Gas Laws: Physics Ii
Gas Laws: Physics Ii
Gas Laws: Physics Ii
PHYSICS II
Technological University of the Philippines-Taguig Campus Department of Electrical Engineering
Properties of Gases
Air is the most important gas to living things on the Earth. The atmosphere of the Earth is a mixture of nitrogen, oxygen, water vapor, argon, and a few trace gases.
4 things
In order to completely describe a gas you need to measure 4 things
1. 2. 3. 4. Pressure Temperature Volume Number of particles
4
Boyle's Law
If the mass and temperature are kept constant, the product of pressure times volume stays the same. Original pressure (N/m2)
P1V1 = P2V2
Original volume (m3) Final volume (m3)
From Boyles law the volume of air available at a pressure of 2.5 bar is
Sample Problems
A scuba divers 12-L tank is filled with air at an absolute pressure of 150 bar. If the diver uses 30 L of air per minute at the same 2.5-bar absolute pressure as the water pressure at her depth of 15 m below the surface, how long can she stay at that depth?
Answer/Solutions:
From Boyles law the volume of air available at a pressure of 2.5 bar is However, 12 L of air remains in the tank, so she can use only 708 L. Hence
Gay-Lussacs Law
Original pressure (N/m2)
If the mass and volume are kept constant, the pressure goes up when the temperature goes up. Final pressure (N/m2)
P1 = P2 T1 T2
Original temperture (K) Final temperature (K)
Sample Problem
A certain amount of gas occupies a volume of 60 L at 300 K temperature. Find the temperature of the gas which has a volume of 100 L. Solution Vi = 60 L, Ti = 300 K, Vf = 100 L Step 1: Substitute the values in the below final temperature equation: Final Temperature(Tf) = VfTi / Vi = (100 x 300) / 60 = 30000 / 60 Final Temperature(Tf) = 500 K
Gay-Lussac's law
Gay-Lussac's law, or the pressure law, was found by Joseph Louis GayLussac in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to the absolute temperature.
Sample Problem
A gas sample occupies 5 ft 3 at 60F and atmospheric pressure of 15 lb/in. (a) Find its volume at 200F and a gauge pressure of 50 lb/in. 2. (b) Find its gauge pressure when it has been compressed to 1 ft 3 and the temperature has been reduced to 0F. Solution
a) Here T 1 = 60 + 460 = 520R, V 1 = 5 ft 3, and p 1 = 15 lb/in. 2.
(b) Now T 2 = 0 + 460 = 460R and V 2 = 1 ft 3. Hence the new absolute pressure is
MOLECULAR ENERGY
According to the kinetic theory of gases, the average kinetic energy of the molecules of a gas is proportional to the absolute temperature of the gas. This relationship is usually expressed in the form
where k = Boltzmanns constant = 1.38 10 2 3 J/K. Actual molecular energies vary considerably on either side of KE av.
SOLVED PROBLEM
What is the average kinetic energy of the molecules of any gas at 100C?
The absolute temperature corresponding to 100C is
THE MOLE
A mole of any substance is that amount of it whose mass is equal to its molecular mass expressed in grams instead of atomic mass units.
In SI units the amount of a substance corresponding to a mole is taken as a basic unit and written as 1 mol. The number of molecules in a mole of any substance is Avogadros number N, whose value is
The number of molecules in a sample of a substance is the number of moles it contains multiplied by N.
SOLVED PROBLEM
Find the mass of (a) the water molecule H 2O and (b) the ethyl alcohol molecule C 2H 6O. The atomic masses of H, C, and O are, respectively, 1.008, 12.01, and 16.00 u. Solution (a)
(b)
MOLAR VOLUME
Equal volumes of all gases, under the same conditions of temperature and pressure, contain the same number of molecules and therefore the same number of moles. This observation is most useful stated in reverse: Under given conditions of temperature and pressure, the volume of a gas is proportional to the number of moles present. Experimentally it is found that 1 mol of any gas at STP occupies a volume of 22.4 L. Thus the molar volume of a gas is 22.4 L at STP.
Avogadro's law
Avogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the molar volume of a gas, which at STP is 22.4 litres. The relation is given by
where n is equal to the number of moles of gas (the number of molecules divided by Avogadro's Number).
According to the ideal gas law the pressure, volume, and temperature of a gas sample obey the relationship pV/T = constant. We can find the value of the constant in terms of the number of moles n of gas in the sample by making use of the fact that the molar volume at STP is 22.4 L. At STP we have T = 0C = 273 K, p = 1 atm, and V = (n)(22.4 L/mol) so that
Gas Constants
The gas constants are different because the size and mass of gas molecules are different.
Volume (m3)
Temperature (K)
Mass (kg)
Sample Problem
(a) What volume does 1 g of ammonia (NH 3) occupy at STP? (b) What volume does it occupy at 100C and a pressure of 1.2 atm? (a) The molecular mass of NH 3 is
(b) From the ideal gas law, Here p 1 = 1 atm, V 1 = 1.32 L, T 1 = 0C = 273 K and p 2 = 1.2 atm, V 2 = ?, T 2 = 100C = 373 K. Hence
Sample Problem
What is the mass of 40 L of uranium hexafluoride (UF 6) at 500C and 4 atm of pressure? Solution
The most direct way to solve this problem is to use the ideal gas law to find the number of moles of UF 6 in the sample. Since pV = nRT and T = 500C = 773 K, we have
so the mass of UF 6 is