Ideal Gases

The ideal gases do not actually exist but they are a good starting point when studing gases. Two assumptions seperate ideal gases from actual gases:

1. Gases have no volume
2. Gases exhibit no attractive or repulsive force between molecules

These assumptions usually work quite well, because at normal conditions gas particles are spread so far apart that their volume and attractive forces are usually negligible. The only place where ideal gas concepts become unrealistics are when conditions reach some kind of extreem. These include place where states of matter changes which obviously indactes different properties.

It is important to identify a few of the constants that you will always see on introduction level chemistry tests. STP means standard temperature and pressure which is 1.00 atm and 273.15K for pressure and temperature respectively. It is always important to notice how units are stated in the problem so one can be sure to be consistent and change the STP units as necissary. Also one mole of any ideal gas at STP will always have a volume of 22.4L.

Thus most of the equations that follow there are definate restrictions and slight inaccuaracy, but they provide a great foundation for most of the chemisty of gases.

Ideal Gas Laws

PV=nRT is debatably the most important gas law. From this one equation and a little common sense logic, one can derive most of the other gas laws, so let's take a moment to examen each of the variables:

• P - Pressure - The current pressure being exerted onto a gas which according to Newton is the same amount the gas is exerting on the container.
• V - Volume - The current volume of the gas.
• n - Moles - The number of moles of particles of the particular gas
• R - Universal Gas Constant - Constant which makes the equation valid.
• T - Temperature - The current temperature of the gas.

The Universal Gas Constant is the part of PV=nRT with which students have the most trouble. This is because when they look on a table of constants for the value they should use they find many and often chose the wrong one. To find the correct one, substitute all the variables into the equation and determine what units you need in the constant. Then choose the closest one and convert it further if necissary.

The beauty of PV=nRT is that it allows the derivation of gas laws that gives one ratios of one property to another. Those equations are:

• Boyle's Law - P_iV_i = P_fV_f
• Gay-Lussac's Law - P_i / T_i = P_f / T_f
• Avogadaro's Principle - n_i / V_i = m_f / V_f

These laws are all linear relationships and can be easily used as will be shown

Examples

What volume will 2.50 mol of 02 occupy at 318 K and 1.50 atm of pressure?

Start by using the Ideal Gas Law:

Substitute in known varibles:

Find the universal gas constant that relates these units:

Solve for v:

A sample of H₂ has a pressure of 58 mmHg and a volume of 155 mL. When all of the H2 is transferred to a 1.00 L flask what will the new pressure be?

Use Boyle's Law and substitute in known variables:

Solve for x: