Ideal gas law pV = nRT: Assumptions and Example

Equations with finding Pressure and Volume
P1/V1 = P2/V2

Equations with Temperature and Volume
V1/T1 = V2/T2

Equations for Pressure and Temperature
P1/T1 = P2/T2

Equations with Volumes and Moles
V1/n1 = V2/n2

The ideal gas law
PV=nRT

STP
Temp: 273k
Pressure: 1atm
Occupies 22.4L

Finding Molar Mass with Ideal Gas Law
M = gRT/PV

Units for Molar Mass and Molecular Mass
Molar Mass: g/mol
Molecular Mass: amu

Value of “R”
0.0821 Latm/mol k

Converting torr to atm
1atm/760torr

Converting mmHg to atm
1atm/760mmHg

Partial Pressure
Ptotal = P1 + P2 + P3 +……etc.
When trying to find out when given percentages:
(% given/ %total) x total pressure =
Then add all answers together to get the pressure total

The purpose of this experiment is to…
experimentally determine the ideal gas constant R.

How many milliliters of hydrochloric acid solution should be placed in the eudiomenters?
20 mL +/- 10%

The beaker of water into which you invert the eudiometer tube should…
need only cover the open end of the eudiometer.

When calculating the ideal gas constant R, what are some common mistakes that are made?
Forgetting to convert the temperature to Kelvin.

Forgetting to subtract the vapor pressure of water.

Forgetting to convert to the volume to Liters.

Forgetting to convert the pressure from torr to atmospheres.

The mass of magnesium metal used when doing this expriment should be…
must be between 0.035 – 0.045 gram.

Why must the mass of magnesium metal used in the eudiometer tube be limited?
If you use too much mass of magnesium, the hydrogen gas produced will fill the eudiometer tube beyond the volume markings and its volume will not be able to be determined.

What temperature should be used in the calculations?
Room temperature in K.

What should be done with the left over reservoir after the experiment is over?
In the waste container labeled PV=nRT.

If the pressure of gas inside the eudiometer is 735.4 mm Hg after a reaction of magnesium metal with excess hydrochloric acid and the vapor pressure of water inside the tube is 23.4 mm Hg, to four significant figures, what is the pressure of hydrogen gas inside the tube in atm?
0.9368 atm

The pressure INSIDE the eudiometer when column of liquid inside the tube is higher than the reservoir is…
less than atmospheric pressure.

Kinetic Theory assumptions about ideal gas.

• Ideal gas is made up of molecules in random motion.
• Collision between the molecules and container walls causes pressure.
• The gas molecules have rigid spheres.
• All collisions are perfectly elastic.
• The average kinetic energy of the molecules determines the gas temperature.

The two ways ideal gases differ from real gases.

1. Negligible intermolecular forces between the gas molecules
2. The negligible volume occupied by the molecules compared to the volume of the container.

Idea gas equation

pV = nRT

“1 mole of any gas occupies 22.4 dm³ at stp (standard temperature and pressure, taken as 0°C and 1 atmosphere pressure)”

P = Pressure (atm)

V = Volume (L)

n = moles 

R = gas constant = 0.0821 atm•L/mol•K

T = Temperature (Kelvin)

Example

Use the ideal gas law to calculate the mass of helium in 5.22 L of the gas at 0.918 ATM and 25°C.

We first need to find the unknown and known.

P = 0.918 atm

V = 5.22L

n = moles = ?

R = gas constant = 0.0821 atm•L/mol•K

T = Temperature (Kelvin) = 25°C + 273 = 298 K

We will use this equation to determine the moles of Helium, and then calculate mass

PV = nRT

n = RT / PV

n = 0.0821 * 298 / 0.918 * 5.22

n = 24.466 / 4.792

n = 5.11 moles

Since we have the number of moles of Helium, we can easily calculate mass

Formula for moles = mass / molar mass (4 g/mol)

Mass = molar mass * moles

Mass = 5.11 moles * 4 g/mol

Mass = 20.44 grams

So the answer is 20.44 grams