All Important Formula — Class 12 Chemistry Notes

Topics covered in All Important Formula

1. 1.Kinetic Theory of Gases Formulas

   1. Boyle’s Law

   Formula:

   PV=constant (at constant temperature)

   
   Explanation:

   Boyle's law states that the pressure (P) of a gas is inversely proportional to its volume (V) if the temperature remains constant. If you decrease the volume, the pressure increases.

   
   Example:

   If a gas occupies 2 liters at a pressure of 3 atm, what will the volume be if the pressure increases to 6 atm?

   P1V1=P2V23×2=6×V2 ⟹ V2=1 liter

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   2. Charles’ Law

   Formula:

   VT=constant (at constant pressure)

   Explanation:

   Charles’ law states that the volume (V) of a gas is directly proportional to its absolute temperature (T) when pressure is kept constant.

   
   Example:

   If a gas has a volume of 3 liters at 300 K, what will the volume be at 600 K?

   V1T1=V2T23300=V2600 ⟹ V2=6 liters

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   3. Ideal Gas Equation

   Formula:

   PV=nRT

   Explanation:

   This equation relates pressure (P), volume (V), number of moles (n), universal gas constant (R), and temperature (T) of an ideal gas.

   
   Example:

   Calculate the pressure of 2 moles of gas at 300 K occupying a volume of 10 liters.
   (R = 0.0821 L·atm/mol·K)

   P=nRTVP=2×0.0821×30010 ⟹ P=4.926 atm

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   4. Mean Square Velocity

   Formula:

   C2=C12+C22+C32+…+Cn2n

   Explanation:

   The mean square velocity is the average of the squares of the velocities of gas molecules.

   
   Example:

   For three molecules with velocities 2 m/s, 3 m/s, and 4 m/s:

   C2=22+32+423=4+9+163=293≈9.67 m2/s2

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   5. Pressure of a Gas

   Formula:

   P=13ρC2

   Explanation:

   This formula relates the pressure (P) of a gas to its density (ρ) and the mean square velocity (C2).

   
   Example:

   If the density of a gas is 0.5 kg/m³ and the mean square velocity is 300 m²/s:

   P=13×0.5×300=50 Pa

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   6. Kinetic Energy per Unit Volume

   Formula:

   KE=32P

   Explanation:

   The kinetic energy per unit volume of a gas is proportional to its pressure.

   
   Example:

   If the pressure is 100 Pa:

   KE=32×100=150 J/m3

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   7. Gas Equation

   Formula:

   PV=13mNC2

   Explanation:

   This equation relates the pressure (P) and volume (V) of a gas to the number of molecules (N), mass (m), and mean square velocity (C2).

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   8. Kinetic Energy of a Mole of Gas

   Formula:

   KE=32RT

   Explanation:

   The kinetic energy of one mole of gas depends on the temperature (T) and gas constant (R).

   
   Example:

   At 300 K (R = 8.314 J/mol·K):

   KE=32×8.314×300=3741.3 J

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   9. Kinetic Energy of a Molecule

   Formula:

   KE=32kT

   Explanation:

   This gives the kinetic energy of a single molecule, where k is the Boltzmann constant.

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   10. Mayer’s Formula

   Formula:

   Cp−Cv=R

   Explanation:

   This formula shows the relationship between the specific heat at constant pressure (Cp) and constant volume (Cv) for a gas.

2. 2.Atoms, Molecules, and Nuclei Formulas

   1. Radioactive Decay

   Formula:

   N=N0e−λt

   Explanation:

   This formula gives the number of undecayed nuclei (N) at time t.

   • N0 = Initial number of nuclei
   • λ = Decay constant
   • t = Time

   Example:

   If N0=1000 and λ=0.001 per second, find N after 1000 seconds:

   N=1000×e−0.001×1000=1000×e−1≈368

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   2. Half-Life Period

   Formula:

   T1/2=0.693λ

   Explanation:

   This formula gives the half-life (T1/2), which is the time taken for half of the radioactive substance to decay.

   
   Example:

   If the decay constant λ is 0.001 per second:

   T1/2=0.6930.001=693 seconds

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   3. Decay Constant Formula

   Formula:

   λ=2.303tlog⁡N0N

   Explanation:

   This formula calculates the decay constant (λ) using the initial and remaining number of nuclei over time t.

   
   Example:

   If N0=1000, N=500, and t=10 seconds:

   λ=2.30310log⁡1000500≈0.0693 per second

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   4. Second Postulate of Bohr's Theory

   Formula:

   mvr=nh2π

   Explanation:

   This formula states that the angular momentum of an electron in a stable orbit is quantized.

   • m = Mass of the electron
   • v = Velocity
   • r = Radius of the orbit
   • n = Principal quantum number
   • h = Planck's constant

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   5. Bohr’s Formula for Wavelength of Emitted Light

   Formula:

   1λ=R(1n12−1n22)

   Explanation:

   This formula calculates the wavelength (λ) of the emitted photon during an electron transition between two energy levels (n1 and n2).

   • R = Rydberg constant

   Example:

   For n1=1 and n2=2 (Lyman series):

   1λ=R(112−122)=R(1−0.25)=0.75R

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   6. Einstein's Energy-Mass Equation

   Formula:

   E=mc2

   Explanation:

   This formula shows the relationship between energy (E) and mass (m), where c is the speed of light.

   
   Example:

   If m=1 kg:

   E=1×(3×108)2=9×1016 joules

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   7. Radius of nth Bohr Orbit

   Formula:

   rn=n2h24π2me2Z

   Explanation:

   This gives the radius of the nth orbit in a hydrogen-like atom.

   • Z = Atomic number

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   8. De Broglie Wavelength of Electron

   Formula:

   λ=hp=hmv=h2meV

   Explanation:

   This formula calculates the wavelength (λ) of a particle with momentum p.

   
   Example:

   For an electron with velocity v=106 m/s (h = 6.63×10−34 Js, m = 9.1×10−31 kg):

   λ=6.63×10−349.1×10−31×106≈7.3×10−10 m

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   9. Number of Photons

   Formula:

   n=Pλhc

   Explanation:

   This formula calculates the number of photons (n) in a beam of light with power P and wavelength λ.

   
   Example:

   For P=3 W, λ=500 nm=500×10−9 m:

   n=3×500×10−96.63×10−34×3×108≈7.5×1015

3. 3.Electrons and Photons Formulas

   1. Velocity of Electron

   Formula:

   V=EB

   Explanation:

   This formula gives the velocity (V) of an electron moving in an electric field (E) and a magnetic field (B).

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   2. Energy of a Photon

   Formula:

   E=hν=hcλ

   Explanation:

   This formula gives the energy (E) of a photon in terms of Planck's constant (h), frequency (ν), speed of light (c), and wavelength (λ).

   
   Example:

   If λ=500 nm,
   h=6.63×10−34 Js, c=3×108 m/s:

   E=6.63×10−34×3×108500×10−9≈3.98×10−19 J

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   3. Wavelength and Frequency Relationship

   Formula:

   λ=cν

   Explanation:

   This formula relates the wavelength (λ) of a photon to its frequency (ν) and the speed of light (c).

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   4. Einstein’s Photoelectric Equation

   Formula:

   EP=hν=12mv2+hν0

   Explanation:

   This equation relates the energy of a photon (hν) to the kinetic energy of the emitted electron and the work function (hν0).

   
   Example:

   If hν=5 eV and hν0=2 eV:

   12mv2=5−2=3 eV

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   5. Threshold Frequency

   Formula:

   ν0=he

   Explanation:

   This formula represents the threshold frequency (ν0) required to emit an electron during the photoelectric effect.

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   6. Maximum Kinetic Energy of Electron

   Formula:

   K.Emax=12mvmax2=h(ν−ν0)

   Explanation:

   This formula gives the maximum kinetic energy of an electron emitted in the photoelectric effect.

   
   Example:

   If hν=4 eV and hν0=2 eV:

   K.Emax=4−2=2 eV

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   7. Kinetic Energy and Frequency Relationship

   Formula:

   K.Emax2=hν2−hν02

   Explanation:

   This formula expresses kinetic energy as a function of photon frequency and threshold frequency.

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   8. Electron Velocity Formula

   Formula:

   12mv2=KEandv=2KEm

   Explanation:

   This formula calculates the velocity of an electron when its kinetic energy (KE) is known.

   
   Example:

   If KE=4×10−19 J and m=9.1×10−31 kg:

   v=2×4×10−199.1×10−31≈9.4×105 m/s

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   9. Wavelength of Electron

   Formula:

   λ=h2meV

   Explanation:

   This formula gives the de Broglie wavelength of an electron accelerated by a potential V.

   
   Example:

   If V=100 V, h=6.63×10−34 Js, and m=9.1×10−31 kg:

   λ=6.63×10−342×9.1×10−31×1.6×10−19×100≈1.23×10−10 m