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Logical ReasoningLevel 3 · Analysis

A chemistry lab prepares 1 M NaCl solution at 25°C and stores it in a sealed bottle in a freezer at 4°C. When retrieved later, the label still says "1 M NaCl" but a student recalculates the molarity using the solution volume at 4°C and gets a slightly different number. Did the solution's concentration change? Is the label wrong?

✦Real Life Hook

Ocean water has a salinity of about 35 g per kilogram of sea water. Oceanographers express this as 35 per mille (‰) — 35 parts per thousand by mass. This is effectively molality (grams per kilogram), not molarity — because sea water temperatures vary from −2°C in polar regions to +30°C near the equator. A concentration unit based on mass doesn't drift with temperature. The same logic drives every laboratory situation where temperature isn't controlled precisely.

Molarity (M)

Molarity is the number of moles of solute dissolved per litre of solution.

$M = \frac{n_{\text{solute}}}{V_{\text{solution (L)}}} = \frac{\text{moles of solute}}{\text{litres of solution}}$

Or equivalently, if you know the mass of solute ( $w$ in grams) and molar mass ( $M_2$ ):
$M = \frac{w \times 1000}{M_2 \times V_{\text{mL}}}$

Units: mol/L, also written mol L⁻¹ or M.

Key limitation: Molarity changes with temperature because volume changes with temperature.

Molality (m)

Molality is the number of moles of solute dissolved per kilogram of solvent.

$m = \frac{n_{\text{solute}}}{m_{\text{solvent (kg)}}} = \frac{w_2 \times 1000}{M_2 \times w_1}$

where $w_2$ = mass of solute in g, $M_2$ = molar mass of solute, $w_1$ = mass of solvent in g.

Units: mol/kg, also written mol kg⁻¹ or m.

Key advantage: Molality is temperature-independent because mass of solvent does not change with temperature.

Molarity vs Molality

Molarity (M)

Moles of solute per litre of solution
Temperature-dependent (volume changes)
Easy to prepare in lab (volumetric flask)
Used in: stoichiometry, titrations
Symbol: M, units: mol/L

Molality (m)

Moles of solute per kg of solvent
Temperature-independent (mass is constant)
Requires weighing solvent separately
Used in: colligative properties, thermodynamics
Symbol: m, units: mol/kg

Molarity (M)

Moles of solute per litre of solution
Temperature-dependent (volume changes)
Easy to prepare in lab (volumetric flask)
Used in: stoichiometry, titrations
Symbol: M, units: mol/L

Molality (m)

Moles of solute per kg of solvent
Temperature-independent (mass is constant)
Requires weighing solvent separately
Used in: colligative properties, thermodynamics
Symbol: m, units: mol/kg

📖NCERT 2.3NCERT Intext

Problem

Calculate the molarity of a solution containing 5 g of NaOH ( $M = 40$ g/mol) dissolved in 450 mL of solution.

📖NCERT 2.4NCERT Intext

Problem

Calculate the mass of urea ( $\ce{NH2CONH2}$ , $M = 60$ g/mol) required to make 2.5 kg of a 0.25 molal aqueous solution.

✦JEE / NEET Exam InsightJEE / NEET

◆Molality in colligative properties: All four colligative property equations (

\Delta T_b

\Delta T_f

, osmotic pressure, lowering of VP) use molality or mole fraction — never molarity. If an exam question gives you molarity and asks for

\Delta T_f

, you must convert first.

◆Conversion formula (requires density

d

and molar mass

M_2

m = \frac{M \times 1000}{1000d - M \times M_2}

◆Mole fraction → molality: If

\chi_2 = x

, then

m = \frac{1000x}{M_1(1-x)}

where

M_1

= molar mass of solvent.

Quick Check

Q1.3.65 g of HCl (M = 36.5 g/mol) is dissolved in water to make 500 mL of solution. What is the molarity?

Logical ReasoningLevel 3 · Analysis

✦Real Life Hook

Molarity (M)

Molarity is the number of moles of solute dissolved per litre of solution.

$M = \frac{n_{\text{solute}}}{V_{\text{solution (L)}}} = \frac{\text{moles of solute}}{\text{litres of solution}}$

Or equivalently, if you know the mass of solute ( $w$ in grams) and molar mass ( $M_2$ ):
$M = \frac{w \times 1000}{M_2 \times V_{\text{mL}}}$

Units: mol/L, also written mol L⁻¹ or M.

Key limitation: Molarity changes with temperature because volume changes with temperature.

Molality (m)

Molality is the number of moles of solute dissolved per kilogram of solvent.

$m = \frac{n_{\text{solute}}}{m_{\text{solvent (kg)}}} = \frac{w_2 \times 1000}{M_2 \times w_1}$

where $w_2$ = mass of solute in g, $M_2$ = molar mass of solute, $w_1$ = mass of solvent in g.

Units: mol/kg, also written mol kg⁻¹ or m.

Key advantage: Molality is temperature-independent because mass of solvent does not change with temperature.

Molarity vs Molality

Molarity (M)

Moles of solute per litre of solution
Temperature-dependent (volume changes)
Easy to prepare in lab (volumetric flask)
Used in: stoichiometry, titrations
Symbol: M, units: mol/L

Molality (m)

Moles of solute per kg of solvent
Temperature-independent (mass is constant)
Requires weighing solvent separately
Used in: colligative properties, thermodynamics
Symbol: m, units: mol/kg

Molarity (M)

Moles of solute per litre of solution
Temperature-dependent (volume changes)
Easy to prepare in lab (volumetric flask)
Used in: stoichiometry, titrations
Symbol: M, units: mol/L

Molality (m)

Moles of solute per kg of solvent
Temperature-independent (mass is constant)
Requires weighing solvent separately
Used in: colligative properties, thermodynamics
Symbol: m, units: mol/kg

📖NCERT 2.3NCERT Intext

Problem

Calculate the molarity of a solution containing 5 g of NaOH ( $M = 40$ g/mol) dissolved in 450 mL of solution.

📖NCERT 2.4NCERT Intext

Problem

Calculate the mass of urea ( $\ce{NH2CONH2}$ , $M = 60$ g/mol) required to make 2.5 kg of a 0.25 molal aqueous solution.

Quick Check

Q1.3.65 g of HCl (M = 36.5 g/mol) is dissolved in water to make 500 mL of solution. What is the molarity?