Saved Bookmarks
| 1. |
what is Ideal gas equation ? Derive equation of ideal gas and give characteristic of R and its value. |
|
Answer» Solution :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)` |
|