MHT-CET Chemistry · Teaching notes

Some Basic Concepts of Chemistry — MHT-CET Chemistry

This is the arithmetic backbone of MHT-CET Chemistry — the chapter that turns grams, litres, molecule-counts and pressures into each other. It is heavily tested (85 PYQs) and mostly straightforward: master a handful of bridges and nearly every question falls in one or two steps. It teaches in six movements, foundations first: (1) SI units, physical properties and average atomic mass — the measurement groundwork; (2) the named laws of chemical combination and percentage composition; (3) the mole concept and its interconversions — the engine room: n = m/M, n = V/22.4, N = n·NA, and vapour density; (4) stoichiometry and concentration — reading mole ratios off a balanced equation, limiting reagent, combining gas volumes and H2O2 volume strength; (5) the gas laws and the ideal gas equation PV = nRT; (6) real gases, Dalton's law of partial pressures and the kinetic theory of gases. Mostly formula concepts with worked numbers; the named laws and KTG postulates live in reference tables. Every PYQ tagged.

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Subtopic notes

PYQ weightage by concept

28 concepts · 53 PYQs — where the marks actually sit, so you know what to drill first

SI Units, Physical Properties and Atomic Abundance6 PYQs · 11%

Concept	PYQs	Share
Common SI derived units	2	4%
The seven SI base units	1	2%
Intensive vs extensive properties	1	2%
Average atomic mass from isotopic abundance	1	2%
Abundance of elements on Earth	1	2%

Laws of Chemical Combination and Percentage Composition7 PYQs · 13%

Concept	PYQs	Share
The five laws of chemical combination	5	9%
Percentage composition by mass	1	2%
Percent atom economy	1	2%

The Mole and Its Interconversions31 PYQs · 58%

Concept	PYQs	Share
Moles from mass and molar mass	11	21%
Molar volume at STP	8	15%
Counting molecules and atoms from moles	4	8%
Counting ions and electrons	4	8%
The mole, Avogadro's number, and one single particle	2	4%
Ratio of molecules from a mass ratio	1	2%
Vapour density to molar mass	1	2%

Stoichiometry and Concentration9 PYQs · 17%

Concept	PYQs	Share
Mole ratios from a balanced equation	6	11%
Combining gaseous volumes and the limiting reagent	2	4%
Concentration: percent by mass and H2O2 volume strength	1	2%

Gas Laws and the Ideal Gas Equation0 PYQs · 0%

Concept	PYQs	Share
Boyle's law — pressure and volumefoundation	—	—
Charles' law — volume and temperaturefoundation	—	—
Gay-Lussac's law — pressure and temperaturefoundation	—	—
Combined gas lawfoundation	—	—
Ideal gas equation, PV = nRTfoundation	—	—
Equal masses in equal volumes — lightest gas, highest pressurefoundation	—	—

Real Gases, Dalton's Law and the Kinetic Theory of Gases0 PYQs · 0%

Concept	PYQs	Share
Dalton's law of partial pressuresfoundation	—	—
Root-mean-square velocityfoundation	—	—
Postulates of the kinetic theory of gasesfoundation	—	—
Real gases and the compressibility factorfoundation	—	—

Formula & revision sheet

22 formulas · 6 reference tables · 47 gotchas across all subtopics — the exam-eve cheat-sheet

SI Units, Physical Properties and Atomic Abundance

Formulas (1)

Average atomic mass from isotopic abundance · Average atomic mass $\bar{m} = \sum_i m_i\,f_i \quad\text{where}\quad \sum_i f_i = 1$

Reference tables (4)

The seven SI base units7 rows

Base quantity	Unit	Symbol
Mass	kilogram	kg
Length	metre	m
Time	second	s
Temperature	kelvin	K Note kelvin has no degree sign: write $300\ \text{K}$ , not $300\ ^\circ\text{K}$ .
Amount of substance	mole	mol
Electric current	ampere	A
Luminous intensity	candela	cdQ The odd one out that PYQs love — candela measures luminous intensity, not energy, force or work.

Learn the pairing in both directions — quantity to unit and unit to quantity.

Common SI derived units6 rows

Quantity	Defining relation	SI derived unit
Volume	length cubed	$\text{m}^3$
Density	mass / volume	$\text{kg m}^{-3}$
Force	mass $\times$ acceleration	newton $\text{N} = \text{kg m s}^{-2}$
Pressure	force / area	pascal $\text{Pa} = \text{N m}^{-2}$
Rate of diffusion	volume / time	$\text{dm}^3\,\text{s}^{-1}$ Q
Coefficient of viscosity	stress / velocity gradient	$\text{N s m}^{-2} = \text{Pa s}$ Q Watch the exponents on $\text{s}$ and $\text{m}$ : the correct form is $\text{N s m}^{-2}$ , not $\text{N s}^{-1}\text{m}^{-2}$ .

Every derived unit is the base units of its defining formula, combined.

Intensive vs extensive properties10 rows

Property	Type	Why
Mass	Extensive	Doubles when the sample doubles.
Volume	Extensive	Scales directly with amount.
Internal energy	Extensive	Total energy grows with amount.
Heat capacity	Extensive	Whole-sample quantity; scales with mass.
Temperature	Intensive	A drop and a bucket of the same liquid share it.
Density	Intensive	Ratio mass/volume — the amounts cancel.
Boiling point	Intensive	Fixed for a pure substance, any amount.
Surface tension	Intensive	A material property, independent of quantity.Q
Viscosity	Intensive	Same for a drop or a barrel of the liquid. Surface tension and viscosity are the intensive pair the bank tests — both material properties, unchanged by sample size.
Specific heat	Intensive	Heat capacity per unit mass — a ratio, so amounts cancel.

Change the sample size in your head: if the value moves, it is extensive.

Abundance of elements on Earth5 rows

Domain	Most abundant element	Approx. share
Earth's crust (by mass)	Oxygen	about 46%Q This is the default 'most abundant element on Earth' answer the bank wants — oxygen.
Earth's crust (2nd)	Silicon	about 28%
Earth's crust (3rd)	Aluminium	about 8%
Whole Earth (by mass)	Iron	about 32%
Universe (by mass)	Hydrogen	about 74%

The winner changes with the domain — match the answer to what the question asks.

Watch out for (5)

Candela measures luminous intensity, not energy
→ The seven SI base units
The exponents on the viscosity unit matter
→ Common SI derived units
Heat capacity is extensive; specific heat is intensive
→ Intensive vs extensive properties
Weight by abundance, not a plain average
→ Average atomic mass from isotopic abundance
Crust versus universe versus whole Earth
→ Abundance of elements on Earth

Laws of Chemical Combination and Percentage Composition

Formulas (2)

Percentage composition by mass · Mass percentage of an element $\%\,\text{element} = \dfrac{n \times A}{M} \times 100$
Percent atom economy · Percent atom economy $\%\,\text{atom economy} = \dfrac{\text{FW of desired product}}{\sum \text{FW of reactants}} \times 100$

Reference tables (1)

The five laws of chemical combination5 rows

Law	Statement	Stock example
Law of conservation of mass	Matter can neither be created nor destroyed in a chemical reaction; total mass of reactants = total mass of products.	$1.7$ g $\text{AgNO}_3 + 0.585$ g $\text{NaCl}$ give $1.435$ g $\text{AgCl} + 0.85$ g $\text{NaNO}_3$ ; both sides total $2.285$ g.
Law of definite (constant) proportions	A given pure compound always contains the same elements in the same fixed proportion by mass, whatever its source.	Water is always $1 : 8$ hydrogen to oxygen by mass.Q Also called Proust's law. The tell-tale phrase in an MCQ is 'a given compound always contains the same proportion of elements'.
Law of multiple proportions	When the same two elements form more than one compound, the masses of one that combine with a fixed mass of the other are in a ratio of small whole numbers.	$\text{CO}$ and $\text{CO}_2$ : oxygen masses per fixed carbon are in a $1 : 2$ ratio.Q The most-asked law here. It ONLY applies when both compounds contain the SAME two elements — this is the whole basis of the 'which pair cannot demonstrate it' questions.
Gay-Lussac's law of combining volumes	Gases combine (and form gaseous products) in volume ratios that are simple whole numbers, at the same temperature and pressure.	$1$ volume $\text{N}_2 + 3$ volumes $\text{H}_2 \to 2$ volumes $\text{NH}_3$ (a $1 : 3 : 2$ ratio). Sometimes phrased as the law of reciprocal proportions in older texts — both express fixed combining relationships; for gases the paper uses the combining-volumes form.
Avogadro's law	Equal volumes of all gases at the same temperature and pressure contain an equal number of molecules.	$22.4$ L of any gas at STP contains $1$ mole $(6.022\times10^{23}$ molecules $)$ .

Recognise the law from either its definition or a worked example.

Watch out for (4)

Multiple proportions needs the SAME two elements
→ The five laws of chemical combination
Definite vs multiple proportions
→ The five laws of chemical combination
Multiply by the number of atoms, not just the atomic mass
→ Percentage composition by mass
Product over reactants, not the other way round
→ Percent atom economy

The Mole and Its Interconversions

Formulas (7)

The mole, Avogadro's number, and one single particle · Mass and volume of one particle $m_{1} = \dfrac{M}{N_A}, \qquad V_{1} = \dfrac{M}{N_A \, \rho}$
Moles from mass and molar mass · Moles from mass $n = \dfrac{m}{M}$
Molar volume at STP · Moles from gas volume at STP $n = \dfrac{V}{22.4}$
Counting molecules and atoms from moles · Particles from moles $N = n \, N_A = \dfrac{m}{M}\, N_A$
Counting ions and electrons · Ions / electrons from moles $N_{\text{ion/e}} = n \, N_A \times k$
Ratio of molecules from a mass ratio · Molecule ratio of two gases $\dfrac{N_A}{N_B} = \dfrac{m_A / M_A}{m_B / M_B}$
Vapour density to molar mass · Molar mass from vapour density $M = 2 \times \text{V.D.}$

Watch out for (13)

Divide by $N_A$ , not multiply, for one particle
→ The mole, Avogadro's number, and one single particle
Volume of one molecule needs the density
→ The mole, Avogadro's number, and one single particle
Convert kg to grams before dividing
→ Moles from mass and molar mass
Use the molar mass of the WHOLE molecule
→ Moles from mass and molar mass
Atoms of an element vs formula units
→ Moles from mass and molar mass
22.4 dm^3 only at STP, and only for gases
→ Molar volume at STP
$1\,\text{m}^3 = 1000\,\text{dm}^3$
→ Molar volume at STP
Atoms need an extra multiplier
→ Counting molecules and atoms from moles
Convert the given volume to dm^3 first
→ Counting molecules and atoms from moles
Ca2+ and Cl- counts differ for the same salt
→ Counting ions and electrons
Electrons per molecule = sum of atomic numbers
→ Counting ions and electrons
Lighter molecule wins for the same mass
→ Ratio of molecules from a mass ratio
Vapour density is HALF the molar mass
→ Vapour density to molar mass

Stoichiometry and Concentration

Formulas (3)

Mole ratios from a balanced equation · Mass of product from a known reactant quantity $m_{\text{target}} = n_{\text{known}} \times \dfrac{\text{coeff}_{\text{target}}}{\text{coeff}_{\text{known}}} \times M_{\text{target}}$
Combining gaseous volumes and the limiting reagent · Product volume from a limiting gaseous reactant $V_{\text{product}} = V_{\text{limiting}} \times \dfrac{\text{coeff}_{\text{product}}}{\text{coeff}_{\text{limiting}}}$
Concentration: percent by mass and H2O2 volume strength · H2O2 molarity from volume strength, and percent by mass $M_{\text{H}_2\text{O}_2} = \dfrac{\text{volume strength}}{11.2} \qquad \%\text{ by mass} = \dfrac{\text{mass of solute}}{\text{mass of solution}}\times 100$

Watch out for (6)

Coefficients are moles, not grams
→ Mole ratios from a balanced equation
Do not skip the fractional ratio
→ Mole ratios from a balanced equation
Identify the limiting reagent before scaling
→ Combining gaseous volumes and the limiting reagent
Volumes need the same T and P
→ Combining gaseous volumes and the limiting reagent
Divide volume strength by 11.2, not 22.4
→ Concentration: percent by mass and H2O2 volume strength
Percent by mass uses the mass of solution, not solvent
→ Concentration: percent by mass and H2O2 volume strength

Gas Laws and the Ideal Gas Equation

Formulas (6)

Boyle's law — pressure and volume · Boyle's law $P_1 V_1 = P_2 V_2 \qquad (T,\, n \text{ constant})$
Charles' law — volume and temperature · Charles' law $\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2} \qquad (P,\, n \text{ constant})$
Gay-Lussac's law — pressure and temperature · Gay-Lussac's law $\dfrac{P_1}{T_1} = \dfrac{P_2}{T_2} \qquad (V,\, n \text{ constant})$
Combined gas law · Combined gas law $\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}$
Ideal gas equation, PV = nRT · Ideal gas equation $PV = nRT = \dfrac{m}{M}RT$
Equal masses in equal volumes — lightest gas, highest pressure · Pressure vs molar mass (equal mass, V, T) $P \propto \dfrac{1}{M} \qquad \left(n = \dfrac{m}{M}\right)$

Watch out for (11)

No unit conversion inside Boyle's law
→ Boyle's law — pressure and volume
Boyle's law is P vs V — not PV vs P
→ Boyle's law — pressure and volume
Kelvin, always — never Celsius in the ratio
→ Charles' law — volume and temperature
Absolute zero is negative
→ Charles' law — volume and temperature
Do not mix up the three simple laws
→ Gay-Lussac's law — pressure and temperature
Absolute temperature here too
→ Gay-Lussac's law — pressure and temperature
T on the DENOMINATOR, in kelvin
→ Combined gas law
Match R's units to the pressure and volume
→ Ideal gas equation, PV = nRT
Watch a printed exponent typo
→ Ideal gas equation, PV = nRT
Equal MASS, not equal moles
→ Equal masses in equal volumes — lightest gas, highest pressure
Lightest gas = highest pressure
→ Equal masses in equal volumes — lightest gas, highest pressure

Real Gases, Dalton's Law and the Kinetic Theory of Gases

Formulas (3)

Dalton's law of partial pressures · Partial pressure from mole fraction $P_i = x_i\,P_{\text{total}} = \dfrac{n_i}{n_{\text{total}}}\,P_{\text{total}}$
Root-mean-square velocity · Root-mean-square velocity and its ratio $v_{rms} = \sqrt{\dfrac{3RT}{M}}\qquad \dfrac{v_1}{v_2} = \sqrt{\dfrac{T_1/M_1}{T_2/M_2}}$
Real gases and the compressibility factor · Compressibility factor and van der Waals equation $Z = \dfrac{PV}{nRT}\qquad \left(P + \dfrac{an^2}{V^2}\right)(V - nb) = nRT$

Reference tables (1)

Postulates of the kinetic theory of gases5 rows

Postulate	Statement
Negligible molecular volume	The actual volume of the gas molecules is negligibly small compared with the total volume of the container; the gas is mostly empty space. This assumption fails at high pressure, when molecules are squeezed close together and their own volume is no longer negligible.
No intermolecular forces	There are no forces of attraction or repulsion between the molecules of an ideal gas; they move completely independently. This assumption fails at low temperature / high pressure, when attractions pull molecules together — the reason gases can be liquefied.
Elastic collisions	Collisions between molecules, and with the walls, are perfectly elastic — the total kinetic energy is conserved during every collision.
Kinetic energy proportional to temperature	The average kinetic energy of the molecules is directly proportional to the absolute temperature; it depends only on T, not on the gas's identity.
Continuous random motion	Molecules are in constant, rapid, random straight-line motion in all directions, colliding with one another and the container walls.

The two bold postulates (zero volume, zero force) are what an ideal gas assumes and a real gas violates.

Watch out for (8)

Partial pressure follows moles, not mass
→ Dalton's law of partial pressures
Use the total moles in the denominator
→ Dalton's law of partial pressures
Take the square root at the end
→ Root-mean-square velocity
Use absolute temperature in kelvin
→ Root-mean-square velocity
Kinetic energy depends on temperature, not on the gas
→ Postulates of the kinetic theory of gases
Ideal gas = zero volume AND zero force
→ Postulates of the kinetic theory of gases
Z = 1 means ideal, in either direction
→ Real gases and the compressibility factor
Multiply, do not add, the ideal molar volume
→ Real gases and the compressibility factor