Molarity, Molality & Mole Fraction
By Abhishek Sengar | CHEMCA – JEE & NEET Chemistry
Recommended Prerequisite
Molarity heavily relies on accurate molar mass calculations and volume conversions. Make sure your Mole Concept basics are completely clear before proceeding! Read our foundational guide here: Some Basic Concepts of Chemistry for Class 11 and JEE/NEET.
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Lecture 9: Some Basic Concepts of Chemistry
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Hello students! Welcome to Lecture 9. In the last session, we discussed physical percentage concentration terms (%w/w, %v/v, %w/v). Today, we tackle the heavyweight chemical concentration terms: Molarity, Molality, and Mole Fraction. These are arguably the most heavily tested concentration concepts in JEE and NEET.
1. Molarity (M)
Molarity is the most common way to express solution concentration. It is defined as the number of moles of solute present per liter of solution.
Molarity (M) = Moles of Solute / Volume of Solution (in Liters)
If Volume is in mL: M = (Moles of Solute × 1000) / Vol (mL)
Unit: Moles/Liter (mol/L) or simply "Molar" (M).
Dilution Problems ($M_1V_1 = M_2V_2$)
When you add solvent (water) to an existing solution, the number of moles of the solute remains perfectly constant. Therefore, we use the dilution equation:
M1V1 = M2V2
Question: What volume of water must be added to 600 mL of 0.2M H2SO4 to change its concentration to 0.05M?
- 0.2 × 600 = 0.05 × V2
- V2 = 120 / 0.05 = 2400 mL (This is the final volume).
- Water added = Final Volume - Initial Volume = 2400 - 600 = 1800 mL.
Mixing Solutions
When mixing two solutions of the same solute, calculate the final Molarity using:
Mfinal = (M1V1 + M2V2) / (V1 + V2)
2. Molality (m)
Molality is unique and highly important because it is the only major concentration term that uses the mass of the Solvent in the denominator, rather than the Solution.
Molality (m) = Moles of Solute / Mass of SOLVENT (in kg)
Unit: Moles/kg (mol/kg) or simply "Molal" (m).
Crucial Trap!
If a question gives you the Mass of the Solution, you MUST subtract the Mass of the Solute to find the Mass of the Solvent before applying the Molality formula!
Relationship: Molarity, Molality & Density
This is a superstar formula for JEE/NEET. It allows you to convert directly between Molarity (M) and Molality (m) if the Density (d) of the solution is given.
m = (M × 1000) / (1000d - M × Msolute)
• m = Molality (mol/kg)
• M = Molarity (mol/L)
• d = Density (MUST BE IN g/L, not g/mL)
• Msolute = Molar Mass of Solute (g/mol)
3. Mole Fraction (χ)
Mole fraction represents the ratio of the moles of one specific component to the total moles of all components in the mixture. It is denoted by the Greek letter Chi (χ) or simply X.
Mole Fraction of A
χA = nA / (nA + nB)
Mole Fraction of B
χB = nB / (nA + nB)
Universal Rule of Mole Fractions:
The sum of the mole fractions of all components in a solution is ALWAYS exactly equal to 1.
χA + χB = 1
4. Decoding the Jargon (Interpretation)
If a question just throws a concentration value at you without amounts, here is how you translate it into workable numbers for formulas:
- "1 M H2SO4" means exactly 1 Mole of H2SO4 is present inside exactly 1 Liter of Solution.
- "1 m H2SO4" means exactly 1 Mole of H2SO4 is present inside exactly 1 kg of Solvent (Water).
- "χH2SO4 = 0.1" means there is 0.1 Mole of H2SO4 inside exactly 1 Total Mole of Solution (meaning 0.9 moles belong to the solvent).
Test Your Understanding! π―
Take this 10-question MCQ quiz to verify your grasp of Lecture 9. Explanations and study recommendations will be revealed upon submission.
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