Gas Laws
(1)Boyle’s law
Introduction
British scientist Robert Boyle in 1662 shows the relation between pressure and volume of a given mass of a gas at constant temperature
When two measurements are inversely proportional, one gets smaller as the other gets bigger. Boyle's Law is expressed by the equation:
P1V1 = P2V2
Definition
"The volume of a given mass of a gas is inversely proportional to pressure at constant temperature".
Mathematical representation of Boyle’s law
According to Boyle’s law
V µ 1/P
V= (constant) (1/P)
PV=constant
At P1 pressure
P1V1 = constant ------------------ (1)
At P2 pressure
P2V2 = constant ------------------ (2)
Comparing (1) & (2)
P1V1 = P2V2
Comparing (1) & (2)
P1V1 = P2V2
Graphical representation of Boyle’s law
Graph between P & V at constant temperature is a smooth curve known as "parabola"
Graph between 1/P & V at constant temperature is a straight line.
(2) Charles law
Introduction
It is quantitative relation between volume and absolute temperature of a gas at constant pressure.
The Temperature-Volume Relationship was established by Jacques CharlesWhen two measurements are directly proportional, as one changes in size the other undergoes the same size change.
Charles' Law is expressed by the equation:
"The volume of a given mass of a gas at constant pressure is directly proportional to absolute temperature"
Second statement"The volume of a given mass of a gas increases or decreases by 1/273 times of it’s original volume at 0 0C for every degree fall or rise of temperature at given pressure."
Mathematical representation
Then according to Charles’s law
V µ T
V = (constant) T
V/T = constant
V1/T1 = k --------------- (1)
At T2 k
V2/T2 = k --------------- (2)
V1/T1 = V2/T2
By using above equation, Charles’s law can also be stated as:
"The ratio of volume to absolute temperature of a gas at given pressure is always constant"
Graphical representation
Graph between Volume and absolute temperature of a gas at constant pressure is a "straight line"
Absolute scale of temperature or absolute zero If the graph between V and T is extra plotted, it intersects T-axis at -273.16 0C At -273.16 0C volume of any gas theoretically becomes zero as indicated by the graph.
But practically volume of a gas can never become zero. Actually no gas can achieve the lowest possible temperature and before -273.16 0C all gases are condensed to liquid. This temperature is referred to as absolute scale or absolute zero. At -273.16 0C all molecular motions are ceased.
The General or Ideal Gas Equation is obtained by combining relations such as Boyle’s Law, Charles’ Law and Avogadro’s Law.
The ideal-gas equation is: PV = nRT
- P is standard pressure in kPa
- V is molar volume
- n is number of moles
- T is standard temperature in K
- R is called the gas constant.
NOTE: here are two commonly used values for R:
Pressure units in atm, R = 0.0821 L-atm/mol-K
Pressure units in Pa, R = 8.314
Units of Gas constant RPressure units in Pa, R = 8.314
1) R = 0.082 liter atm deg-1 mol-1
2) R = 8.31 ´ 107 ergs deg-1 mol-1
3) R = 8.31 J deg-1 mol-1
4) R = 2 cal K-1 mol-1
We know that 1 mole of an ideal gas occupies 22.4 liter at S.T.P. (Standard Temperature & Pressure, i.e 1 atm. pressure and 273 K )
An ideal-gas equation modification
- The number of moles, n, can be expressed as:
Mass (m) / molecular mass (M)
- The equation then becomes:
- J/mol-K
Established by John Dalton, states: the total pressure of a mixture of gases equals the sum of the pressures that each would exert if it were present alone.
The pressure exerted by a particular component of a mixture of gases is called the partial pressure of that gas.
Dalton's Law of Partial Pressures is expressed by the equation:
Ptotal = P1 + P2 + P3 . . .
Dalton's Law is helpful when collecting a gas "over water". This diagram shows the collection of a gas by water displacement. A collecting tube is filled with water and inverted in an open pan of water. Gas is then allowed to rise into the tube, displacing the water. By raising or lowering the collecting tube until the water levels inside and outside the tube are the same, the pressure inside the tube is exactly that of the atmospheric pressure.
A gas collected "over water" is a mixture of the gas and water vapor. Dalton's law of partial pressures describes this situation as:
Ptotal = Pgas + PH2O
Charts like this one are readily available that give water vapor pressure at any common temperature.
Dalton's Law Problems
The Quantity-Volume Relationship is named for Amedeo Avogadro
Avogadro's Hypothesis states: Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules.
At 0 oC and 1 atm, 22.4 L of any gas contains 6.02 X 1023 gas molecules.
Avogadro's Law states: The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of the gas.
Avogadro's Law is expressed by the equation:
(4)Graham's Law of Diffusion and Effusion of Gases
The Graham’s law of diffusion and effusion of gases states that:“The rate of diffusion or effusion of gases is inversely proportional to the square roots of their densities or molecular weights at the same conditions of temperature and pressure”
Suppose two gases with densities d1 and d2 diffuse into each other at the same condition of temperature and pressure. If the rate of diffusion of gases are r1 and r2 respectively ,then according to Graham’s Law;
For gas 1
and for gas 2
-----------------------Equation 2
Equation 1 Dived By equation 2
Similarly M1 and M2 are the molecular Mass of the two gases.
The Graham’s law of diffusion and effusion of gases has the same definition and mathematical expression.
SrNo.
|
Gas Laws
|
Mathematical Expression
|
At Constant
|
1.
|
Boyle’s
|
P1V1 = P2V2
|
Temperature
|
2.
|
Charles
|
V1/ V2 = T1/T2
|
Pressure
|
3.
|
Pressure-Temperature
|
P1/T1 = P2/T2
|
Volume
|
4.
|
Graham’s
|  |
Temperature
Pressure
|
5.
|
Gas equation
|
PV = nRT
|
--
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