# Ideal Gas Law

The ideal gas law is the equation of state of a hypothetical ideal gas. It obeys Boyle's Law and Charles Law.

Ideal Gas Law Formula :

General Gas Equation: PV = nRT

Pressure(P) = nRT / V

Volume(V) = nRT / P

Temperature(T) = PV / nR

Moles of Gas(n) = PV / RT

where,

P = pressure,

V = volume,

n = moles of gas,

T = temperature,

R = 8.314 J K-1 mol-1, ideal gas constant.

Ideal Gas Law Example:

Case 1: Find the volume from the 0.250 moles gas at 200kpa and 300K temperature. P = 200 kPa, n = 0.250 mol, T = 300K, R = 8.314 J K-1 mol-1 Step 1: Substitute the values in the below volume equation: Volume(V) = nRT / P

= (0.250 x 8.314 x 300) / 200

= 623.55 / 200

Volume(V) = 3.12 L

This example will guide you to calculate the volume manually.

Case 2: Find the temperature from the 250ml cylinder contaning 0.50 moles gas at 153kpa. V = 250ml -> 250 / 1000 = 0.250 L, n = 0.50 mol, P = 153 kPa, R = 8.314 J K-1 mol-1 Step 1: Substitute the values in the below temperature equation: Temperature(T) = PV / nR

= (153 x 0.250) / (0.50 x 8.314)

= 38.25 / 4.16

Temperature(T) = 9.2 K

This example will guide you to calculate the temperature manually. Gay-Lussac's Law:

Gay-Lussac's Law states that the pressure of a fixed amount of gas at fixed volume is directly proportional to its temperature in kelvins.

Gay-Lussac's Law Formula :

Gas Equation: Pi/Ti = Pf / Tf

Initial Pressure(Pi) = PfTi / Tf

Initial Temperature(Ti) = PiTf / Pf

Final Pressure(Pf) = PiTf / Ti

Final Temperature(Tf) = PfTi / Pi

where,

Pi = Initial Pressure,

Ti = Initial Temperature,

Pf = Final Pressure. Tf = Final Temperature,

Gay-Lussac's Law Example:

Case 1: A cylinder contain a gas which has a pressure of 125kPa at a temperature of 200 K. Find the temperature of the gas which has a pressure of 100 kPa. Pi = 125 kPa, Ti = 200 K, Pf = 100 kPa

Step 1: Substitute the values in the below final temperature equation: Final Temperature(Tf) = PfTi / Pi

= (100 x 200) / 100

= 20000 / 125

Final Temperature(Tf) = 160 K

This example will guide you to calculate the final temperature manually.

Case 2: Find the final pressure of gas at 150 K, if the pressure of gas is 210 kPa at 120 K. Pi = 210 kPa, Ti = 120 K, Tf = 150 K

Step 1: Substitute the values in the below pressure equation: Final Pressure(Pf) = PiTf / Ti

= (210 x 150) / 120

= 31500 / 120

Final Pressure(Vf) = 262.5 kPa

This example will guide you to calculate the pressure manually. oyle's/Mariotte's Law:

Boyle's law states that the volume of a gas increases when the pressure decreases at a constant temperature.

Boyle's/Mariotte's Law Formula :

Gas Equation: PiVi = PfVf

Initial Pressure(Pi) = PfVf / Vi

Initial Volume(Vi) = PfVf / Pi

Final Pressure(Pf) = PiVi / Vf

Final Volume(Vf) = PiVi / Pf

where,

Pi = Initial Pressure,

Vi = Initial Volume,

Pf = Final Pressure,

Vf = Final Volume.

Boyle's/Mariotte's Law Example:

Case 1: A certain amount of gas contains a volume of 4 L at 100 kPa pressure. Find the pressure of the gas if it occupies in 15 L container. Pi = 100 kPa, Vi = 4 L, Vf = 15 L

Step 1:Substitute the values in the below final pressure equation: Final Pressure(Pf) = PiVi / Vf

= (100 x 4) / 15

= 400 / 15

Final Pressure(Pf) = 26.67 kPa

This example will guide you to calculate the final pressure manually.

Case 2: Find the final volume of gas, from 8 L of gas at 150 kPa until the pressure becomes 125 kPa. Pi = 150 kPa, Vi = 8 L, Pf = 125 kPa

Step 1: Substitute the values in the below volume equation: Final Volume(Vf) = PiVi / Pf

= (150 x 8) / 125

= 1200 / 125

Final Volume(Vf) = 9.6 L

This example will guide you to...

Please join StudyMode to read the full document