Notes On Gaseous State: Ideal Gas Equation - Uttar Pradesh board Class 11 Chemistry

The relationship between volume, number of moles, pressure and temperature is described by three laws. They are Boyle's Law, Charles' Law and Avogadro's Law.

Boyle's Law describes the relationship between pressure and volume. It states that volume is inversely proportional to pressure at constant temperature and number of moles.

Charles' Law describes the relationship between temperature and volume. It states that volume is directly proportional to temperature at constant pressure and number of moles.

Avogadro's Law describes the relationship between volume and number of moles. It states that at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles present in the gas.

Ideal gas equation can be obtained by combining these laws,

Boyle's law  V ∝ 1/P (T, n)  
V ∝ Tn/P
V = RTn/P
Charles' law  V ∝ T (P, n)
Avogadro's law  V ∝ n (T, P)

Ideal gas equation - PV =nRT

R is Universal gas constant and it can be calculated as

         R = PV/nT
Temperature = 0° C or 273.15 K
pressur = 101.3 kPa or 105 Pa
Number of moles = 1
Volume = 22.4 l or 22.4 dm3
       
       R = (101.3 x 22.4)/(1 x 273.15)
          = 8.314 j kelvin-1 mole-1

According to the Ideal Gas Equation, the volume occupied by a gas increases in direct proportion to the amount of gas at constant pressure and temperature.

Deducing the relationship between density and molar mass using ideal gas equation

       V = nRT/P
   n/V  = P/RT
m/MV = P/PT  (Where M is the Molecular Mass of Gas)
   d/M = P/RT
      M = dRT/P

Where 'm' is mass of the gas in gram and 'M' is molecular mass of the gas.

Summary

The relationship between volume, number of moles, pressure and temperature is described by three laws. They are Boyle's Law, Charles' Law and Avogadro's Law.

Boyle's Law describes the relationship between pressure and volume. It states that volume is inversely proportional to pressure at constant temperature and number of moles.

Charles' Law describes the relationship between temperature and volume. It states that volume is directly proportional to temperature at constant pressure and number of moles.

Avogadro's Law describes the relationship between volume and number of moles. It states that at constant pressure and temperature, the volume of a gas is directly proportional to the number of moles present in the gas.

Ideal gas equation can be obtained by combining these laws,

Boyle's law  V ∝ 1/P (T, n)  
V ∝ Tn/P
V = RTn/P
Charles' law  V ∝ T (P, n)
Avogadro's law  V ∝ n (T, P)

Ideal gas equation - PV =nRT

R is Universal gas constant and it can be calculated as

         R = PV/nT
Temperature = 0° C or 273.15 K
pressur = 101.3 kPa or 105 Pa
Number of moles = 1
Volume = 22.4 l or 22.4 dm3
       
       R = (101.3 x 22.4)/(1 x 273.15)
          = 8.314 j kelvin-1 mole-1

According to the Ideal Gas Equation, the volume occupied by a gas increases in direct proportion to the amount of gas at constant pressure and temperature.

Deducing the relationship between density and molar mass using ideal gas equation

       V = nRT/P
   n/V  = P/RT
m/MV = P/PT  (Where M is the Molecular Mass of Gas)
   d/M = P/RT
      M = dRT/P

Where 'm' is mass of the gas in gram and 'M' is molecular mass of the gas.

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