1) An equation of state relates macroscopic variables like pressure, volume, temperature, and number of moles that describe a substance. The ideal gas law is the equation of state for gases. 2) Standard temperature and pressure (STP) are defined as 0°C (273.15 K) and 1 atmosphere (101.3 kPa). At STP, 1 mole of any gas occupies 22.4 L of volume. 3) Experiments on gas behavior led to Boyle's, Charles', and Gay-Lussac's laws, which combined form the ideal gas law: PV=nRT, relating pressure, volume, moles, and temperature.

1. Behavior of Gases
Equations of State

2. What is an equation of state?
An equation relating the
macroscopic variables that
describe some type of matter.
• The ideal gas law is an
equation of state for gases.

3. Standard Temperature and Pressure
• Standard temperature is equal to 0 °C, which is 273.15 K.
• Standard Pressure is 1 atm, 101.3 kPa or 760 mmHg or torr.
• STP is the "standard" conditions often used for measuring gas
density and volume.
• At STP, 1 mole of any gas occupies 22.4L.
Density calculations
• Density of a gas at STP= molar mass/22.4L

4. Boyle’s Law Graphs
Pressure vs. Volume Volume vs. 1/Pressure

5. Charles’ Law Graph

6. Gay-Lussac’s Law Graph

7. Avogadro’s Law

8. Avogadro's Law: Volume and Moles
• states that the volume V of a
sample of gas is directly
proportional to the number
of moles n in the sample at
constant temperature T and
pressure P.
𝑽 𝟏
𝒏 𝟏
=
𝑽 𝟐
𝒏 𝟐

9. Ideal Gas Equation

10. A hypothetical setup for
studying the behavior of
gases. By heating the gas, and
adding more gas, we can
control the gas pressure P,
volume V, temperature T, and
number of moles n.

11. Measurements of the
behavior of various gases
lead to three conclusions:

12. 1. The volume V is proportional to the number of moles
n. If we double n, keeping pressure and temperature
constant, the volume doubles.
V α n

13. 2. The volume varies inversely with the absolute pressure
P. If we double P while holding the temperature T and
number of moles n constant, the gas compresses to
one-half of its initial volume. In other words,
PV = constant when n and T are constant.

14. 3. The pressure is proportional to the absolute
temperature T. If we double T, keeping the volume and
number of moles constant, the pressure doubles. In
other words,
P = (constant) ∙ T when n and V are constant

15. We can combine these three relationship into a single
ideal-gas equation:
PV = nRT
Gas pressure
Gas volume
Number of moles of gas
Absolute temperature of gas
Gas constant
𝐑 = 𝟎. 𝟎𝟖𝟐𝟎𝟔
𝐋 ∙ 𝐚𝐭𝐦
𝐦𝐨𝐥 ∙ 𝐊

16. Alternatively (recall concepts)
Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’s Law
V  1/P V  T (Kelvin) P  T (Kelvin) V  n
Constant T, n Constant P, n Constant V, n Constant T, P
So 𝑉 
1
𝑃
∙ 𝑛 ∙ 𝑇

17. Alternatively (recall concepts)
• To turn a proportionality into an equation, insert
a constant: V = RnT/P
• Or multiply both sides by P:
• PV = nRT where R is the ideal gas law constant.
If three of the variables are known, the 4th can be
determined.
• The units of R depend on the units used for P, T,
and V.

18. • An ideal gas is one for which the previous equation
holds precisely for ALL pressures and temperatures
• It works best at very low pressures and high
temperatures, when the gas molecules are far apart
and in rapid motion
• In other words, the postulates in Kinetic Molecular
Theory

19. When only the amount of gas
is constant, the combined gas
law describes the relationship
among pressure, volume, and
temperature

20. Combined Gas Equation

21. For a constant mass (or constant number
of moles) of an ideal gas the product nR is
constant, so the quantity PV / T is also
constant. Hence,
PV = nRT
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐

22. You can derive the other laws from the
combined gas law by holding one variable
constant.
Suppose you hold the temperature
constant (T1 = T2)
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐

23. Rearrange the combined gas law so that
the two temperature terms on the same
side of the equation.
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
𝑷 𝟏 𝑽 𝟏 =
𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
𝑻 𝟐

24. Because (T1 = T2), the ratio of T1 to T2 is
equal to one (1).
Multiplying by 1 does not change a value in an
equation.
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
𝑷 𝟏 𝑽 𝟏 =
𝑷 𝟐 𝑽 𝟐 𝑻 𝟏
𝑻 𝟐

25. So when temperature is constant, you can
delete the temperature ratio from the
rearranged combined gas law
What you are left with is the equation for Boyle’s
law
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
𝑷 𝟏 𝑽 𝟏 = 𝑷 𝟐 𝑽 𝟐

26. A similar process yields Charles’ law when
pressure remains constant.
Another similar process yields Gay-
Lussac’s law when volume remains
constant.
𝑷 𝟏 𝑽 𝟏
𝑻 𝟏
=
𝑷 𝟐 𝑽 𝟐
𝑻 𝟐
𝑽 𝟏
𝑻 𝟏
=
𝑽 𝟐
𝑻 𝟐
𝑷 𝟏
𝑻 𝟏
=
𝑷 𝟐
𝑻 𝟐