Ideal Gas Law
Gases
- Fluid that explains to fill the space that contains it.
- Free molecules undergoing breif, elastic collisons.
- Highly compressible,
- Flows from higher to lower pressure,
- Generally act “ideally”.
Pressure
Pressure is described as Force Exerted / Area of affected region. Also commonly know as Newtons / m^2
$ Pressure = \frac{(kg)(s^-2)}{m} $
This unit is called the Pascal (Pa)
- Units
- IUPAC: Standard Pressure = 100,000 Pa = 1 bar
- mmHg: millimeters of mercury in a barometer = 1 Torr
- $ 1 Atm = 760 Torr = 101325 Pa = 101.325 kPa = 1.01325 bar = 14.6959 psi $
The Gas Laws
- The properties of gases were elucidated over many tears by several scientists.
- Pressure-Volume: Robert Boyle and Robert Hooke
- Volume-Temperature: J.A.C. Charles
- Volume-Amount: Amedeo Avogadro
- Pressure-Temperature: Guiaume Amontons
- $ PV = nRT $ <– Ideal Gas Law
Ideal Gas Law
- Law applies STRICKLY to ideal, non-interacting gases.
- Law applies APPROXIMATELY under condictions where gas molecules interact only weakly.
-
Most common gases act like “ideal gases” under typical conditions.
- PV = nRT
- n is Number of moles.
- T is temperature in moles.
- P is pressure
- V is Volume
- R is the Gas Constant
- Equal to about $ 8.31432×10^3 $
- Boyles Law:
- If n and T are constant:
- $ PV = (nRT) = C $
- $ P_1V_1 = P_2V_2 $
- If n and T are constant:
- Charles’s Law:
- Keeping P and n constant:
- $ V (nR/P)T = CT $
- $ (V_1/T_1) = (V_2/T_2) $
- Keeping P and n constant:
- Avogadro’s Law:
- Keep P and T constant:
- $(V_1/n_1) = (V_2/N_2)$
- $V = (RT/P)n = Cn$
- Keep P and T constant:
Using the Ideal Gas Law
Solve for Volume:
- $ V = nRT/P $
Solve for pressure:
- $ P = nRT / V $
Solve for amount:
- $ n = PV/RT $
Gas Constants
Value | Units | Pressure | Volume |
---|---|---|---|
8.31446 | m^3 Pa K mol | Pa | m^3 |
8.31446x10^-5 | m^3 bar K mol | bar | m^3 |
8.31446x10^-2 | L bar K mol | bar | L |
62.36358 | L Torr K mol | Torr | L |
8.205734x10^-2 | L atm K mol | Atm | L |