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Relationship between Pressure- Volume (Boyle's Law)
•The volume of a fixed mass of gas at constant temperature is inversely proportional to the pressure exerted on it.
•P ∞ 1 / V then PV equals a constant value.
P1V1 = P2V2 at constant temperature.
Relationship between Temperature- Volume (Charles' Law)
•The volume of a fixed mass of gas at constant pressure is directly proportional to its absolute temperature (kelvin scale).
•V ∞ T then V / T equals a constant value.
V1 = V2 at constant pressure
Relationship between Volume-Mole (Avogadro's Law)
Avogadro postulated that equal volumes of gases at the same temperature and pressure contain equal numbers of particles.
V ∞ n or V= kn where k is a constant.
Molar gas Volume
•Molar Gas Volume is the volume of 1 mole of a particular gas.
•It has been found experimentally that 1 mole of any gas at STP occupies a volume of 22.7 L.
•The molar volume of a gas at SLC is 24.8 L.
VSTP = 22.7 L
VSLC = 24.8 L
STP- 0 oC and 100kPa
SLC – 25 oC and 100KPa
There is a direct relationship between the number of moles of a gas and its molar volume.
n = V
n is the number of moles of gas
V is the actual volume of gas
Vm is the molar volume of the gas
•Combine Boyle’s and Charles’ Laws:
PV equals a constant value
V / T equals a constant value
to get PV / T equals a constant value.
•Combined Gas Law:
P1V1 = P2V2 for a constant amount of gas.
•P ∞ 1 / V (Boyle’s Law)
•P ∞ T (Gay Lussac’s Law)
•P ∞ n
•Combine these proportionalities:
P ∞ nT / V
Universal gas equation
•Replace proportionality with equality sign.
•Introduce a general gas constant, R and we get the general gas equation.
PV = nRT
Pressure (P) is measured in kilopascals (kPa)
Volume (V) is measured in litres (L)
Temperature (T) is measured in kelvin (K)
Number of moles (n) – unit (mol)
General Gas Constant (R) = 8.31JK-1mol-1
Boyle's Law animation courtesy of By NASA's Glenn Research Center - http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4448761
Charle's Law animation courtesy of By NASA's Glenn Research Center - http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html, Public Domain, https://commons.wikimedia.org/w/index.php?curid=4448734
Sample Problem using the universal gas equation
Find the volume of 6.30 mol of carbon dioxide gas at 23oC and 550 kPa pressure. (R = 8.31 JK-1mol-1)
Step 1: Write down given data in correct units.
P = 550 kPa
V = ???
n = 6.30 mol
T = 23oC = 296 K
R = 8.31 JK-1mol-1
Step 2: Use general gas equation to calculate volume.
PV = nRT
V = nRT / P
= 6.30 x 8.31 x 296 / 550
= 28.2 L