List and describe the gas laws?

You don't have to memorize all the gas laws. If you can identify what variable is assumed constant, you can do a problem by deriving an equation from the ideal gas law.

For an ideal gas, we really only have one ideal gas law for General Chemistry:

#\mathbf(PV = nRT)#

where:

• #P# is the pressure; for instance, in #"bar"#.
• #V# is the volume, generally in #"L"#.
• #n# is the number of #\mathbf("mol")#s.
• #R# is the universal gas constant. If using #P# in #"bar"# and #V# in #"L"#, then #R = "0.083145 L"cdot"bar/mol"cdot"K"#
• #T# is the temperature in #"K"#.

If you wanted, you could derive the remaining simpler gas laws.

BOYLE'S LAW

Suppose the temperature was held constant. Then #nRT# is constant. Therefore, for an initial state and a final state, we have:

#P_1V_1 = nRT#
#P_2V_2 = nRT#

Therefore, we really have

#color(blue)(P_1V_1 = P_2V_2)#,

which is Boyle's Law. It tells us that with a constant temperature, a change in pressure is inversely proportional to a change in volume.

CHARLES'S LAW

Suppose the pressure was held constant. Then #(nR)/P# is constant. Therefore, for an initial state and a final state, we have:

#PV_1 = nRT_1#
#PV_2 = nRT_2#

#->(nR)/P = V_1/T_1#
#->(nR)/P = V_2/T_2#

Therefore, we really have

#color(blue)(V_1/T_1 = V_2/T_2)#,

which is Charles's Law. It tells us that with a constant pressure, a change in temperature is directly proportional to a change in volume.

GAY-LUSSAC'S LAW

Suppose the volume was held constant. Then #(nR)/V# is constant. Therefore, for an initial state and a final state, we have:

#P_1V = nRT_1#
#P_2V = nRT_2#

#->(nR)/V = P_1/T_1#
#->(nR)/V = P_2/T_2#

Therefore, we really have

#color(blue)(P_1/T_1 = P_2/T_2)#,

which is Gay-Lussac's Law. It tells us that with a constant volume, a change in pressure is directly proportional to a change in temperature.

AVOGADRO'S PRINCIPLE

Suppose the pressure AND temperature were held constant, yet the number of #"mol"#s can change. Then #(RT)/P# is constant. Therefore, for an initial state and a final state, we have:

#PV_1 = n_1RT#
#PV_2 = n_2RT#

#->(RT)/P = V_1/n_1 = barV_1#
#->(RT)/P = V_2/n_2 = barV_2#

Therefore, we really have

#color(blue)(V_1/n_1 = barV_1 = V_2/n_2 = barV_2)#,

which is Avogadro's Principle. It tells us that with a constant pressure and temperature, a change in #"mol"#s of gas is directly proportional to a change in volume (that should be obvious).