The Properties of Gases
Pressure- it is defined as force divided by the area to which the force is applied.
- Measured with a barometer.
p = F/A
F = mg
F = ρAgh
p = F/A = ρAgh
A
Therefore, p = ρgh
Temperature- it is the property that indicates the direction of the flow of energy through a thermally conducting, rigid wall.
- a boundary is diathermic if a change of state is observed when two objects at different temperatures are brought into contact.
- A boundary is adiabatic if no change occurs even though the two objects have different temperatures.
Thermal equilibrium is established if no change of state occurs when two objects are in contact through a diathermic boundary.
Zeroth law of thermodynamics-
If A is in thermal equilibrium with B and B is in thermal equilibrium with C, then C is also in thermal equilibrium with A.
The Gas Laws-
Boyle's law-
At constant temperature, the pressure of a sample of gas is inversely proportional to its volume.
P α 1/V
Charles's law-
At constant pressure volume is directly proportional to temperature.
Gay-lussac's law-
At constant volume pressure is directly proportional to temperature.
V = constant × temperature
P = constant × temperature
Avogadro's principle-
At constant pressure and temperature volume of the gas is directly proportional to the amount of molecules (in moles) present in it.
V = constant × n
The perfect gas law-
pV = constant × nT
pV = nRT
Combined gas equation-
P1V1 = nR
T1
P2V2 = nR
T2
Therefore,
P1V1 = P2V2
T1 T2
Dalton's law-
The pressure exerted by a mixture of gases is the sum of the partial pressure of the gases.
p = pA + pB + …..
Mole fractions and partial pressure-
The mole fraction xJ, is the amount of J expressed as a fraction of the total amount of molecules, n, in the sample.
xJ = nJ/n
n = nA + nB + ….
Partial pressure, pJ, of a gas J in a mixture is
pJ = xJp
the sum of the partial pressures is equal to the total pressure.
pA + pB + …. = (xA + xB + …..)p = p
Real gases-
- do not obey the perfect gas law because molecules interact with each other.
The compression factor-
The compression factor, Z, of a gas is the ratio of its molar volume, Vm, to the molar volume of a perfect gas, Vºm, at the same pressure and temperature.
Vm
Z = Vºm
Virial equation of state, pVm = RT (1 + B/Vm + C/V²m + ……)
Here B, C … are virial coefficient.
Boyle temperature- the temperature at which dZ/dp = 0 as p→ 0
Vapour pressure is the pressure of a vapour in equilibrium with its condensed phase.
Critical point is the point at which the volumes at each end of the horizontal part of the isotherm have merged to a single point.
The temperature, pressure and molar volume at the critical point are called the critical temperature, Tc, critical pressure, pc, and critical molar volume, Vc, of the substance.
The van der Waals equation-
p = nRT/ (V-nb) - a (n/V) ²
Here a and b are van der Waals coefficients.
Van der Waals loops - unrealistic oscillations in the van der Waals isotherms.
Maxwell construction - the equal area rule for the replacement of the van der waals loops by straight lines.
Critical compression factor- it is the value of Z at the critical point.
The principle of corresponding states-
Reduced variables - the actual variable divided by the corresponding critical constant.
Principle of corresponding states- real gases at the same reduced volume and reduced temperature exert the same reduced pressure.
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