The Gas laws were proposed very early at the end of the 18th century, when scientists started realizing the relationships between the pressure, volume and temperature of any sample of gas. It came out of the basic logic that the state of a gas is a function of the pressure, volume and temperature. If one quantity is varied keeping the other quantities constant, we get gas laws. There are basically five gas laws namely,

Its named came after Robert Boyle that gives the relation between the volume and the pressure of a given mass of a gas at constant temperature which states that :
At constant temperature, the pressure of an ideal gas varies inversely to its volume. At constant temperature T, if P is the pressure of a certain mass of a gas and V is its volume at a temperature T K then
P $\propto$ $\frac{1}{V}$
If the pressure is P_{1 }at volume V_{1} and pressure is P_{2} at volume V_{2} then,
P_{1}V_{1} = P_{2}V_{2}
$\therefore$ PV = constant.
Its named came after Jacques Charles. He carried on series of experiment to test the Boyle's law, to determine the effect of temperature changes that have on gases. He discovered the relationship between temperature and volume at constant temperature which states that:
At constant pressure, the volume of an ideal gas varies directly to the absolute temperature.
V $\propto$ TIf the volume is V_{1} at temperature T_{1} and volume is V_{2} at temperature T_{2} then,
$\frac{V_1}{T_1}$ = $\frac{V_2}{T_2}$
$\therefore$ $\frac{V}{T}$ = constant.
In 1787, Jacques Charles studied the effect of change of temperature on the volume of a given mass of a gas at constant pressure, but he did not publish his results, Joseph Louis GayLussac discovered in 1802 that the volume of a gas increased linearly with increase of temperature if the pressure is kept constant . Hence, this laws is also called Gay Lussac Law.
Mathematically, it is given as pressure P is proportional to temperature T given as,
$\frac{P_1}{T_1}$ = $\frac{P_2}{T_2}$
$\therefore$ $\frac{P}{T}$ = Constant.
Mathematically, it is given as pressure P is proportional to temperature T given as,
P $\propto$ T
$\frac{P_1}{T_1}$ = $\frac{P_2}{T_2}$
$\therefore$ $\frac{P}{T}$ = Constant.
In 1811, Amedeo Avogadro proposed the law, that gives a relationship between the volume of a gas and the number of molecules in it at a given temperature and pressure which states that:
Equal volumes of gases at the same temperature and pressure contain same number of molecules regardless of molecules. It is stated as,
where, n_{1} is the number of molecules in one gas and n_{2} is the number of molecules in another gas
n_{1} = n_{2}
where, n_{1} is the number of molecules in one gas and n_{2} is the number of molecules in another gas
Hence, the equal volumes V of all gases if measured under the same temperature T and pressure P conditions will have equal number of molecules n.
Mathematically,
V $\propto$ n
$\frac{V_1}{n_1}$ = $\frac{V_2}{n_2}$
$\frac{V}{n}$ = constant.
PV = constant
or
P_{1}V_{1} = P_{2}V_{2}
According to Charles law, at constant pressure
V $\propto$ T
If the volume is V_{1} at temperature T_{1} and volume is V_{2} at temperature T_{2} then
$\frac{V_1}{T_1}$ = $\frac{V_2}{T_2}$
$\therefore$ $\frac{V}{T}$ = constant.
According to GayLussac's law, also known as pressure law
P $\propto$ T
$\frac{P_1}{T_1}$ = $\frac{P_2}{T_2}$
$\therefore$ $\frac{P}{T}$ = Constant.Now, according to Avogadro's law
$\frac{V}{n}$ = constant
By introducing the Avogadro's law in the combined gas law equation, we get
$\frac{PV}{nT}$ = constant
The constant is represented by RSo by rearranging, we obtain the expression for the ideal gas law
PV = nRT
Lets see some examples on gas law problems:Solved Examples
Question 1: An air bubble is released at the bottom of a lake where the temperature is $4^{0}$^{}C and the pressure is 3.40 atm. If the bubble was 10.0 mL to start, what will itâ€™s volume be at the surface, where the water temperature is $12^{0}$^{}C and the pressure is $10^{3}$^{} kPa.
Solution:
Given that,
P_{1} = 3.40 atm
P_{2 }= 10^{3} kPa = 1.0165 atm
T_{1} = 4^{0} C = 277 K
T_{2 }= 12^{0} C = 285 K
V_{1 }= 10 mL = 0.01 L
V_{2} = ?
Solution:
Given that,
P_{1} = 3.40 atm
P_{2 }= 10^{3} kPa = 1.0165 atm
T_{1} = 4^{0} C = 277 K
T_{2 }= 12^{0} C = 285 K
V_{1 }= 10 mL = 0.01 L
V_{2} = ?
Using $\frac{P_1 V_1}{T_1}$ = $\frac{P_2 V_2}{T_2}$
$\frac{3.4 atm \times 0.01 L}{277 K}$ = $\frac{1.0165 atm \times V_2}{285 K}$
V_{2} = 0.0344 L = 34.4 mL.
$\frac{3.4 atm \times 0.01 L}{277 K}$ = $\frac{1.0165 atm \times V_2}{285 K}$
V_{2} = 0.0344 L = 34.4 mL.
Question 2: What is the temperature of 0.70 moles of a gas that occupies 0.47 L at a pressure of 150 kPa?
Solution:
According to Ideal Gas Law,
PV = nRT
By rearranging,
T = $\frac{PV}{nR}$
T = $\frac{150 kPa \times 0.47 L}{0.7 mol \times 8.3}$
T = 12 K.
Solution:
According to Ideal Gas Law,
PV = nRT
By rearranging,
T = $\frac{PV}{nR}$
T = $\frac{150 kPa \times 0.47 L}{0.7 mol \times 8.3}$
T = 12 K.