Ideal Gas Law
PV = nRT
Brings together gas properties.
Can be derived from experiment and theory.
Ideal Gas Equation
Volume
Pressure
PV=nRT
No. of moles
R = 0.0821 atm L / mol K
R = 8.314 kPa L / mol K
Kelter, Carr, Scott, Chemistry A Wolrd of Choices 1999, page 366
Universal Gas Constant
Temperature
PV = nRT
P
V
T
n
R
=
=
=
=
=
pressure
volume
temperature (Kelvin)
number of moles
gas constant
Standard Temperature and Pressure (STP)
T = 0 oC or 273 K
P = 1 atm = 101.3 kPa = 760 mm Hg
1 mol = 22.4 L @ STP
Solve for constant (R)
PV
nT
Recall: 1 atm = 101.3 kPa
Substitute values:
(1 atm) (22.4 L) = R
(1 mole)(273 K)
R = 0.0821 atm L / mol K
R = 0.0821 atm L
mol K
or
(101.3 kPa)
( 1 atm)
= 8.31 kPa L
mol K
R = 8.31 kPa L / mol K
Ideal Gas Law
What is the volume that 500 g of iodine will occupy under the conditions:
Temp = 300oC and Pressure = 740 mm Hg?
Step 1) Write down given information.
mass = 500 g iodine
T = 300oC
P = 740 mm Hg
R = 0.0821 atm . L / mol . K
Step 2) Equation: PV = nRT
Step 3) Solve for variable
V =
nRT
P
Step 4) Substitute in numbers and solve
(500 g)(0.0821 atm . L / mol . K)(300oC)
V =
740 mm Hg
V=
What MISTAKES did we make in this problem?
What mistakes did we make in this problem?
What is the volume that 500 g of iodine will occupy under the conditions:
Temp = 300oC and Pressure = 740 mm Hg?
Step 1) Write down given information.
mass = 500 g iodine  Convert mass to gram;
recall iodine is diatomic (I2)
x mol I2 = 500 g I2(1mol I2 / 254 g I2)
n = 1.9685 mol I2
T = 300oC Temperature must be converted to Kelvin
T = 300oC + 273
T = 573 K
P = 740 mm Hg Pressure needs to have same unit as R;
therefore, convert pressure from mm Hg to atm.
x atm = 740 mm Hg (1 atm / 760 mm Hg)
P = 0.8 atm
R = 0.0821 atm . L / mol . K
Ideal Gas Law
What is the volume that 500 g of iodine will occupy under the conditions:
Temp = 300oC and Pressure = 740 mm Hg?
Step 1) Write down given information.
mass = 500 g iodine
n = 1.9685 mol I2
T = 573 K (300oC)
P = 0.9737 atm (740 mm Hg)
R = 0.0821 atm . L / mol . K
V=?L
Step 2) Equation: PV = nRT
Step 3) Solve for variable
V =
nRT
P
Step 4) Substitute in numbers and solve
(1.9685 mol)(0.0821 atm . L / mol . K)(573 K)
V =
0.9737 atm
V = 95.1 L I2
Ideal Gas Law
What is the volume that 500 g of iodine will occupy under the conditions:
Temp = 300oC and Pressure = 740 mm Hg?
Step 1) Write down given information.
mass = 500 g iodine
T = 300oC
P = 740 mm Hg
R = 0.0821 atm . L / mol . K
Step 2) Equation: PV = nRT
Step 3) Solve for variable
V =
nRT
P
Step 4) Substitute in numbers and solve
(500 g)(0.0821 atm . L / mol . K)(300oC)
V =
740 mm Hg
V=
What MISTAKES did we make in this problem?