CHEMISTRY 4
Chapter 4
Introduction to Gases
1The Kinetic Theory of Gases and The Ideal Gas Model
Gases consist of molecules moving randomly in straight lines in all directions.
Molecules collide with each other and with the container walls without loss of kinetic energy.
Gas molecules are very widely spaced. The volume of molecules is negligible compared to the space they occupy.
Molecules have no attraction for one another.
The average kinetic energy of a molecule is proportional to the absolute temperature.
Particle motion explains why gases fill their container.
The compressibility and the mixing capability of gases are attributable to the large distances between molecules.
The pressure exerted by a gas on an object is the result of the collisions that the molecules have with the object surface.
2 Gas Measurement
Volume, pressure, temperature, and amount of gas are quantities that are closely related.
Pressure
Pressure is, by definition, the force exerted on a unit area
Pressure ≡ Force / area or P ≡ F/ A
The SI unit of pressure is the pascal ( Pa ), which is one newton per square meter ( The newton is the SI unit of force, the weight of an apple is about 1 newton). One pascal is a very small pressure. Other units of pressure are pounds per square inch (psi), millimeter of mercury (mm Hg) or the torr, and atmosphere (atm). Atmospheric pressure (due to the weight of the atmosphere) is about one atm. Atmospheric pressure is often measured by a barometer. In a mercury barometer, the space above the mercury is a vacuum, and the pressure of a column of mercury is balanced by the pressure of the atmosphere
Atmospheric pressure = density of Hg x acceleration of gravity x height
PAtm. = d.g.h
The height of the mercury column ( h ) is directly proportional to the atmospheric pressure ( PAtm.)
The definition of atm is given below:
1 atm = 760 mm Hg ≡ 760 torr ( definition of atm)
1 atm = 101.3 kPa = 29.92 in. Hg = 14.69 psi
Example : Express 746 torr in atmosphere.
Given 746 torr
Wanted atm
path torr------> atm
Factor 1 atm / 760 torr and 760 torr / 1 atm
Calculation setup 746 torr x 1 atm / 760 torr = 0.982 atm
Check small number (0.982) for larger unit (atm) and large number (746) for small unit. The cancellation of unit gives the right unit at the end.
Temperature
Temperature of a substance is a measure of the average kinetic energy of the particles in the sample. The average kinetic energy ( mv2/2) of particles is directly proportional to absolute temperature.
mv2/2 = (3/2) kT
where k is known as Boltzmann’s constant.
3 Charles’ Law
The volume of a fixed quantity of gas at constant pressure is directly proportional to the absolute temperature.
V = k T
or
V2 = V1 x (T2 / T1)
Example : A gas with initial volume of 1.67 liters, measured at 32 0C, is heated to 55 0C at constant pressure. What is the new volume of the gas?
Volume Temperature Pressure Amount
______
Initial Value (1) 1.67 L 320C, 305 K constant constant
Final Value (2) V2 550C, 328 K constant constant
______
V2 = 1.67 L x (328 K / 305 K) = 1.80 L
4 Boyle’s Law
The pressure of a fixed amount of gas at constant temperature is inversely proportional to the volume. When the volume of a gas is decreased, there are more molecules in one unit of volume, so there are more collision with an unit of area of the wall in an unit of time. The pressure will be increased.
PV = Constant
or
P1 V1 = P2 V2
Where 1 and 2 correspond to initial and final states of the system. One way to solve a gas problem is to prepare a table showing the initial and final values of all variables.
Example : A certain gas sample occupies 5.18 liters at 776 torr. Find the volume of the gas sample if the pressure is changed to 827 torr. Temperature and amount remain constant.
Volume Temperature Pressure Amount
______
Initial Value (1) 5.18 L Constant 776 torr constant
Final Value (2) V2 Constant 827 torr constant
______
V2 = V1 x P1 / P2 = 5.18 L x 776 torr / 827 torr = 4.86 L
5 Gay-Lussac’s Law.
The pressure of a fixed quantity of gas in a container of constant volume is directly proportional to the absolute temperature. As the temperature is raised, the molecules strike the wall more often (the number of collisions per unit of time is proportional to the velocity v) and with greater force (the force exerted during one collision is proportional to mv, where m is the mass of the molecule). Thus the pressure is proportional to the average kinetic energy ( mv2/2) of particles, hence to the absolute temperature.
P = k T
or
P / T = k
or
P1 / T1 = P2 / T2
Example : The gas in a flask exerts a pressure of 0.97 atm at 18 0C. What will the pressure be if the temperature is raised to 31 0C ? Volume remains constant.
Volume Temperature Pressure Amount
______
Initial Value (1) Constant 180C, 291 K 0.97 atm constant
Final Value (2) Constant 310C, 304 K P2 constant
______
P2 = P1 x T2 / T 1 = 0.97 atm x 304 K / 291 K = 1.01 atm
5 The Combined gas law
We have seen that:
1)-the temperature, T, and the pressure, P, are directly proportional.
2) the temperature, T, and the volume, V, are directly proportional
Whenever the same quantity (T) is proportional to each of two other quantities (P and V), it is proportional to the product of those quantities (PV)
PV = k T
or
PV / T = Constant
or
P1V1 / T1 = P2V2 / T2
A cylinder in an automobile engine has a volume of 352 cm3. This engine takes in air at 210C and at 0.945 atm pressure. The compression stroke squeezes this gas until the temperature is 95 0C and the pressure is 4.95 atm. What is the final volume in this cylinder?
Volume Temperature Pressure Amount
______
Initial Value (1) 352 cm3 210C, 294 K 0.945 atm constant
Final Value (2) V2 95 0C, 368 K, 4.95 atm constant
______
V2 = V1 x P1/ P2 x T2 / T1
V2 = 352 cm3 x (0.945 atm / 4.95 atm) x (368K / 294 K) = 84.1 cm3
The volume of a fixed quantity of gas depends on its temperature and pressure. To compare the amount of gases, temperature and pressure must be given. Standard temperature and pressure ( STP) are respectively 0 0C (273 K ) and 1 atm ( 760 mm Hg or 760 torr)
Example: What would be the volume at STP of 3.62 liters of nitrogen gas, measured at 0.843 BAR and 16 0C
Volume Temperature Pressure Amount
______
Initial Value (1) 3.62 L 16 0C, 289 K 0.843 bar constant
Final Value (2) V2 0 0C, 273 K 1 bar constant
______
V2 = V1 x (P1 / P2 ) x (T2 / T1)
V2 = 3.62 L x (0.843 bar/ 1 bar) x (273 K/289 K) = 2.88 L
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