Equation of State

nV

p

1V

Tp

nRTpV

Where:P = pressure (Pa)V = volume (m3) n = number of moles (mols) R = ideal gas constant R= 8.31451 J/mols.K R= 0.08206 L.atm/mol.K T = temperature (K)

Ideal-gas Equation

nRTpV

Equation of State

Where:P = pressure (Pa)V = volume (m3) n = number of moles (mols) R = ideal gas constant R= 8.31451 J/mols.K R= 0.08206 L.atm/mol.K T = temperature (K)

Example 1: Volume of gas at STP: The condition called standard temperature and pressure (STP) for a gas is defined to be a temperature of 0oC=273.15 K and a pressure of 1atm = 1.013x105 Pa. If you to keep a mole of an ideal gas in your room at STP, how big a container you need?

Ans: 22.4L

Example 2: Compressing gas in an automobile engine. In an automobile engine, a mixture of air and gasoline is compressed in the cylinder before being ignited. A typical engine has a compression ratio of 9.00 to 1; this means that gas in the cylinders is compressed to 1/(9.00) of its original volume (see Fig.). The initial pressure is 1.00 atm, and the initial temperature is 27oC. If the pressure after compression is 21.7 atm, find the temperature of compressed gas, Ans: 450oC

Example 1: Mass of air in a scuba tank: A typical tank used for scuba diving has a volume of 11.0L (about 0.4ft3) and a gauge pressure, when full, of 2.10x107 Pa (about 3000psig). The “empty” tank contains 11.0L of air at 21oC and 1atm (1.013x105 Pa). When the tank is filled with hot air from a compressor, the temperature is 42oC and the gauge pressure is 2.10x107 Pa. What mass of air is added? (Air is a mixture of gases, about 78% nitrogen, 21% oxygen, and 1% miscellaneous; its average molar mass is 28.8 g/mol=28.8x10-3kg/mol.)

Ans: 2.54 kg.

pV diagram

Isotherm, or contant temperature curves, for a constant amount of an ideal gas. For each curve, the product pV=nRT is constant, so p is proportional to 1/V; the proportionality constant increases with increasing T.

A pV-diagram for a non-ideal gas, showing isotherms for temperatures above and below the critical temperature Tc The liquid-vapor equilibrium region is shown as a green shaded area. At still lower temperatures the material might undergo phase transitions from liquid to solid or from gas to solid.

Answer: a) 56.2 mol b) 6.81x106 Pa =67.2 atm

Seat Work 1: A 20.0 L tank contains 0.225 kg of Helium at 18.0 oC. The molar mass of helium is 4.00 g/mol. a) How many moles of helium are in the tank, in pascals and in atmosphere?

Answer: 0.959 atm

Seat Work 2: A cylindrical tank has a tight-fitting piston that allows the volume of the tank to be changed. The tank originally contains 0.110m3 of air at a pressure of 3.4 atm. The piston is slow ly pulled out until the volume of the gas is increased to 0.390 m3. If the temperature remains constant, what is the final value of the pressure?

Answer: 3.36x105 Pa atm

Seat Work 3: A large cylindrical tank contains 0.750 m3 of nitrogen gas at 27 oC and 1.50x105 Pa (absolute pressure). The tank has a tight-fitting piston that allows the volume to be changed. What will be the pressure if the volume is decreased to 0.480 m3 and temperature is increased to 157oC?