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# Ideal Gas Law

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## Jessica Kool

on 15 January 2014

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#### Transcript of Ideal Gas Law

Ideal Gas Law
Ideal Gas Law
Equation
PV=nRT
P = Pressure
Measured in atmospheres (atm)
760mmHg = 1 atm = 101.3 kPa

V = Volume
SI unit of volume is liters = L

n = # of moles

R = Gas Constant:
SI value of R is 0.0820574 L•atm•mol-1K-1

T = Temperature:
Temperature must be in Kelvin not in Celsius
*Add 273 to the temperature if it is given in Celsius.
Real World Application
Hot Air Balloon:
As the air is heated the pressure increases on the inside of the balloon, causing the molecules to expand and the volume to increase. Also, the air inside the balloon is less dense than the outside air, allowing it to float.
Liquid Nitrogen Experiment
Practice Problems
Background
The Ideal Gas Law is a combination of three separately discovered laws by three different chemists:

- Boyle's Law
- Gay-Lussac's Law.
- Charles' Law
Explanation
Temperature
Liquid nitrogen is really, really cold.
Process called the "thermal expansion/contraction".
A decrease in temperature results in a decrease of frequency and magnitude, causing the molecules to obtain less energy and collide less frequently.
The loss of energy causes the balloon to deflate.
Pressure
When the balloon deflates, the pressure of the molecules on the balloon decrease on the inside.
Volume
As pressure inside the balloon decreases, volume also decreases.
When the temperature increases, the pressure in the balloon increases. This causes the molecules to expand, which increases the volume.
Ideal gases can be characterized by 3 state variables:
Absolute Pressure (P)
Volume (V)
Absolute Temperature (T) in Kelvin not in Celsius
P= nRT/V
V = nRT/P
n = PV/RT
T = PV/nR
R = nT/PV
Football:
On a cold day, the molecules inside a football move slower, which causes the volume to decrease (fewer collisions). This is the reason why footballs must be regularly pumped with air after the winter season.
As a result, the molecules are not hitting the sides of the balloon equally on the inside and outside, therefore causing and implosion.
5.600 g of soild CO2 is put in an empty sealed 4.00 L container at a temperature of 300 K. When all the solid CO2 becomes gas, what will be the pressure in the container?
1) Determine moles of CO2
5.600 g x 44.009 g/ 1mol = 0.1272467 mol

2) Use PV = nRT
(P) (4.00 L) = (0.1272467 mol) (0.08206) (300 K)
P = 0.7831 atm
Question 1
Question 2
5.0 g of neon is at 256 mm Hg and at a temperature of 35º C. What is the volume?
Step 1: Write down your given information:
P = 256 mmHg
V = ?
n = 5.0 g
R = 0.0820574 L•atm•mol-1K-1
T = 35º C

Step 2: Convert as necessary:
Pressure: 256mmHg∗(1atm/760mmHg)=0.3368atm
Moles: 5.0gNe∗(1mol/20.1797g)=0.25molsNe
Temperature: 35ºC+273=308K

Step 3: Plug in the variables into the appropriate equation.
V=(nRT/P)
V=[(.25mol)(0.08206Latm/Kmol)(308K)/(.3368atm)]
V=19L
Question 3
A sample of argon gas at STP occupies 56.2 liters. Determine the number of moles of argon and the mass in the sample.
1) Rearrange PV = nRT:
n = PV / RT

2) Substitute:

n = [ (1.00 atm) (56.2 L) ] / [ (0.0820574 L•atm•mol-1K-1) (273.0 K) ]
n = 2.50866 mol

3) Multiply the moles by the atomic weight of Ar to get grams:
2.50866 mol times 39.948 g/mol =
100 g
It is said that Avogadro may have had a version of the law, but so many scientists were working on Ideal Gas Law at the same time that there is no specific scientist given credit for the combined Ideal Gas Law. However, it was Emile Clapeyron who made the decision to combine the laws.
There are no intermolecular forces between the gas molecules.

The volume occupied by the molecules is unimportant in regards to the volume of the container.

Gas molecules are in constant motion, but travel in random straight lines.

The molecules act as tiny rigid spheres.

Pressure is due to the molecules colliding with each other and the walls of the object.

There is no loss of kinetic energy during any of the collisions.

Temperature is directly proportional to average kinetic energy of the molecules.
When dealing with ideal gases, we assume:
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