Gas is a state of matter without a definite shape or volume, and the volume of which changes with the change in temperature and pressure. The molecules of a gas are in random motion .Gases have weaker intermolecular forces (called van der Waals forces) but the average speed of the molecules is quite high. Gases tend to occupy the whole volume of the container they are kept in as they don’t have a boundary like liquids and solids do.
The average distance between the molecules in gas are large that’s why they have weaker intermolecular forces and the average molecular speed is high. Since, the average distance between the molecules it makes them highly compressible or therefore volume decreases with the increase in pressure. And with the increase in the temperature the average speed of the molecules increases and their kinetic energy goes up.
There is definite relationship between the mass, pressure, volume, density and temperature of the gaseous state. An equation relating pressure, volume, temperature and amount of gas is known as equation of state. We will come to this later.
Therefore, in measuring volume or amount of the gas the temperature and volume should also be specified.
There are two standard temperature and pressure conditions normally used to measure the data of gases. They are:
| Condition | Temperature | Pressure | Molar mass |
| STP/NTP (Standard temperature and Pressure/Normal temperature and Pressure) | 273.15 K | 1 atm | 22.414 L |
| SATP Standard Ambient Temperature and Pressure | 298.15 K | 1 atm | 22.788 L |
Pressure of a gas is pressure exerted by the molecules on the walls of the container. The molecules are numerous in number and the pressure exerted by each molecule is also different but as a whole the force applied is uniform.
Pressure is defined as force applied per unit area. Its SI unit is Pascal, which in 1 Newton per m2.
Mathematically, Pressure = (force / area)
p = F/A or dF/dA
Where, p = pressure,
F = normal force,
A is the area.
Other units of pressure are:
|
| Pascal (Pa) | Bar (bar) | Atmosphere (atm) | torr (Torr) |
| 1 Pa | = 1N/ m2. | 10-5 | 1.0195 X 10-5 | 7.5006 X 10-5 |
| 1 bar | 100,000 | = 106 dyn/cm2 | 0.98692 | 750.06 |
| 1 atm | 101,325 | 1.01325 | = 1 atm | 760 |
| 1 torr | 133.322 | 1.3332×10?3 | 1.3158×10?3 | ? 1 Torr; ? 1 mmHg |
Atmospheric pressure is also measured in terms of height of mercury column.
1 atm is also expressed as 76cm of mercury column. Though, dimensionally cm has the dimensions of length and not pressure. We can find the corresponding pressure from height of mercury column by the formula:
| P = hdg |
Where,
h = height of the mercury column supported by the barometer.
d = density of mercury,
g = acceleration due to gravity.
Depending upon the units of h, d and g used we get pressure in one of its units.
Pressure is measured using the manometer which has the desired fluid (gases in most cases) on one end and its open on the other end , and pressure of the fluid is measured by change in the length of the mercury (or any other liquid used).
(Image taken from www.efunda.com)
[SolvedExample]
Example1
Convert the given values in atm.
a) 38 cm Hg
b) 400 Torr.
Solution
a) 76 mm Hg is = 1 atm
Therefore, 38 cm of Hg = (1/ 76) X 38 atm = 0.5 atm
b) 760 Torr = 1 atm
Therefore, 400 Torr = (1 / 760) X 400 atm
= 0.52 atm.
[/SolvedExample]
[SolvedExample]
Example2:
If the density of mercury becomes 13 X 103 Kg/m3 find the drop in pressure of 76 cm of mercury (Assuming other factors remain unchanged).
Solution:
Pressure = hdg.
ΔP = Pi - Pf
= hdig - hdfg
= hg(di - df)
= 76 X 10-2 X 9.8 X ( 13.6 – 13 ) X 103 Pa.
= 4468.8 Pa
[/SolvedExample]
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