Volume of a solution changes with change in temperature, then, will the molality of the solution be affected b

NCERT Exemplar · Q33

Q. Volume of a solution changes with change in temperature, then, will the molality of the solution be affected by temperature? Give reason for your answer.

Rajasthan RbseShort· 2mImportance★★★★★est

87% · 77/89 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Concept understanding — Molecular Mass Calculation

What is Molecular Mass? The Intuition

Imagine you're at a market buying apples. You don't weigh each apple individually — you put a dozen on a scale. The total weight tells you something about the apples, but it also depends on how many apples you have.

Atoms and molecules are unimaginably tiny. A single water molecule ( $H_2O$ ) weighs about $3 \times 10^{-23}$ grams. That number is useless for practical chemistry. So instead of working with individual molecules, chemists count them in huge fixed numbers — specifically, $6.022 \times 10^{23}$ molecules, which is called one mole.

Molecular mass is simply the mass of one mole of a substance, expressed in grams per mole (g/mol). It answers the question: "If I have $6.022 \times 10^{23}$ molecules of this compound, how much would they weigh on a lab balance?"

Note

The number $6.022 \times 10^{23}$ is Avogadro's constant. It's chosen so that the mass of one mole of carbon-12 atoms is exactly 12 grams — matching the atomic mass unit scale perfectly.

The Precise Definition

Molecular mass (also called molar mass) is the mass of one mole of a molecular substance. It is numerically equal to the sum of the atomic masses of all atoms in the molecule, expressed in g/mol.

For example:

Water ( $H_2O$ ): 2 hydrogen atoms + 1 oxygen atom
Atomic mass of H = 1.008 g/mol
Atomic mass of O = 16.00 g/mol
Molecular mass of $H_2O$ = $2(1.008) + 16.00 = 18.016$ g/mol

\text{Molecular mass} = \sum (\text{number of atoms of each element} \times \text{atomic mass of that element})

How to Calculate It — Step by Step

Let's take glucose, $C_6H_{12}O_6$ , as a worked example.

Step 1: Identify each element and its count

Carbon (C): 6 atoms
Hydrogen (H): 12 atoms
Oxygen (O): 6 atoms

Step 2: Look up atomic masses (from the periodic table)

C: 12.01 g/mol
H: 1.008 g/mol
O: 16.00 g/mol

Step 3: Multiply and add

\text{Molecular mass} = 6(12.01) + 12(1.008) + 6(16.00)

= 72.06 + 12.096 + 96.00

= 180.156 \text{ g/mol}

Tip

Always keep at least 2 decimal places from the periodic table. For exam problems, they usually give you atomic masses — use exactly what's provided.

Why This Matters

Molecular mass is the bridge between the microscopic world (atoms and molecules) and the macroscopic world (grams you can weigh). Once you know the molecular mass, you can:

Convert grams to moles: $\text{moles} = \frac{\text{mass in grams}}{\text{molecular mass}}$
Convert moles to grams: $\text{mass} = \text{moles} \times \text{molecular mass}$
Determine the number of molecules: $\text{molecules} = \text{moles} \times 6.022 \times 10^{23}$

Watch out

Do not confuse molecular mass with atomic mass. Atomic mass refers to a single element (like oxygen = 16.00 g/mol). Molecular mass refers to a compound (like $CO_2$ = 44.01 g/mol). Also, for ionic compounds like NaCl, we use formula mass (same calculation, but the substance isn't molecular).

Common Exam Pitfalls

Forgetting to multiply by the subscript. In $H_2SO_4$ , there are 2 hydrogens, not 1. …

Why this formula?

Stoichiometry & Mole Calculation: The "Why" Behind the Formula

Let's build this from the ground up — not as a list of formulas to memorise, but as a logical chain of reasoning.

1. The Core Question: What is a Mole?

A mole is simply a counting unit, like a dozen (12) or a gross (144). But instead of 12, a mole contains $6.022 \times 10^{23}$ particles (Avogadro's number, $N_A$ ).

Why this number?

It was chosen so that 1 mole of any substance has a mass in grams equal to its atomic/molecular mass in amu.

Example: 1 atom of carbon-12 has mass 12 amu.
1 mole of carbon-12 has mass 12 grams.

This is the bridge between the microscopic (atoms/molecules) and the macroscopic (grams we can weigh).

2. The Fundamental Relationship

The key formula is:

n = \frac{m}{M}

Where:

$n$ = number of moles
$m$ = mass of substance (in grams)
$M$ = molar mass (in g/mol)

Why does this work?

Think of it as a conversion factor:

If 1 mole of a substance weighs $M$ grams, then $m$ grams contains $\frac{m}{M}$ moles.

Derivation logic:

Molar mass $M$ tells you: "1 mol = $M$ g"
So the conversion factor is $\frac{1 \text{ mol}}{M \text{ g}}$
Multiply mass $m$ by this factor: $m \times \frac{1}{M} = \frac{m}{M}$ moles

3. Connecting to Number of Particles

n = \frac{N}{N_A}

Where:

$N$ = number of particles (atoms, molecules, ions)
$N_A = 6.022 \times 10^{23}$ particles/mol

Why?

1 mole = $N_A$ particles
So $N$ particles = $\frac{N}{N_A}$ moles

Combine both formulas:

\frac{m}{M} = \frac{N}{N_A}

This single equation ties mass, molar mass, number of particles, and Avogadro's number together.

4. The Gas Volume Connection (for gases at STP)

For gases only:

n = \frac{V}{22.4 \text{ L/mol}}

Why 22.4 L?

From the ideal gas law: $PV = nRT$

At STP (Standard Temperature and Pressure: 0°C, 1 atm):

$P = 1$ atm
$T = 273.15$ K
$R = 0.0821$ L·atm/(mol·K)

For $n = 1$ mole:

V = \frac{nRT}{P} = \frac{1 \times 0.0821 \times 273.15}{1} \approx 22.4 \text{ L}

So 1 mole of any ideal gas occupies 22.4 L at STP. This is a consequence of the gas laws, not a definition.

5. The Stoichiometry Chain: From One Substance to Another

In a balanced chemical equation like:

aA + bB \rightarrow cC + dD

The coefficients tell you the mole ratio:

\frac{\text{moles of A}}{\text{moles of B}} = \frac{a}{b}

Why this works: …

Start your 14-day free trial to unlock the full solution →

Molality depends only on the mass of solvent, not on volume. Since mass is invariant with temperature, molality does not change when temperature changes — unlike molarity, which does change because volume expands or contracts.

Why this question matters

This is a classic distinction between molality and molarity — two ways to express concentration. Many students memorise that “molality is temperature independent” but cannot explain why. The key is to look at what each quantity actually measures.

Molarity ( $M$ ) = moles of solute per litre of solution. Volume changes with temperature (liquids expand when heated, contract when cooled), so the denominator changes — molarity changes.

Molality ( $m$ ) = moles of solute per kilogram of solvent. Mass does not change with temperature. Whether the solution is hot or cold, the solvent’s mass stays the same. So molality remains constant.

Watch out

A common mistake is to think that because the solution expands, the solvent mass somehow changes. It doesn’t. Mass is a measure of the amount of matter, not the space it occupies. Temperature affects volume, not mass.

Step-by-step reasoning

Define molality Molality is given by:

m = \frac{\text{moles of solute}}{\text{mass of solvent (in kg)}}

The numerator (moles) depends only on the number of solute particles — that doesn’t change with temperature. The denominator is a mass, which is a measure of the amount of solvent present.

What happens to mass when temperature changes?

Mass is an intrinsic property. Heating a solution does not add or remove solvent molecules — it only makes them move faster and spread out. The mass of the solvent remains exactly the same regardless of temperature.
What happens to volume when temperature changes? …

Start your 14-day free trial to unlock the full solution →

Here’s a breakdown of the common mistakes students make on this question, along with how to avoid each.

The Core Concept

Molality ( $m$ ) is defined as the number of moles of solute per kilogram of solvent.

m = \frac{\text{moles of solute}}{\text{mass of solvent (in kg)}}

Volume changes with temperature because liquids expand or contract. However, mass is independent of temperature.

Since molality depends on mass (of the solvent), not on volume, a change in temperature does not affect the molality.

Common Mistake #1: Confusing Molality with Molarity

The Mistake: Students think that because volume changes, any concentration unit that involves volume must also change. They then incorrectly apply this logic to molality.

Why it happens: Molarity ( $M = \frac{\text{moles}}{\text{volume in L}}$ ) does change with temperature because volume is in the denominator. Students often mix up the definitions of $M$ and $m$ .

How to Avoid:

Memorise the definitions with a focus on the denominator.
- Molarity (M): Volume of solution (changes with $T$ ).
- Molality (m): Mass of solvent (constant with $T$ ).
Use a memory trick: Think of "Molality = Mass" (both start with 'M' and 'a' — Mass, Molality). Mass does not change with temperature.

Common Mistake #2: Thinking "Solution Volume" Affects the Solvent Mass

The Mistake: Students reason: "Volume changes, so the mass of the solution changes, therefore molality changes."

Why it happens: They forget that molality specifically uses the mass of the solvent, not the mass of the whole solution. While the volume of the solution expands, the mass of the solvent (e.g., the kilograms of water) remains exactly the same.

How to Avoid:

Draw a clear mental picture. Imagine 1 kg of water with 1 mole of sugar dissolved in it.
- At $25^\circ C$ , the solution has a certain volume.
- At $50^\circ C$ , the solution expands (volume increases).
- Question: Did the 1 kg of water disappear? Did the 1 mole of sugar vanish? No. The mass of the solvent is still 1 kg. …

Start your 14-day free trial to unlock the full solution →

←Previous questionQ32 — The density of 3 molal solution of NaOH is 1.110g mL⁻¹. Calculate the …→Next questionQ34 — If 4 g of NaOH dissolves in 36 g of H₂O, calculate the mole fraction o…

Q.Volume of a solution changes with change in temperature, then, will the molality of the solution be affected by temperature? Give reason for your answer.

Concept understanding — Molecular Mass Calculation

What is Molecular Mass? The Intuition

The Precise Definition

How to Calculate It — Step by Step

Why This Matters

Common Exam Pitfalls

Why this formula?

Stoichiometry & Mole Calculation: The "Why" Behind the Formula

1. The Core Question: What is a Mole?

2. The Fundamental Relationship

Why does this work?

3. Connecting to Number of Particles

Why?

4. The Gas Volume Connection (for gases at STP)

Why 22.4 L?

5. The Stoichiometry Chain: From One Substance to Another

Why this works: …

Why this question matters

Step-by-step reasoning

Concept: Temperature Dependence of Concentration Units

Method: Mass-Based vs Volume-Based Analysis

The Core Concept

Common Mistake #1: Confusing Molality with Molarity

Common Mistake #2: Thinking "Solution Volume" Affects the Solvent Mass

Q.Volume of a solution changes with change in temperature, then, will the molality of the solution be affected by temperature? Give reason for your answer.

Why this question matters

Step-by-step reasoning

🎓Unlock everything free for 14 days

Unlock everything free for 14 days