Gases

Chapter 5

Substances that exist as gases

Elements that exist as gases at 250C and 1 atmosphere

5.1

Our Atmosphere:

• exerts pressure on earth• more at sea level• less on mountain top• The air we breathe:• 79% N2

• 21% O2Sea level1 atm

4 miles 0.5 atm

10 miles 0.2 atm

Atmospheric pressure

1 atm = 760 mmHg = 760 torr(1 torr = 1mm Hg)

1 atm = 101,325 Pa1 atm = 101 kPa

Pressure of Gas

The Gas Laws

Pressure and Temperature• Pressure = force/area(we will use torr, mm Hg, Pa & atm)• Always use Kelvin temperature (K)K = ° C + 273

4 variables are involved:• P = pressure• V = volume• n = # of moles• T = temperature (in Kelvin)

R is the gas constant

PV = nRT Ideal Gas Equation

Ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can be completely accounted for by the ideal gas equation.

What is the pressure of the gas (in atm) when 5.0 moles of CO gas are present in a container of 20.0 L at 27 oC?

n= 5.0mole, V=20.0L, T= 27 oC=(27+273.15)K=300.15K

PV=nRT

P=nRT / V= 5.0mole*0.082 L• atm / (mol • K)*300.15K/20.0L= 6.15 atm

The conditions 0 0C and 1 atm are called standard temperature and pressure (STP).

R = 0.0821 L • atm / (mol • K) = 8.314 J/(K·mol)

Experiments show that at STP, 1 mole of an ideal gas occupies 22.414 L.

Molar volume of gas

1 mole of gas at STP = 22.4 Liters

2 moles of gas at STP = 44.8 L

What is the volume (in liters) occupied by 49.8 g of HCl at STP?

n = 49.8 g x 1 mol HCl36.45 g HCl

= 1.37 mol

V = 1.37 mol x 22.4 L/mol = 30.6 L

1 mole of gas at STP = 22.4 Liters

Argon is an inert gas used in lightbulbs to retard the vaporization of the filament. A certain lightbulb containing argon at 1.20 atm and 18 0C is heated to 85 0C at constant volume. What is the final pressure of argon in the lightbulb (in atm)?

PV = nRT n, V and R are constantnRV = P

T = constant

P1

T1

P2

T2=

P1 = 1.20 atmT1 = 291 K

P2 = ?T2 = 358 K

P2 = P1 x T2

T1

= 1.20 atm x 358 K291 K

= 1.48 atm

Density (d) Calculations

d = mV = PM

RTm is the mass of the gas in gM is the molar mass of the gas

Molar Mass (M ) of a Gaseous Substance

dRTPM = d is the density of the gas in g/L

5.4

What is the density of HCl gas in grams per liter at 700 mmHg and 25 oC?

d = mV = PM

RT

P=700mmHg=700/760atm=0.92atm

T= 25 oC=25+273.15K=298.15K

d =0.92 atm x 36.45 g/mol

x 298.15 K 0.0821 L•atmmol•K

=1.37g/L

What is the molar mass (g/mol) of 7.10 grams of gas whose volume is 5.40 L at 741 torr and 40 oC?

dRTPM = d = m

V7.10 g5.40 L

= = 1.31 gL

M =1.31 g

L

0.975 atm

x 0.0821 x 313.15 KL•atmmol•K

M = 34.6 g/mol

T=313.15K P= 741torr=741/760atm=0.975atm

Gas Stoichiometry

The combustion process for methane is  CH4(g) + 2 O2(g) CO2(g) + 2 H2O(l) 

If 15.0 moles of methane are reacted, what is the volume of carbon dioxide (in L) produced at 23.0 oC and 0.985 atm?

V = nRT

P

15mol x 0.0821 x 296.15 KL•atmmol•K

0.985 atm= = 369.8 L

x 1CO2/1CH4 15 mole CH4 ---------------- 15 mole CO2

Dalton’s Law of Partial Pressures

Partial pressure is the pressure of the individual gas in the mixture.

V and T are

constant

P1 P2 Ptotal = P1 + P2

Consider a case in which two gases, A and B, are in a container of volume V.

PA = nARTV

PB = nBRTV

nA is the number of moles of A

nB is the number of moles of B

PT = PA + PB XA = nA

nA + nBXB =

nB

nA + nB

PA = XA PT PB = XB PT

Pi = Xi PT mole fraction (Xi) = ni

nT

A sample of natural gas contains 8.24 moles of CH4, 0.421 moles of C2H6, and 0.116 moles of C3H8. If the total pressure of the gases is 1.37 atm, what is the partial pressure of propane (C3H8)?

Pi = Xi PT

Xpropane = 0.116

8.24 + 0.421 + 0.116

PT = 1.37 atm

= 0.0132

Ppropane = 0.0132 x 1.37 atm = 0.0181 atm

Kinetic Molecular Theory of Gases1. A gas is composed of molecules that are separated from

each other by distances far greater than their own dimensions. The molecules can be considered to be points; that is, they possess mass but have negligible volume.

2. Gas molecules are in constant motion in random directions, and they frequently collide with one another. Collisions among molecules are perfectly elastic.

3. Gas molecules exert neither attractive nor repulsive forces on one another.

4. The average kinetic energy of the molecules is proportional to the temperature of the gas in kelvins. Any two gases at the same temperature will have the same average kinetic energyKE = ½ mu2 u2 = (u1

2 + u22 + …+ uN

2)/N KE T

Mean square speed