Pressure

1
Pressure

• Pressure of air is measured with a BAROMETER
  (developed by Torricelli in 1643)
• Hg rises in tube until force of Hg (down)
  balances the force of atmosphere (pushing up). P
  of Hg pushing down is related to
• Hg density
• column height
• 1 standard atm 760 mm Hg (mm Hg torr)(gt 10
  meters of water!)
• SI unit is PASCAL, Pa, where 1 atm 101.325 kPa
  1.01325 bar

2
Boyles Law

• If n and T are constant, then
• PV (nRT) k
• This means, for example, that P goes up as V goes
  down.

Robert Boyle (1627-1691). Son of Earl of Cork,
Ireland.
A bicycle pump is a good example of Boyles
law-As the volume of the air trapped in the pump
is reduced, its pressure goes up, and air is
forced into the tire.
3
Charless Law

• If n and P are constant, then
• V (nR/P)T kT
• V and T are directly related.

Jacques Charles (1746-1823). Isolated boron and
studied gases. Balloonist
Temperature Scale absolute temperature units of
Kelvin (K) T (Kelvin) 273.15 T (Celsius)
4
Avogadros Hypothesis

• Equal volumes of gases at the same T and P have
  the same number of molecules.
• V n (RT/P) kn
• V and n are directly related.

twice as many molecules
5
The Gas Constant
Combining all of these laws leads to

• Boyles law V ? 1/P
• Charless law V ? T
• Avogadros law V ? n

PV nRT
The proportionality constant, R
0.082057 L atm mol-1 K-1
6
IDEAL GAS LAW
P V n R T

• Brings together gas properties.
• Can be derived from experiment and theory.

7
Using PV nRT

• How much N2 is needed to fill a small room with a
  volume of 960 cubic feet (27,000 L) to P 745 mm
  Hg at 25 oC?
• R 0.082057 Latm/Katm
• Solution
• 1. Get all data into proper units
• V 27,000 L
• T 25 oC 273 298 K
• P 745 mm Hg (1 atm/760 mm Hg) 0.980
  atm

8
Using PV nRT

• How much N2 is needed to fill a small room with a
  volume of 960 cubic feet (27,000 L) to P 745 mm
  Hg at 25 oC?
• R 0.082057 Latm/Kmol
• Solution
• 2. Now calculate n PV / RT

n 1.1 x 103 mol (or about 30 kg of N2 gas)
9
Determining a Molar Mass with the Ideal Gas
Equation. Example
Propylene is an important commercial chemical.
It is used in the synthesis of other organic
chemicals and in plastics production. A glass
vessel weighs 40.1305 g when clean, dry and
evacuated it weighs 138.2410 when filled with
water at 25C (r0.9970 g cm-3) and 40.2959 g
when filled with propylene gas at 740.3 mm Hg and
24.0C. What is the molar mass of polypropylene?
Determine mgas- from the mass difference
Determine Vflask- using the density of water
Use the Gas Equation mgas/moles of gas
Strategy
10
Determining a Molar Mass with the Ideal Gas
Equation. Example
Determine Vflask
Vflask mH2O dH2O (138.2410 g 40.1305 g)
(0.9970 g cm-3)
98.41 cm3 0.09841 L
11
Determining a Molar Mass with the Ideal Gas
Equation. Example
Use the Gas Equation
PV nRT
M 42.08 g/mol
12
Using the Ideal Gas Law An example from Midterm
1 2004
A chemist placed 32.5 g of a gas in an evacuated
constant volume container. The temperature and
pressure were 22ºC and 1 atm respectively. The
container was heated to 212ºC and, in order to
maintain constant pressure, some of the gas was
allowed to escape. What mass of gas was released
from the container? Solution
13
Using the Ideal Gas Law An example from Test 1
2004
Initial conditions 32.5 g of a gas, Temperature
22ºC and Pressure 1 atm. Final Temperature
212ºC, constant pressure (P 1atm). What mass of
gas was released from the container? Solution
Initial P1V1 n1RT1 Final P2V2 n2RT2 The
volume is constant and the pressure is kept
constant in the experiment by allowing some gas
to escape. n1RT1 n2RT2 (m1/MW)T1
(m2/MW)T2 m1T1 m2T2 m1T1/T2 m2 m2 32.5g x
(22273.15K)/(212 273.15K) 19.77 g loss of
mass 32.5-19.77 12.73g
14
Gases and Stoichiometry

• 2 H2O2(liq) ? 2 H2O(g) O2(g)
• Decompose 1.1 g of H2O2 in a flask with a volume
  of 2.50 L. What is the pressure of O2 at 25 oC?
  What is the P of H2O?
• Strategy
• Calculate moles of H2O2
• Calculate moles of O2 and H2O using stoichiometry
• Finally, calculate P from n, R, T, and V.

15
Gases and Stoichiometry

• 2 H2O2(liq) ? 2 H2O(g) O2(g)
• Decompose 1.1 g of H2O2 in a flask with a volume
  of 2.50 L. What is the pressure of O2 at 25 oC?
  What is the P of H2O?
• Solution

16
Gases and Stoichiometry

• 2 H2O2(liq) ? 2 H2O(g) O2(g)
• Decompose 1.1 g of H2O2 in a flask with a volume
  of 2.50 L. What is the pressure of O2 at 25 oC?
  What is the P of H2O?
• Solution
• P of O2 0.16 atm
• What is P of H2O?

17
Mixtures of Gases and Daltons Law of Partial
Pressures
In the previous example,
2 H2O2(liq) ? 2 H2O(g) O2(g)

• What is the total pressure in the flask?
• 0.16 atm
• 0.32 atm
• 0.48 atm
• 0.80 atm

18
Mixtures of Gases and Daltons Law of Partial
Pressures
In the previous example,
2 H2O2(liq) ? 2 H2O(g) O2(g)

• What is the total pressure in the flask?
• Ptotal in gas mixture PA PB ...
• Therefore, Ptotal P(H2O) P(O2)
• Ptotal 0.48 atm 2(0.16 atm) 0.16 atm
• Daltons Law total P is sum of PARTIAL
  pressures.