of molecular-kinetic theory Ideal gas Presentation

Learning Objectives

Four variables can adequately describe a gas sample:

T = Temperature (generally expressed in Kelvin)
n = amount of material (generally in moles)
P = pressure (atmospheres is most common)
V = volume (litres is most common)

An ideal gas: one that can be described by the ideal-gas equation; PV = nRT

The usual value of the ideal gas constant is
R = 8.3145 J/(K·mol)
Temperature must be expressed in Kelvin and the units of volume and pressure must match the units of R

STP: The conditions 0.00 °C (273.15 K) and 1 atm are referred to as standard temperature and pressure, STP. At STP, the volume of 1 mol of an ideal gas is 22.41 L. this known as the molar volume of a gas at STP

Question:

The gas pressure in an aerosol can is 1.5 atm at 25oC.
Assuming that the gas obeys the ideal-gas equation what would the pressure be if the can was heated to 450oC?

Answer:
Step 1: Identify the unknown quantity and tabulate the known quantities in units consistent with those in R.

Answer:
Step 2: Since the can is a closed container, the volume and # of moles cannot change; V1 = V2 and n1 = n2. Therefore:

Answer:
Step 3: Rearrange and calculate P2

P2 =


=


=

3.6 atm

=

The root-mean-square speed (rms speed) of a gas, , is given by Maxwell’s Equation

As temperature increases, the rms speed of the gas increases.

As molecular mass increases, the rms speed of the gas decreases.