Q.What is the relation between vapour density and molecular mass of a gas?
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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 (H2O) weighs about 3×10−23 grams. That number is useless for practical chemistry. So instead of working with individual molecules, chemists count them in huge fixed numbers — specifically, 6.022×1023 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 6.022×1023 molecules of this compound, how much would they weigh on a lab balance?"
The number 6.022×1023 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 (H2O): 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 H2O = 2(1.008)+16.00=18.016 g/mol
Molecular mass=∑(number of atoms of each element×atomic mass of that element)
How to Calculate It — Step by Step
Let's take glucose, C6H12O6, 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
Molecular mass=6(12.01)+12(1.008)+6(16.00)
=72.06+12.096+96.00
=180.156 g/mol
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: moles=molecular massmass in grams
- Convert moles to grams: mass=moles×molecular mass
- Determine the number of molecules: molecules=moles×6.022×1023
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 CO2 = 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 H2SO4, 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 6.022×1023 particles (Avogadro's number, NA).
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=Mm
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 Mm moles.
Derivation logic:
- Molar mass M tells you: "1 mol = M g"
- So the conversion factor is M g1 mol
- Multiply mass m by this factor: m×M1=Mm moles
3. Connecting to Number of Particles
n=NAN
Where:
- N = number of particles (atoms, molecules, ions)
- NA=6.022×1023 particles/mol
Why?
- 1 mole = NA particles
- So N particles = NAN moles
Combine both formulas:
Mm=NAN
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=22.4 L/molV
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=PnRT=11×0.0821×273.15≈22.4 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→cC+dD
The coefficients tell you the mole ratio:
moles of Bmoles of A=ba
Why this works: …
Vapour density (VD) is the density of a gas relative to hydrogen gas measured under the same conditions of temperature and pressure. Since molar mass is proportional to density at fixed T and P, the molar mass of hydro …
Molecular mass equals twice the vapour density, because vapour density is defined relative to hydrogen (M = 2 g/mol).
Vapour density of a gas is defined as:
VD = density of the gas / density of hydrogen (at the same temperature and pressure)
At the same temperature and pressure, density is directly proportional to molar mass (from the ideal gas equation, PM = dRT, so d is proportional to M for fixed P, T). Therefore:
VD = M(gas) / M(H2)
Since M(H2) = 2 g/mol:
VD = M(gas) / 2
…
- CBSE 2025Set ANNUAL1 markMCQQ.The molecular weight of glucose (C6H12O6) molecule is(a) 90 U(b) 120 U(c) 180 U(d) 360 U
›Reveal solutionSolution
Glucose (C6H12O6) has a molecular mass of 180 u.
Atomic masses: C = 12 u, H = 1 u, O = 16 u.
…
- CBSE 2025Set sz1 markMCQQ.Select the correct one: Which of the following is the standard for atomic mass?(a) 1/1 H(b) 12/6 C(c) 14/6 C(d) 16/8 O
›Reveal solutionSolution
The modern standard for atomic mass is the carbon-12 isotope; 1 amu = 1/12 the mass of a 12/6 C atom.
Before 1961, both oxygen-16 and hydrogen-1 standards were tried, but chemists and physicists used slightly different oxygen-based scales, causing confusion. In 1961 IUPAC adopted a single unified standard: the carbon-12 isotope (12/6 C) was assigned a mass of exactly 12 atomic mass units (amu), and 1 amu is defined as 1/12th of the mass of one …
- CBSE 2024Set ANNUAL1 markMCQQ.What is the molar mass of H2O in gm/mol?(a) 44(b) 18(c) 17(d) 60
›Reveal solutionSolution
Molar mass of H₂O = 2 × (atomic mass of H) + 1 × (atomic mass of O) = 2(1) + 16 = 18 g/mol.
Atomic mass of H ≈ 1 u, atomic mass of O ≈ 16 u.
…
- CBSE 2024Set ANNUAL1 markMCQQ.Molecular mass of volatile substance is determined by:(a) Kjeldahl's method(b) Duma's method(c) Victor Mayer's method(d) Leibig's method
›Reveal solutionSolution
Victor Meyer's method determines the molecular mass of a volatile substance by measuring the volume of air displaced when a known mass of the substance is vaporised.
Each method listed determines something different:
- Kjeldahl's method — estimates the percentage of nitrogen in an organic compound, not molecular mass.
- Dumas' method — also estimates % nitrogen (by converting it to N₂ gas and measuring its volume), not molecular mass of a volatile substance directly. …
- CBSE 2023Set ANNUAL1 markMCQQ.Molar mass of CO2 is:(a) 22(b) 38(c) 44(d) 28
›Reveal solutionSolution
Adding one carbon (12 u) and two oxygens (16 u each) gives the molar mass of CO2 as 44 g/mol.
Molar mass = sum of atomic masses of all atoms in the formula.
…
- CBSE 2022Set TERM11 markMCQQ.The molar mass of CH4 is(a) 16 u(b) 20 u(c) 10 u(d) 24 u
›Reveal solutionSolution
Add up the atomic masses of all atoms in one CH4 molecule: 1 carbon + 4 hydrogens.
Molar mass is the sum of the atomic masses of every atom in the formula.
…
- CBSE 2022Set ANNUAL1 markQ.Write right or wrong: Molecular mass of water is 18.
›Reveal solutionSolution
The statement is Right: the molecular mass of water (H2O) is 18 u.
Molecular mass is the sum of the atomic masses of all atoms in the molecular formula. Water's formula is H2O: two hydrogen atoms (average atomic mass about 1 u each) plus one oxygen atom (average atomic mass about 16 u): Mo …
- CBSE 2022Set sz1 markQ.What is the relation between vapour density and molecular mass of a gas?
›Reveal solutionSolution
Molecular mass equals twice the vapour density, because vapour density is defined relative to hydrogen (M = 2 g/mol).
Vapour density of a gas is defined as:
VD = density of the gas / density of hydrogen (at the same temperature and pressure)
At the same temperature and pressure, density is directly proportional to molar mass (from the ideal gas equation, PM = dRT, so d is proportional to M for fixed P, T). Therefore:
VD = M(gas) / M(H2)
Since M(H2) = 2 g/mol:
VD = M(gas) / 2
…
- CBSE 2018Set ANNUAL1 markQ.Calculate the molecular weight of the following compounds:(i) C6H12O6(ii) H2SO4
›Reveal solutionSolution
The molecular weight of C6H12O6 (glucose) is 180 g/mol and of H2SO4 (sulphuric acid) is 98 g/mol, found by summing the atomic weights of each constituent atom.
Using standard atomic weights C = 12, H = 1, O = 16, S = 32:
(i) C6H12O6:
C: 6 × 12 = 72
H: 12 × 1 = 12
O: 6 × 16 = 96
Total = 72 + 12 + 96 = 180 g/mol
…
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