Ideal Gas Law

Chapter 14.3

Ideal Gas Law

• The ideal gas law combines:– pressure– temperature– volume– # of particles (amount)

Increasing Amount of Particles

• If the amount of gas particles increases:– the pressure will increase OR– the volume will increase

Effects of increased numbers of particles

• Since P1V1 = P2V2

T1 T2

PV = k

T

stays constant as long as the number of particles stays the same

Effects of increased numbers of particles

PV = k

T

• k varies with the amount of gas particles (n)

• k = nR

• R was determined experimentally

• R is called the ideal gas constant

Vocabulary Word

• ideal gas law: describes the physical behavior of an ideal gas in terms of the temperature, volume and pressure and the number of moles of a gas that are present

• PV = nRT

Ideal Gas Constant

• R has different numerical values depending on the unit for pressure:– Patm R = 0.0821

– PkPa R = 8.314

– PmmHg R = 62.4

Units for the Ideal Gas Law

• Volume (liters)

• Temp (Kelvin)

• n (moles)

Properties of Ideal Gases

• the gas particles have no intermolecular forces of attraction or repulsion

• in the real world gas particles DO have a small but measurable volume

Real Gases

• most gases behave like ideal gases at many temperatures and pressures

• we can use the ideal gas law to get a very close approximation of experimentally verified values

Real Gases

• at extremely high pressures or low temperature intermolecular forces become important

• this allows gases to liquify

Intermolecular Forces• size and geometry

(shape) can increase the intermolecular forces of attraction,

• values calculated with the ideal gas law will be off– polar gases (water

vapor)

– larger gases (butane)

Using the ideal gas law to calculate moles (n)

• when any 3 values are given, the 4th value can be calculated

• If P = 3.18 atm and V = 0.044L at 25oC, how many moles of gas are present?

P = 3.18 V = 0.044 T = 25 + 273 = 298

Using the ideal gas law to calculate moles (n)

P = 3.18 V = 0.044 T = 25 + 273 = 298

PV = nRT

(3.18) (0.044) = n (0.0821) (298)

Using the ideal gas law to calculate moles (n)

(3.18) (0.044) = n (0.0821) (298)

(3.18) (0.044) = n

(0.0821) (298)

6.9 x 10-3 mol = n

Using the ideal gas law to calculate temperature

n = 2.49 mol

V = 1L

P = 143 kPa

T = ?

(143) (1) = (2.49) (8.314) Tk

Using the ideal gas law to calculate temperature

(143) (1) = (2.49) (8.314) Tk

(143) (1) = Tk

(2.49) (8.314)

6.91 = Tk

- 266o = oC

Using the ideal gas law to calculate volume

• n = 0.323 mol

• T= 265K

• P = 0.900 atm

(0.900) V = (0.323) (0.0821) (265)

V = (0.323) (0.0821) (265) = 7.821 L

(0.900)

Using the ideal gas law to molar mass

• The ideal gas law can be used to determine the molar mass of a gas

• moles of a gas = mass of the gas

molar mass

• PV = nRT becomes PV = mRT

M

PV = mRT

M

solve for M, and M = mRT

PV