Chem 110 - Class Guide: PV=nRT Applications and Partial Pressure (Chapter 10, Sections 5-6)
Chapter 10, Sections 5-6 Learning Goals
Upon completion of these sections, you should be able to:
Use the ideal gas law to calculate the molar mass of a gas.
Use the ideal gas law to calculate the density of a gas.
Given the mass or volume of reactants or products in a given chemical reaction, calculate either
mass or volume of another reactant or product.
Using Dalton’s Law, calculate either the partial pressure or the mole fraction of a gas in a
mixture of non-reactive gases.
Chapter Reading Guide: Chapter 10, Sections 5-6
Section 5: FURTHER APPLICATIONS OF THE IDEAL GAS LAW
Using algebra, we can rearrange the ideal gas law equation to solve for the density of a gas:
d = density (g/L)
µ = molar mass (g/mol)
P = pressure (atm)
R = gas constant
d
P
RT
T = temperature (K)
We can also rearrange it to solve for the molar mass of an unknown gas:
µ = molar mass (g/mol)
d = density (g/L)
R = gas constant
T = temperature (K)
P = pressure (atm)
Try Practice Exercises 10.7 and 10.8
dRT

P
You know how to do stoichiometry with solids and aqueous solutions (remember chapter
3?) and with enthalpies of reactions (chapter 6). Now we get to do it with gases!
In stoichiometry, we use the mole ratio to get from one reagent to another or to a product
in a balanced equation. We do the same thing here, except you might have to find the
moles of a gas using PV = nRT before you can do stoichiometry, or you might have to find
the volume of a gas after you’ve completed stoichiometry.
Be careful! You can only put a gas into PV = nRT, so pay attention to those phase labels in
the equation!
After the examples, try practice exercise 10.9.
Example 1: Given the reaction below, how many grams of NaN3 do you need to produce 4.5
L of N2 at 25 °C and 1.33 atm? R = 0.08206 (L*atm)/(mol*K).
2 NaN3 (s)  2 Na (s) + 3 N2 (g)
First, we find moles of N2 so we can use the balanced equation:
n=
1.33 atm  4.5 L 
PV
=
= 0.25 mol N 2
L*atm 
RT 
 0.08206
  298 K 
mol*K 

Now we do stoichiometry like normal to get grams of NaN3:
Mass (g) NaN3 = 0.25 mol N2
2 mol NaN3 65.02 g NaN3
= 11 g NaN3
3 mol N 2 1 mol NaN3
Example 2: Given the reaction below, how many liters of N2 will be produced when 35.5 g
NaN3 reacts at 25 °C and 1.33 atm? R = 0.08206 (L*atm)/(mol*K).
2 NaN3 (s)  2 Na (s) + 3 N2 (g)
First, we find moles of N2 using the balanced equation:
mol N 2 = 35.5 g NaN3
1 mol NaN3 3 mol N 2
= 0.819 mol N 2
65.02 g NaN3 2 mol NaN3
Now we use PV = nRT to find liters of N2 (note that we couldn’t put NaN3 into PV = nRT
because it’s a solid!):
V=
nRT
=
P
 0.819 mol   0.08206
L*atm 
  298 K 
mol*K 

=15.1 L
1.33 atm
Section 6: GAS MIXTURES AND PARTIAL PRESSURES
Dalton’s Law states that the pressure of a mixture of gases is the sum of the pressure of
each gas, or:
PT = P1 + P2 + P3 + . . . + P x
Unfortunately, it’s difficult to measure the individual pressures in a mixture. It’s easier to
measure the overall pressure, so we can re-write Dalton’s Law in a more useful way:
n
P1   1
 nT

 PT  1PT

Where n = number of moles; and
Χ = mole fraction
Try practice exercises 10.10 and 10.11.
You can skip ‘Collecting Gases over Water’.
Learning Resources
Chapter Learning Goals
Chapter 10, Section 5-6 Learning Goals
Pre Class Assignment: This assignment must be completed prior to the next class. Check your syllabus
for the exact due date and time.
Complete the pre class assignment
(http://berks.psu.edu/clt/chem110/PV=nRTApplications_HW.doc)
Submit a copy to the dropbox located in ANGEL called “Pre Class Assignment Submission: PV =
nRT Applications and Partial Pressure”
End of Chapter Problems:
Practice with these problems if you are having difficulty with any of the concepts covered in this
class guide AFTER we have met in class. If you cannot easily complete these problems, seek
help from your instructor, your mentor, or the learning center.
Chapter 10: 49, 53, 57, 59, 65, 71, 75, 111