We studied the meaning of the gas laws in some detail. Robert Boyle discovered the relationship between pressure and volume. He found that as you increased the pressure on a fixed amount of gas, the volume decreased, and vice versa. In other words, pressure is inversely proportional to volume. That is, P α 1/V. As an equation, this can be written as PV=K where K is a constant.
Then, the French scientist Jacques Charles, while working for the Montgolfier brothers to help them with their hot air balloon, discovered that volume of a fixed amount of gas is directly proportional to temperature. That is, V α T. As an equation, this is V/T = K where K is a constant.
And another Frenchman, Joseph Gay-Lussac, found that pressure of a fixed amount of gas was also proportional to temperature. That is, P α T. As an equation, this is P/T = K.
We demonstrated Boyle's law with a plastic syringe and mini marshmallows. As pressure was applied, the marshmallow (inside the syringe) "shrunk." When the plunger was pulled back, air inside the marshmallow caused it to expand. We demonstrated Charles' law by fitting a balloon to a flask and heating it. As the air was heated, the air inflated. When we added a small amount of water and heated it, the steam inflated the balloon quite a bit. After the water had all evaporated, the temperature of the steam continued to increase and the balloon inflated even more. For considering Gay-Lussac's law, we discussed what happened when an aerosol can of hair spray was used. It takes energy to expand and that energy comes from the molecules inside the can. Consequently, as the container valve is operated, the spray leaves it and heat is removed from the rest of the spray in the container, cooling it. This is how air conditioners work, too.
The three laws were combined in the -- logically enough -- "combined gas law," P₁V₁/T₁ = P₂V₂/T₂. This was based on the fact that PV/T = a constant, so if the same amount of gas has any condition changed, the other conditions will adjust to maintain the constant.
The combined gas law says that for a fixed amount of gas at a given pressure, temperature and volume, if you change anything, at least one other condition will change. For example, for a gas initially at 1 atmosphere pressure (same as 14.7 pounds per square inch, or 760 mm Hg, or 760 torr), occupying 1 liter volume, and at zero degrees Celsius, if it is warmed by 10 degrees, but the container volume is kept constant, then the pressure will go up. If the container is allowed to expand, the pressure will stay constant.
Since PV/T = constant = K, a good question is "What is the nature of the constant? Just what IS 'K'?" By specifying the conditions to apply to just one mole of gas, we can explore this point. Through experiments it was discovered that one mole of gas occupies 22.414 liters at standard temperature and pressure, STP. What is STP? It is a pressure of one atmosphere at zero degrees Celsius. Let K =nR where "n" is the number of moles and R is titled the "Gas Constant." Then PV/T = nR. This is usually written "PV = nRT." Here, we rearrange to solve for R. That is R = PV/nT.
By the way, T is in units of Kelvins, or K. This unit was named in honor of William Thompson who was dubbed "Lord Kelvin" due to the importance of his discovery. He found absolute zero, the temperature at which motion stops. It is 273.15 below zero on the Celsius scale.
So, to solve the ideal gas law for R we have: R = (1 atm)(22.414 liters)/(1 mole) (273.15 K).
This yields R = 0.0802 liter ‧ atm/mole ‧ K.
Clearly, if you use different units for the volume or pressure, the value of R will change.
Importantly, when you are given problems, you can generally just plug in the appropriate values to solve them.
FOR TOMORROW: We will explore the experiment by Lord Kelvin to find absolute zero. We will examine how the volume of a gas changes with temperature, and then extrapolate on a graph to the intersect with the temperature axis. That intersect represents absolute zero.
REMINDERS:
1. Have your class notes ready to hand in so I can grade them for your three-week report.
2. You will have another on-line quiz over the weekend. It will cover the gas laws and the barometer.
3. If you can finish the absolute zero experiment on Thursday, I'll have you do another one on Friday involving calculation of the amount of reactants and products from the volume of a gas produced in the reaction.
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