gas law notes

A.    Gay- Lussac’s law- Pressure is directly proportional to the KELVIN temperature if the volume and mass remain constant.  

B.     When a gas is heated at constant volume, the pressure increases.

C.     When one variable increases, the other variable increases

EXAMPLE PROBLEM: The pressure in a car tire is 198 kPa at 27^oC.  After a long drive, the pressure is 225 kPa.  What is the temperature of the air in the tire?  Assume that the volume is constant.           

Given:  P₁ = 198 kPa , T₁ = 27 ^oC , P₂ = 225 kPa

                           

                         198kPa/27^oC = 225 kPa/ T₂

                               T₂ = 225(27)/198

                                    = 30.7^oC

      The temperature of the air in the tire after the long drive is 30.7^oC.     


Evaluate: According to Gay - Lussac's Law, temperature is directly proportional to pressure, and since the pressure increases, the resulting answer is greater than the original temperature.                                                                                                                                                                                                                

1. Combined gas law

A.    The combined gas law allows you to do calculations for situations in which only the amount of gas is constant

EXAMPLE PROBLEM:  A 5.00 L air sample has a pressure of 107 kPa at a temperature of -50.0^oC. IF the temperature is raised to 102^oC and the volume expands to 7.00 L, what will the new pressure be?             

  Given: V₁ = 5.00 L6,  P₁ = 107kPa , T₁ = -50.0 ^oC , T₂ = 102^oC , V₂ = 7.00 L

                                                                 107kPa (5.00L) / -50^oC = P₂ (7.00L) / 102^oC

                                               P₂ = (5.00L) (107 kPa) (102^oC) / (-50^oC) (7.00L)

                                                    = -155.91 kPa

       The new pressure is -155.91 kPa after the temperature was raised to 102 ^oC and the volume expands to 7.00 L.    

Tips for Gas Law Problems

1) Determine which gas law you need

n       Pressure and volume = Boyle’s

n       Temperature and volume = Charles’

n       Temperature and Pressure = Gay-Lussac’s

n       Temperature, pressure, and volume = Combined

2) Identify your variables.  Be sure you put the proper numbers together

3) Change all variables into the correct units

n       Temperature must be Kelvin

n       Pressure units must match

n       Volume units must match

4) Put numbers into the gas law equation and solve

Ideal gas Law

Goals for this section:

-          Calculate the value of an unknown variable using the ideal gas law

-          Compare and contrast real and ideal gases

-          Terms to know: ideal gas law, ideal gas constant

VI.  Ideal Gas Law

A.     Ideal gas- A gas that conforms to the gas laws.

a.       Particles exhibit     no attractive or repulsive force. 

b.      Volume of particles is assumed to be negligible compared to the total volume occupied by the gas. This means you can     ignore the volume of the particles.                       

B.     Real gases do not behave ideally when they have             high pressure or low temperature. 

a.       Under these conditions, gases tend to _condense.

C.      When is a gas ideal? 

a.       When it has            large volume and low pressure and/or high temperature.

b.      Under these circumstances, attractive forces are not important.

D.    ideal gas law:  .  

P = pressure  (must be in units of kPa)

V = volume  (must be in units of L)

n = moles    (may need to convert grams or molecules to moles first)

R = 8.31 LkPa/(Kmol)

 T = temperature   (must be in units of K)

Partial Pressures, Diffusion, Effusion

Goals for this section:

-          Relate the total pressure of a mixture of gases to the partial pressures of the component gases

-          Explain how the molar mass of a gas affects the rates at which the gas diffuses and effuses

-          Compare and contrast effusion and diffusion

-          Terms to know: partial pressure, Dalton’s law of partial pressures, diffusion, effusion, Graham’s law of effusion/diffusion

VII.            Partial Pressures, Diffusion, Effusion

a.       Partial Pressure:

                                                              i.      The contribution each gas in a mixture makes to the total pressure is called the          partial pressure exerted by that gas

                                                            ii.      Dalton’s law of partial pressures;  In a mixture of gases, the total pressure is the   sum of the partial pressures of the mixture of each individual gases.       

1.      Provided the temperature and volume remain the same

b.      Diffusion is the tendency of molecules to move toward areas of         low concentration until the concentration is uniform throughout

c.       During effusion, a gas escapes through a         very small hole in the container. 

d.      Gases of          lower molar mass            diffuse and effuse faster than gases of higher molar mass.

e.       Graham’s law of effusion states that the rate of effusion of a gas is inversely proportional to the square root of the gas’s molar mass. This law can also be applied to the diffusion of gases.