Gas Laws
Boyle's Law
"Volume of a fixed quantity of gas is inversely proportional to its pressure"
V = constant × 1/P 
PV = constant 

Charles' Law
"The volume of a fixed quantity of gas at constant pressure increases as the temperature Increases"
V = constant × T 
V / T = constant 

Note:
When temperature is measured in °C, the intercept on the temperature axis is − 273.15°C (called absolute zero)
Avogadro's Law
"The volume of a gas at a given temperature and pressure is directly proportional to the number of moles of the gas"
V = constant × n
Based on the three laws, we obtain V = constant × nT/P
Hence the Ideal Gas Law, V = R × nT/P →
Ideal Gas Law
PV = nRT
Where R is gas constant and its value depends on the units of P, V, T used.
STP (Standard Temperature & Pressure)are: T: 0°C; 273.15 K, P: 1 atm.
Volume of 1 mol of gas at STP is:
V = nRT/P = (1 mol)(0.08206 L·/mol·K)(273.15K)/ 1.000 atm = 22.4 L
For an ideal gas under 2 sets of conditions:
P_{1}V_{1} = n_{1}RT_{1} & P_{2}V_{2} = n_{2}RT_{2}
Hence, R = P_{1}V_{1} / n_{1}T_{1} & R = P_{2}V_{2} / n_{2}T_{2}
→ P_{1}V_{1} / n_{1}T_{1} = P_{2}V_{2} / n_{2}T_{2}
Rearranging the gas law yields: n/V = P/RT
Multiply by the molar mass (M): nM/V = PM/RT
Since nM = w in grams)
(Gas density) d = PM/RT → (Molar Mass) M = dRT/P
Gas mixtures and partial pressures
"In a gas mixture the total pressure is given by the sum of partial pressures of each component"
Hence, P_{total} = P_{1} + P_{2} + P_{1} + ....
Dalton's Law
Remark: If each gas obeys the ideal gas equation:
P_{i} = n(RT/V) where P_{i} is called Partial Pressure.
→ P_{total} = (n_{1} + n_{2} + n_{3} + ....)(RT/V)
If n_{i} is the number of moles of gas (i) exerting a partial pressure
P_{i} = X_{i} P_{total}
where X_{i} (mole fraction) = n_{i}/n_{total}
Exercises on Gas Laws
Exercise I on Finding Total Pressure
Check your answers here:
Solution to the Exercise I on Finding Total Pressure
Exercise II on Finding Total Pressure
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Solution to the Exercise II on Finding Total Pressure
Exercise III on Finding Total Pressure
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Solution to the Exercise III on Finding Total Pressure
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Date of last modification: 2024