Gas Laws - 2

(c) Avogardo’s Law: Equal volume of all gases under same conditions of temperature & pressure contain equal no of molecules.
   V = Kn But n = (m = mass, M = Molar gas)
V = = Kd     d density
=> density of gas is directly proportional to its molar mass.

M d

III. Ideal Gas Equation:

Volume of constant K depends only upon amount of gas taken. If n is no. of moles of gas taken.

K n

K = nR

R Universal gas constant.
= nR
PV = nRT Ideal Equation.


Derivation:

According to Boyles law
at constant T ................................................................ (1)
According Charle's law
V T at constant P ................................................................ (2)
According to Avogardo's law
V n at constant T & P ................................................................ (3)
Combing (1), (2) & (3)
      x T x n
=> PV = nRT     K .......

Ideal Gas Equation (in terms of density):
If M is mass of gas in gm & M is molar mass of gas, then
    n =
PV = RT = RT
    P =

Volume of Gas constant (R):
R = = 0.082 L atm K^-1 mol^-1
In SI unit
R = 8.314 J K^-1 mol^-1
In terms of calori e
R = = 1.987 Cal K^-1 mol^-1>

Illustration: Temperature at foot of mountain is 30⁰C & pressure is 760 mm whereas at top of mountain there are 0⁰C & 710 mm. Compose densities at top & bottom of mountain.
Ans: d =
      


If two or more unreaching gases are enclosed in a vessel, total pressure exerted by gaseous mixture is equal to sum of all partial pressures that eact gas would exert when present alone in same vessel at vessel temperature.

P = P1 + P2 + P3 + .................. + Pn

Applications:

(i) In determination of pressure of dry gas e:

Pdry gas = Pmoist gas - Aqueous tension

Dumb Question: What is equation tension ?
Ans: Pressure exerted by water vapours in moist gas.

(ii) In calculation of partial pressure:

           PV = nRT
           P_A = n_B        P_B = n_B
           P_A & P_B Partial pressure.

By Dalton's law
Total pressure, P = P_A + P_B + P_C + ...................

                        = (n_A + n_B + n_C + ..................)
= x_A(mol.Fraction of A)

PA = = P x xA

Question: 27⁰C & 746.5 mm pressure. Calculate volume of gas at 0⁰C & 760 mm pressure (Aq. tension at 27⁰C is 26.5 mm).
Ans:
[Dumb question: Why there is no ag. tension at 0⁰C ?
Ans: At 0⁰C, there is no water vapours. So, no, ag. tension at 0⁰C.]
Initial Condition              Final condition
V₁ = 38 ml                     V₂ = ?

P₁ = 746.5 - 26.5            P₂ = 760 mm

    = 720 mm
T₁ = 27 + 273 = 300 K    T₂ = 0 + 273 = 273 K

By gas equation

V₂ = 32.76 ml.

Illustration: A gaseous mix contains 56g N₂, 44g CO₂ & 16g CH₄. Total pressure of mix is 720 mm Hq. What is partial pressure of CH₄ ?

Ans: ⁿN₂ = 56/28 = 2    ⁿCO₂ = 44/44 = 1

       ⁿCH₄ = 16/16 = 1

       ⁿTotal = 2 + 1 + 1 = 4

        x Total pressure

            = 1/4 x 720 = 180 mm.

Diffusion: Spreading of molecules of a gas throughout available space.

Sffusion: In this process gas under pressure escapes out of fine hole.

At constant temperature & pressure, rates of diffusion of different gases are inversely proportional to square root of their densities.

Rate of diffusion/effusion =

Mol. Mass = 2 x V.P.

Note: If pressure is different of two gases then greater pressure, greater is no. of molecules hitting per unit area, greater is rate of diffusion.

r₁ = v₁/t      r₂ = v₂/t

v₁ Volume diffused of I gas.

v₂ Volume diffused of II gas.

Time ia constant for two gases.
Volume of two gases is constant.

Question: 200 c,, HCl gas & NH₃ are allowed to enter. At what distance NH₄Cl will I^st appear ?
Ans: By Graham's law of diffusion

Thus, NH₃ travels 1.465 times faster than HCl.
In other words. Since area of x-section is square, NH₃ will travel 1.465 cm in same time in which HCl travel 1 cm.
   Length of tube = 200 cm
Distance travelled in tube by NH₃ = x Total distance
                                                   x 200 = 118.9 cm
So, NH₄Cl will I^st appear at distance of 118.9 cm from NH₃ and or 81.1 cm from HCl end.