MHT-CET Chemistry · Formula sheet

States of Matter formulas

9 formulas, 1 reference table and 19 common traps for MHT-CET Chemistry States of Matter, grouped by subtopic.

Gas Laws and the Ideal Gas Equation

Boyle's law — pressure and volume

Boyle's law

P_1 V_1 = P_2 V_2 \qquad (T,\, n \text{ constant})

$P_1, V_1$ initial pressure and volume
$P_2, V_2$ final pressure and volume

Charles' law — volume and temperature

Charles' law

\dfrac{V_1}{T_1} = \dfrac{V_2}{T_2} \qquad (P,\, n \text{ constant})

$V_1, V_2$ initial and final volume
$T_1, T_2$ initial and final absolute temperature (K)

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})

$P_1, P_2$ initial and final pressure
$T_1, T_2$ initial and final absolute temperature (K)

Combined gas law

\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}

$P_1, V_1, T_1$ initial pressure, volume, absolute temperature
$P_2, V_2, T_2$ final pressure, volume, absolute temperature

Ideal gas equation, PV = nRT

Ideal gas equation

PV = nRT = \dfrac{m}{M}RT

$P$ pressure (Pa with R = 8.314; atm with R = 0.0821)
$V$ volume (m^3 with R = 8.314; L with R = 0.0821)
$n$ number of moles, = m/M
$R$ gas constant (8.314 J K^-1 mol^-1 or 0.0821 L atm K^-1 mol^-1)
$T$ absolute temperature (K)

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)

$P$ pressure exerted by the gas
$M$ molar mass of the gas
$m$ mass of gas (same for all in the comparison)

Common traps

No unit conversion inside Boyle's law

Because P and V appear on both sides, they only need to be consistent, not SI. Keep atm with atm and mL with mL — converting to Pa or m3 wastes time and invites arithmetic slips.

Boyle's law is P vs V — not PV vs P

In a 'which graph explains Boyle's law?' question, the answer is the P-vs-V hyperbola. A straight horizontal line is the

PV

-vs-

P

plot (also a consequence, but not the direct Boyle graph the bank usually wants).

Kelvin, always — never Celsius in the ratio

V/T

is constant only for the absolute temperature. Plugging in

99

and

80

(degrees C) instead of

372

and

353

K gives a badly wrong answer. Convert first:

T(\text{K}) = t(^{\circ}\text{C}) + 273

Absolute zero is negative

0\ \text{K} = -273.15\,^{\circ}\text{C}

, not

+273.15

. All molecular motion ceases here, and it is the temperature at which a gas's extrapolated volume would reach zero.

Do not mix up the three simple laws

V/T = \text{const}

is Charles' law, and

PV = \text{const}

is Boyle's law. Gay-Lussac's law is

P/T = \text{const}

at constant volume — the odd one out that fixes V, not T or P.

Absolute temperature here too

P/T

is constant only with T in kelvin. Convert any Celsius temperature before forming the ratio.

T on the DENOMINATOR, in kelvin

The temperature sits under PV:

PV/T

. A common slip is writing

PVT = \text{const}

or leaving T in Celsius. Keep the form

\dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2}

with kelvin temperatures.

Match R's units to the pressure and volume

Using

R = 0.0821

with pressure in Pa, or

R = 8.314

with volume in litres, gives an answer off by orders of magnitude. Decide the R value FIRST from the units given, then convert everything to match (litres <-> m

^3

, atm <-> Pa).

Watch a printed exponent typo

For

3.4

mol in

68\ \text{mL} = 68 \times 10^{-6}\ \text{m}^3

at 300 K,

P = \dfrac{nRT}{V} = \dfrac{3.4 \times 8.314 \times 300}{68 \times 10^{-6}} = 1.247 \times 10^{8}\ \text{Pa} = 1.247 \times 10^{5}\ \text{kPa}

. Some printed papers mis-type this as

1.247 \times 10^{2}

kPa — trust your derivation; the mantissa 1.247 is what matches.

Equal MASS, not equal moles

This trick only works because the masses are equal — then

P \propto 1/M

. If instead the moles were equal, all four gases would exert the SAME pressure (same n, V, T). Read whether the question fixes mass or moles.

Lightest gas = highest pressure

It is easy to guess the heaviest gas (

\text{Cl}_2

) exerts the most pressure — the opposite is true. Fewer moles per gram means

\text{Cl}_2

gives the lowest pressure;

\text{H}_2

gives the highest.

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

Learn this subtopic in the notes

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}}

$P_i$ partial pressure of component i
$x_i$ mole fraction of component i
$n_i$ moles of component i
$P_{\text{total}}$ total pressure of the mixture

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}}

$v_{rms}$ root-mean-square velocity
$R$ universal gas constant
$T$ absolute temperature (K)
$M$ molar mass (kg/mol in SI)

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

$Z$ compressibility factor (1 for ideal, ≠ 1 for real)
$a$ van der Waals constant for intermolecular attraction
$b$ van der Waals constant for molecular volume

Postulates of the kinetic theory of gases

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.

Common traps

Partial pressure follows moles, not mass

Equal masses of two gases do NOT exert equal partial pressures. Convert every mass to moles first: the lighter gas (smaller

M

) has more moles and the larger partial pressure. For equal masses of

\text{H}_2

and He, the ratio is

2:1

, not

1:1

Use the total moles in the denominator

Mole fraction is

x_i = n_i / n_{\text{total}}

, where

n_{\text{total}}

is the sum over all gases in the mixture. Forgetting one component inflates every mole fraction and the sum of all

x_i

will not equal 1.

Take the square root at the end

The molar-mass and temperature factors sit inside a square root. If the combined ratio inside works out to

4

, the velocity ratio is

\sqrt{4} = 2

, not

4

. Forgetting the root is the most common error in these ratio problems.

Use absolute temperature in kelvin

v_{rms} = \sqrt{3RT/M}

needs

T

in kelvin. Never plug in Celsius — convert

t\,^\circ\text{C}

T = t + 273

K first.

Kinetic energy depends on temperature, not on the gas

The average kinetic energy of gas molecules depends only on the absolute temperature — at the same

T

\text{H}_2

and

\text{O}_2

have the same average kinetic energy. They differ in speed (the lighter gas moves faster), not in energy.

Ideal gas = zero volume AND zero force

An ideal gas assumes both that molecules have no volume and that there are no forces between them. A real gas violates both, which is why it deviates most where these matter — at high pressure and low temperature.

Z = 1 means ideal, in either direction

A gas is ideal only when

Z = 1

. Both

Z > 1

(repulsion / molecular volume dominates) and

Z < 1

(attraction dominates) mean the gas is real — the deviation, not its sign, is what matters.

Multiply, do not add, the ideal molar volume

V_{\text{real}} = Z \times V_{\text{ideal}}

. For

Z = 1.05

at STP that is

1.05 \times 22.4 = 23.52\,\text{dm}^3

, not

22.4 + 1.05

. Z is a multiplying factor, not an offset.

States of Matter formulas

Gas Laws and the Ideal Gas Equation

Boyle's law — pressure and volume

Charles' law — volume and temperature

Gay-Lussac's law — pressure and temperature

Ideal gas equation, PV = nRT

Equal masses in equal volumes — lightest gas, highest pressure

Common traps

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

Dalton's law of partial pressures

Root-mean-square velocity

Real gases and the compressibility factor

Postulates of the kinetic theory of gases

Common traps

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