1st… Let’s Review Gases

In Lab, we often collect gas by water displacement:

When you’re done, there are many H2 particles and some H2O particles.

To get the pressure of just the hydrogen in the flask:

• You subtract the partial pressure of the water vapor from the total pressure in the flask.  (Table on page 859)

• PH2 gas = Ptotal - PH2O vapor • IE: If the pressure in the room is 762 mmHg and

the temp. in the room is 21 C, then the partial pressure of just H2 would be:

• 762-19 mm Hg = 743 mm Hg• (If you look up Water Vapor Pressure on Pg. 859,

it’s 19 mm Hg at 21 C.)

Boyle’s Law and Charles’s Law

The Ideal Gas LawPV = nRT

• P = pressure in atm

• V = volume in liters

• n = moles of the gas

• T = temperature in Kelvin • R = 0.0821 (gas constant)Kmol

atmL

There are two kinds of gas law problems:

• 1. Solve for one variable in PV=nRT in the same conditions

• 2. Solve for a variable after a change in the conditions (a change in P, V, n, or T)

How to Solve for one variable:

• 1. Manipulate PV=nRT to isolate the variable you need using algebra

• 2. Convert all units to L, atm, moles, & K and plug in the values to solve for the isolated variable.

• A balloon is filled with 34.0 g of methane. The temperature is 33 C and the pressure inside the balloon is 1450 mm Hg. What is the volume of the balloon?

Solution:

• PV=nRT, isolate V

• V = nRT P

• n=2.12 moles4

4

44 CH12.2

CH02.16CH1

CH0.34 molsg

molg

Solution (cont’)

• Temp in K?

• K = 33° + 273° = 306 K

• P in atm?

AtmAtmmm

mmP 91.1

/Hg760Hg1450

Now, plug in:

• So the balloon has 27.9 Liters in it.

Litersatm

KKmol

atmLmols

P

nRTV 9.27

91.1

)306)(0821)(.12.2(

A sample problem:

• A 44.0 gallon steel barrel with some water in it is heated to 300 ºC. The pressure is measured to be 7.82 atm.

• How many grams of water are in the barrel?

• Assume no other gas is in the barrel. Also, 1 gallon is 3.78 Liters.

Before & After Problems:

• Look for words & numbers that indicate a change has taken place. The best way is to write out all the variables using subscripts 1 & 2 to show if it’s before or after.

Example:

• A sample of N2 gas has a pressure of 825 mm Hg at 25 ºC. What temperature is required to increase the Pressure to 8.5 atm, assuming fixed volume & amount of N2?

Solution:

• P1 = 825 mm Hg = 825/760 = 1.09 atm

• P2 = 8.5 atm

• T1 = 25° + 273° = 298 K

• T2 = ?

• This means that n & V don’t change

• R never changes.

Here’s an easy way to isolate what you need:

• Always start with this, since:

22

22

11

11

TnVP

TnVP

R

Remove the variables which don’t change:

• Remove n and V:

2

2

1

1

TP

TP

Isolate the variable you want:

• Now isolate T2 from the rest using the

simple moving to the other side techniques:

Katm

KatmPTP

T 230009.1

)298)(5.8(

1

122

Sample Problem:

• A 3.50 mL bubble of air forms deep in a lake where the Temp. is 7.0 C and the Pressure is 1.95 atm.

• The bubble rises to just below the surface of the lake, where the Temp. is 18 C and the pressure is 750 mm Hg.

• What’s the volume of the bubble just before it hits the surface of the lake?