One of the statements of Dalton's atomic theory is given below: "Compounds are formed when atoms of different

NCERT Exemplar · Q22

Q. One of the statements of Dalton's atomic theory is given below: "Compounds are formed when atoms of different elements combine in a fixed ratio" Which of the following laws is not related to this statement? (Note: this is a multiple-correct question; two or more options may be correct.)

(i) Law of conservation of mass

(ii) Law of definite proportions

(iii) Law of multiple proportions

(iv) Avogadro law

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Concept understanding — Unit Conversion

Unit Conversion: Why 1 Metre and 100 Centimetres Are the Same Thing

Imagine you're measuring the length of your desk. You pull out a ruler marked in centimetres and find it's 120 cm long. Your friend, using a metre stick, says it's 1.2 m. You're both right — you've just used different units to describe the same physical length.

That's the core idea: unit conversion is the process of changing how you express a quantity without changing the quantity itself.

The Intuition: Same Quantity, Different Labels

Think of a pizza. Whether you call it "one pizza" or "8 slices," the amount of pizza hasn't changed. You've just used a different unit (pizza vs. slice) to describe it.

Similarly, 1 metre and 100 centimetres are the same length — just like 1 pizza and 8 slices are the same amount. The number changes (1 becomes 100, or 1 becomes 8), but the actual thing being measured stays identical.

Note

This is the most important idea to hold onto: conversion changes the number, not the quantity. If you ever feel like the quantity has changed, you've made a mistake.

The Precise Statement

Unit conversion is the multiplication of a quantity by a conversion factor — a fraction equal to 1 — that cancels the old unit and introduces the new one.

A conversion factor looks like this:

\frac{\text{new unit}}{\text{old unit}} = 1

For length: $\frac{1 \text{ m}}{100 \text{ cm}} = 1$ and $\frac{100 \text{ cm}}{1 \text{ m}} = 1$ .

Why are these fractions equal to 1? Because 1 metre is 100 centimetres. The numerator and denominator describe the same physical length, so their ratio is exactly 1.

How to Convert: The Only Rule You Need

Multiply by a conversion factor that cancels the unit you have and leaves the unit you want.

Let's convert 120 cm to metres:

Start with what you have: $120 \text{ cm}$
Choose the conversion factor that has "cm" in the denominator (to cancel it) and "m" in the numerator: $\frac{1 \text{ m}}{100 \text{ cm}}$
Multiply:

120 \text{ cm} \times \frac{1 \text{ m}}{100 \text{ cm}} = \frac{120}{100} \text{ m} = 1.2 \text{ m}

The "cm" units cancel just like numbers do: $\frac{\text{cm}}{\text{cm}} = 1$ .

Tip

Always write the units explicitly. If the units don't cancel correctly, you've used the wrong conversion factor. This catches 90% of conversion mistakes.

The Reverse: Metres to Centimetres

Now convert 1.2 m to cm. This time, you want "cm" to remain and "m" to cancel. Use $\frac{100 \text{ cm}}{1 \text{ m}}$ :

1.2 \text{ m} \times \frac{100 \text{ cm}}{1 \text{ m}} = 1.2 \times 100 \text{ cm} = 120 \text{ cm}

Notice: when going from a larger unit (m) to a smaller unit (cm), the number gets larger (1.2 → 120). When going from smaller to larger, the number gets smaller (120 → 1.2). This is a useful sanity check.

Common Conversion Factors You'll Use

Quantity	Relationship	Conversion Factors
Length	1 m = 100 cm	$\frac{1 \text{ m}}{100 \text{ cm}}$ , $\frac{100 \text{ cm}}{1 \text{ m}}$
Mass	1 kg = 1000 g	$\frac{1 \text{ kg}}{1000 \text{ g}}$ , $\frac{1000 \text{ g}}{1 \text{ kg}}$
Time	1 h = 60 min	$\frac{1 \text{ h}}{60 \text{ min}}$ , $\frac{60 \text{ min}}{1 \text{ h}}$
Speed	1 km/h = $\frac{1000}{3600}$ m/s	$\frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}}$

Why this formula?

Dimensional Analysis: Why the Key Principles Hold

Dimensional Analysis is a powerful tool in physics and engineering that lets us check the consistency of equations, derive relationships, and convert units. But why does it work? Let's build the reasoning from the ground up.

1. The Core Idea: Physical Quantities Have Dimensions

Every physical quantity (like length, time, mass) can be expressed in terms of fundamental dimensions. The most common set in mechanics is:

L = Length
M = Mass
T = Time

For example:

Speed has dimensions $[L T^{-1}]$
Force has dimensions $[M L T^{-2}]$
Energy has dimensions $[M L^2 T^{-2}]$

Why this matters: Two quantities can only be meaningfully compared or equated if they have the same dimensions. You cannot add apples to oranges — and you cannot add length to time.

2. The Principle of Dimensional Homogeneity

The key formula that underpins everything is:

Every valid physical equation must be dimensionally homogeneous.

This means: the dimensions on the left-hand side must equal the dimensions on the right-hand side.

Why must this hold?

Consider an equation like:

v = u + at

Left side: $[v] = L T^{-1}$
Right side: $[u] = L T^{-1}$ , $[at] = (L T^{-2})(T) = L T^{-1}$

Both sides have dimensions $L T^{-1}$ . If they didn't match, the equation would be physically meaningless — you'd be comparing quantities that cannot be equal in any real experiment.

Reasoning: Physical laws describe relationships between measurable quantities. If the dimensions don't match, the equation cannot represent a real physical relationship, because the numerical value would depend on the arbitrary choice of units.

3. The Buckingham Pi Theorem: Why We Can Derive Relationships

This is the deeper mathematical reason. The Buckingham Pi Theorem states:

If a physical problem involves $n$ variables and $k$ fundamental dimensions, then it can be reduced to $n-k$ independent dimensionless groups (called $\pi$ groups).

Why does this work?

Imagine you have a relationship:

f(Q_1, Q_2, \dots, Q_n) = 0

where each $Q_i$ has dimensions. Because the equation must be dimensionally homogeneous, we can rearrange it into a function of dimensionless products only:

F(\pi_1, \pi_2, \dots, \pi_{n-k}) = 0

The reasoning: Dimensions act as constraints. Each fundamental dimension (M, L, T) gives one constraint. So if you have $n$ variables and $k$ constraints, you only have $n-k$ independent dimensionless combinations.

Example: For a simple pendulum, the period $T$ depends on length $L$ , mass $m$ , and gravity $g$ . That's 4 variables with 3 dimensions (M, L, T). So $4-3 = 1$ dimensionless group: $\pi = \frac{T^2 g}{L}$ . This tells us $T \propto \sqrt{L/g}$ without solving any differential equation.

4. Why We Can Convert Units Using Dimensional Analysis

The conversion factor formula:

\text{Value in new unit} = \text{Value in old unit} \times \left(\frac{\text{old unit}}{\text{new unit}}\right)^{\text{dimension exponent}}

Why this works: …

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Dalton's statement about atoms combining in fixed ratios directly explains the Law of Definite Proportions and the Law of Multiple Proportions. The Law of Conservation of Mass and Avogadro's Law are not directly related to this specific aspect of compound formation. The correct options are (i) and (iv).

Dalton's atomic theory was a revolutionary step in understanding the nature of matter. The statement "Compounds are formed when atoms of different elements combine in a fixed ratio" is fundamental to how we understand chemical composition. It describes how elements come together to form new substances with distinct properties. To determine which laws are not related to this statement, we need to understand what each law implies and how it connects to the idea of fixed ratios of atoms.

Concept and Intuition: The Essence of Fixed Ratios

Dalton's statement means that for any given compound, say water ( $\text{H}_2\text{O}$ ), hydrogen and oxygen atoms always combine in a specific, unchanging whole-number ratio (2 hydrogen atoms for every 1 oxygen atom). This fixed atomic ratio is what gives a compound its unique identity and properties. If the ratio changed, it would be a different substance (e.g., hydrogen peroxide, $\text{H}_2\text{O}_2$ , has a different ratio and is a different compound). This idea of fixed, simple whole-number ratios at the atomic level is key to understanding the macroscopic laws of chemical combination.

Let's examine each law in relation to this core idea:

Analyze Dalton's Statement:

The statement "Compounds are formed when atoms of different elements combine in a fixed ratio" focuses on the composition of compounds. It implies that atoms are discrete, indivisible units that combine in specific numerical relationships to form molecules or formula units.
Evaluate Option (i) Law of Conservation of Mass:

This law states that mass is neither created nor destroyed in any chemical reaction. The total mass of the reactants equals the total mass of the products.
- Relationship to Dalton's statement: While Dalton's overall atomic theory supports the Law of Conservation of Mass (because atoms are merely rearranged, not destroyed or created during a reaction), the specific statement about atoms combining in a "fixed ratio" to form compounds does not directly explain or imply the conservation of mass. The fixed ratio describes how atoms combine, not the total mass balance of the reaction itself.
Evaluate Option (ii) Law of Definite Proportions (or Law of Constant Composition):

This law states that a given chemical compound always contains its component elements in fixed ratio by mass, regardless of its source or method of preparation.
- Relationship to Dalton's statement: This law is directly explained by Dalton's statement. If atoms of different elements combine in a fixed number ratio (e.g., 2 hydrogen atoms to 1 oxygen atom in water), and each type of atom has a fixed mass, then the mass ratio of the elements in the compound must also be fixed. For example, in $\text{H}_2\text{O}$ , the mass ratio of hydrogen to oxygen is $(2 \times \text{atomic mass of H}) : (1 \times \text{atomic mass of O})$ , which is a constant value.
Important

Dalton's idea of fixed atomic ratios provides the atomic-level explanation for the macroscopic observation described by the Law of Definite Proportions.
Evaluate Option (iii) Law of Multiple Proportions:

This law states that when two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in ratios of small whole numbers. …

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Here are the common mistakes students make with this question, along with how to avoid each.

Mistake 1: Misreading the Question as "Single Correct"

The most frequent error is treating this as a "choose the one correct option" question. The prompt explicitly states it is a multiple-correct question, meaning two or more options may be correct.

How to avoid: Always read the instruction line carefully. If it says "multiple correct" or "two or more options may be correct," you must evaluate each option independently. Do not stop after finding one "wrong" answer.

Mistake 2: Confusing the Law of Definite Proportions with the Statement

The statement in the question is essentially the Law of Definite Proportions (also called Proust's Law). It says a compound always contains the same elements in the same proportion by mass.

The Mistake: Students think, "The statement is about fixed ratios, so the Law of Definite Proportions must be related." They then incorrectly mark it as "not related."
How to avoid: The question asks which law is not related to the statement. Since the statement is the Law of Definite Proportions, this law is directly related. Therefore, option (ii) is not a correct answer for "not related." You must eliminate it.

Mistake 3: Forgetting the "Fixed Ratio" Implication for Multiple Proportions

The Law of Multiple Proportions deals with different compounds formed from the same elements (e.g., CO and CO₂). It states that the masses of one element that combine with a fixed mass of the other are in a ratio of small whole numbers.

The Mistake: Students think, "Both laws talk about ratios, so they must be related."
How to avoid: The key difference is fixed ratio (one compound) vs. multiple ratios (different compounds). The given statement is about a single compound forming in a fixed ratio. The Law of Multiple Proportions is about different compounds having different fixed ratios. Therefore, the statement does not describe the Law of Multiple Proportions. Option (iii) is a correct answer for "not related."

Mistake 4: Assuming "Conservation of Mass" is Always Related to Dalton's Theory

Dalton's theory does include the idea that atoms are indestructible, which implies mass is conserved in a chemical reaction.

The Mistake: Students see "Dalton" and "atoms" and automatically assume the Law of Conservation of Mass is related to this specific statement. …

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Q.One of the statements of Dalton's atomic theory is given below: "Compounds are formed when atoms of different elements combine in a fixed ratio" Which of the following laws is not related to this statement? (Note: this is a multiple-correct question; two or more options may be correct.)

Concept understanding — Unit Conversion

Unit Conversion: Why 1 Metre and 100 Centimetres Are the Same Thing

The Intuition: Same Quantity, Different Labels

The Precise Statement

How to Convert: The Only Rule You Need

The Reverse: Metres to Centimetres

Common Conversion Factors You'll Use

Why this formula?

Dimensional Analysis: Why the Key Principles Hold

1. The Core Idea: Physical Quantities Have Dimensions

2. The Principle of Dimensional Homogeneity

Why must this hold?

3. The Buckingham Pi Theorem: Why We Can Derive Relationships

Why does this work?

4. Why We Can Convert Units Using Dimensional Analysis

Why this works: …

Concept and Intuition: The Essence of Fixed Ratios

Concept: Dalton's Atomic Theory and the Laws of Stoichiometry

Method: Law–Statement Matching

Mistake 1: Misreading the Question as "Single Correct"

Mistake 2: Confusing the Law of Definite Proportions with the Statement

Mistake 3: Forgetting the "Fixed Ratio" Implication for Multiple Proportions

Mistake 4: Assuming "Conservation of Mass" is Always Related to Dalton's Theory

Q.One of the statements of Dalton's atomic theory is given below: "Compounds are formed when atoms of different elements combine in a fixed ratio" Which of the following laws is not related to this statement? (Note: this is a multiple-correct question; two or more options may be correct.)

Concept and Intuition: The Essence of Fixed Ratios

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