what is Ideal gas equation ? Derive equation of ideal gas and give characteristic of R and its value.

Explanation

Ideal gas equation : The equation get through the combination of Boyle.s, Charle.s and Avogadro.s law is called ..Ideal Gas Equation...
Ideal gas equation : pV = nRT …..(Eq. -i)
Ideal gas equation is a relation between four variables (p, V, n, R). It describe the state of any gas, so it is called equation of state.
Derivation the equation of ideal gas :
(i) Boyle.s law : `V prop (1)/(p)` ....(constant T and n)
(ii) Charles. Law : `V prop T` ....(constant p and n)
(iii) ASvogadro Law : `V prop n` ....(constant p and T)
Thus, `V prop (nT)/(p)" "` ....(Eq. -i)
Id standard constant = R,
`therefore V =R((nT)/(p)) " "` ....(Eq. - ii)
Thus, [pV = nRT]
This (Eq. -i) is know as ideal gas equation.
Characteristic of gas constant and value R :
R is known as gas constant.
Value of R is same for each gases. So it is known as universal gas constant.
Value of R depends upon the measurements unit p, V and T.
Calculation of R value : Volume of one mole of an ideal gas under STP conditions (273.15 K temperature and 1 bar pressure) is 22.710981 L `mol^(-1)`. Value of R for 1 mole of an ideal gas can be calculated under these conditions as follows :
where, p = 1 bar `= 10^(5)` Pa
V = mole volume `= 22.71 mol^(-1) = 22.71xx10^(-3)m^(3)`
n = 1 mol, T = 273.15 K
pV = nRT .....(according to Eq. -5.24)
`therefore R=(pV)/(nT) " "` ...(Eq. -5.26)
`therefore R=((10^(5)Pa)(22.71xx10^(-3)m^(3)))/((1mol)(273.15 K))`
`= 8.3141 Pa m^(3)mol^(1)K^(-1)`
`therefore R = 8.3141xx10^(-2)` bar L `K^(-)mol^(-1)`
`R=8.314 J K^(-1)mol^(-1)`
At STP conditions `0^(@)C` (273.15 K) and 1 atm.
pressure value of R is as under.
`R = 8.20578xx10^(-2)` L atm `K^(-1)mol^(-1)`
= 0.082 L atm `K^(-1) mol^(-1)`