Revision: Study of Gas Laws Chemistry (English Medium) ICSE Class 9 CISCE

The volume of a given mass of a dry gas varies inversely as the pressure and directly as the absolute temperature.

V ∝ \[\frac {1}{P}\] × T or \[\frac {PV}{T}\] = k (constant)

If volume changes from V₁​ to V_2​, pressure from P_1​ to P₂​, and temperature from T₁ to T₂​, then:

\[\frac {P_1V_1}{T_1}\] = \[\frac {P_2V_2}{T_2}\] = k (constant)

A temperature scale with absolute zero (zero kelvin) as the starting point is called the absolute scale or the kelvin scale.

Charles's Law

At constant pressure, the volume of a given mass of a dry gas increases or decreases by 1/273^rd of its original volume at 0°C for each degree centigrade rise or fall in temperature.

V ∝ T (at constant pressure)
At temperature T₁ (K) and volume V₁ (cm³):

`"V"_1 ∝ "T"_1 "or" "V"_1/"T"_1 = "K"` = constant...(i)

At temperature T₂ (K) and volume V₂ (cm³):

`"V"_2 ∝ "T"_2 "or" "V"_2/"T"_2 = "K"` = constant….(ii)

From (i) and (ii),

`"V"_1/"T"_1 = "V"_2/"T"_2` = constant

For Temperature = Conversion from Celsius to Kelvin

1 K = °C + 273

Example:

20°C = 20 + 273 = 293 K

A hypothetical gas whose molecules have no volume and exert no intermolecular forces; obeys PV = μRT exactly.

Extending a graph line beyond the measured data to predict values.

One kelvin = 1/273.16 of the difference between absolute zero and the triple point of water.

A constant in the ideal gas equation; R = 8.31 J mol⁻¹ K⁻¹.

The unique temperature & pressure at which solid, liquid, and gas phases of a substance coexist in equilibrium.

The lowest theoretically possible temperature (0 K = −273.15 °C), where ideal gas molecules have zero kinetic energy.

The SI absolute temperature scale starting at absolute zero. Written as K (no degree symbol °).

Temperature is a parameter which tells the thermal state of a body (i.e., the degree of hotness or coldness of the body). It determines the direction of flow of heat when two bodies at different temperatures are placed in contact.

Coefficient of Linear expansion is equal to the change in length of a rod of length 1m when its temperature rises by 1°C.

The temperature at which the pressure and volume of a gas theoretically reach zero is called absolute zero.

The standard values chosen are 0 °C or 273K for temperature, and 1 atmospheric unit (atm) or 760 mm Hg for pressure. These standard values are known as standard temperature and pressure. 

Master Conversion Formula:

\[\frac {T_C}{100}\] = \[\frac {(T_{F}-32)}{180}\] = \[\frac {(T_{K}-273.15)}{100}\]

It states that the volume of a given mass of dry gas is inversely proportional to its pressure at a constant temperature.
P₁V₁ = P₂V₂ = k at constant temperature

It states that volume of a given mass of a dry gas is directly proportional to its absolute (kelvin) temperature, if the pressure is kept constant.

OR

The pressure remaining constant, the volume of a given mass of a dry gas increases or decreases by 1/273 of its volume for each 1°C increase or decrease in temperature respectively.

\[\frac {V_1}{T_1}\] = \[\frac {V_2}{T_2}\] = k at constant pressure

Robert Boyle systematically studied the relationship between pressure and volume of gases. In 1662, he found that, at a constant temperature, the volume of a fixed mass of a dry gas decreased by half when the pressure on it was doubled, and it became four times its original volume when its pressure was decreased to one-fourth. He described this behaviour in the form of a law, known as Boyle’s Law. 

Boyle’s Law: Temperature remaining constant, the volume of a given mass of dry gas is inversely proportional to its pressure.

V α `1/P` = T = Constant

• Gases expand linearly with temperature, making them useful for thermometers. This consistent behaviour suggests the existence of a lowest temperature limit.
• Absolute zero (−273.15 °C or 0 K) is the temperature where an ideal gas would have zero pressure. It is the lowest possible temperature.
• The Kelvin scale begins at absolute zero and uses the triple point of water (273.16 K) as a reference point. It is the SI temperature scale.
• The ideal gas equation (PV = μRT) combines all gas laws into a single relationship among pressure, volume, and temperature. It works best for gases at low pressure and high temperature.

• If no heat flows between two bodies in contact, they are said to be at the same temperature, even though their thermal energies may be different.
• The S.I. unit of temperature is kelvin (K), and absolute zero (0 K) is the temperature at which molecular motion ceases.