Ideal Gas Law

Topics: Ideal gas law, Gas laws, Boyle's law Pages: 6 (1162 words) Published: April 14, 2013
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...