, the stated mass is per 100 g of solution, so the solvent mass is 100−(solute mass).
Solution
M(NaOH)=23+16+1=40 g mol−1. …
- GUJCET 2014Set A1 markMCQQ.If 10 ml of 0.1 M aqueous solution of NaCl is divided in to 1000 drops of equal volume, what will be the concentration of one drop? (A) 0.01 M (B) 0.10 M (C) 0.001 M (D) 0.0001 M
›Reveal solutionSolution
[!TLDR] Concentration is an intensive property; dividing a solution into drops does not change its molarity, so each drop is 0.10 M.
Concept
Molarity =volume of solution (L)moles of solute. Both the moles of solute and the volume scale down together when you take a small portion, so their ratio — the concentration — stays the same. Concentration does not depend on how much of the solution you take.
Solution
Total moles =0.1 M×10×10−3 L=1×10−3 mol in 10 mL. …
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