## Properties of Gases

• First, we know that a gas has no definite volume or shape; a gas will fill whatever volume is available to it. Contrast this to the behavior of a liquid, which always has a distinct upper surface when its volume is less than that of the space it occupies.

• The other outstanding characteristic of gases is their low densities, compared with those of liquids and solids. The most remarkable property of gases, however, is that to a very good approximation, they all behave the same way in response to changes in temperature and pressure, expanding or contracting by predictable amounts. This is very different from the behavior of liquids or solids, in which the properties of each particular substance must be determined individually.

• All gases expand equally due to equally due to equal temperature difference.

• **Diffusion of gases**: The phenomenon in which a substance mixes with another because of molecular motion, even against gravity- is called diffusion.

• **The pressure of a gas**: The molecules of a gas, being in continuous motion, frequently strike the inner walls of their container. As they do so, they immediately bounce off without loss of kinetic energy, but the reversal of direction (acceleration) imparts a force to the container walls. This force, divided by the total surface area on which it acts, is the pressure of the gas.

• The unit of pressure in the SI system is the pascal (Pa), defined as a force of one newton per square metre (1 Nm– 2 = 1 kg m–1 s–2.)

• **Temperature and Temperature Scales**: Temperature is defined as the measure of average heat. Temperature is independent of the number of particles or size and shape of the object. The water boiling temperature is same for all type of containers.

• **Thermometer**: The device which is used to define the measure of temperature of an object is Thermometer.

• **Temperature scale**: A reference scale with respect to which the temperatures can be measured is known as ‘scale of temperature’. Various scales of temperatures are in use. Important scales of temperature are:

• Celsius scale

• Kelvin scale

• Fahrenheit scale

• To devise a scale of temperature, fixed reference points (temperature) are required, with respect to which all other temperatures are measured. For both Celsius and Fahrenheit Scales of temperatures, the fixed points are as follows:

• **Lower fixed point**: Melting point of pure ice at normal atmospheric pressure is regarded as the lower fixed point.

• **Upper fixed point**: Boiling point of pure water at normal atmospheric pressure is regarded as the lower fixed point.

•** Celsius scale**: In this scale the lowest fixed point is the freezing temperature of pure substance. The upper fixed point is the boiling point of water. The interval is divided into 100 divisions all are at equal distance. Every division being denoted as one degree Celsius(0C). The Celsius scale is also

called as centigrade scale because the range of temperature is divided into 100 equal divisions.

• **Kelvin scale**: Another type of scale which is used to define the measure of temperature is Kelvin scale. The Kelvin scale is also known as absolute scale of temperature. The lowest fixed point is taken from the lowest temperature to which a substance to be cooled such as

-273.150C. According to the scale, a temperature is denoted by simply K .

• **Absolute zero:** The temperature at which a given mass of gas does not occupy any volume or does not exert pressure is called the “absolute zero”. Absolute zero i.e., 0K or -273oC is the lowest possible temperature that can be reached. At this temperature the gas has a theoretical volume of zero. In the Kelvin scale, the lowest possible temperature is taken as zero. This temperature is called as absolute zero.At the point absolute zero there is no molecular motion and there is no heat energy. At absolute zero all atomic and molecular motions stop. Hence the absolute zero is the lowest possible temperature which is denoted by 0K or -273.150 C.

• **Fahrenheit Scale of Temperature**: The lower and upper fixed points in this scale are considered as 320 F and 2120 F respectively. The interval of 1800 F is divided into 180 equal parts. Each part is known as 10 F. This is widely used by doctors.

• The volume of a gas is simply the space in which the molecules of the gas are free to move. If we have a mixture of gases, such as air, the various gases will coexist within the same volume. In these respects, gases are very different from liquids and solids, the two condensed states of matter. The SI unit of volume is the cubic metre, but in chemistry we more commonly use the litre and the millilitre (ml). The cubic centimetre (cc) is also frequently used; it is very close to 1 milliliter (mL).

• **Compressibility**: Particles of a gas have large intermolecular spaces among them. By the application of pressure much of this space can be reduced and the particles be brought closer. Hence the volume of a gas can be greatly reduced. This is called compressing the gas.

## Gas Laws

• All gases, irrespective of their chemical composition, obey certain laws that govern the relationship between the volume, temperature and pressure of the gases. A given mass of a gas, under definite conditions of temperature and pressure, occupies a definite volume. When any of the three variables is altered, then the other variables get altered. Thus these Gas laws establish relationships between the three variables of volume, pressure and temperature of a gas.

• **Boyle’s Law**: Robert Boyle (1627 – 1691) discovered this law in 1662 and it was named after him. It can be restated as “The product of the volume and pressure of a given mass of dry gas is constant, at constant temperature”. P “1/ V( at constant temperature) or PXV= K (where K is constant).

• **Charles’ Law**: “At constant pressure, the volume of a given mass of gas increases or decreases by 1/273 of its original volume at 32oF, for each degree centigrade rise or lowering in temperature.” Assume a given mass of gas has a volume of V1 at a temperature T1 Kelvin at a constant pressure, then, according to Charles’ Law we can write: V “T or VT=K (Constant).

• **Pressure Law**: Volume remaining constant, the pressure of a given mass of gas increases or decreases by a constant fraction (=1/273) of its pressure at 00C for each degree celsius rise or fall of temperature. If the pressure of a given mass of gas at 00C be Po; then for a rise or fall of temperature of T0C, its pressure Pt is given by Pt= Po{1±(t/273)}

•** Avogadro’s Law**: This is quite intuitive: the volume of a gas confined by a fixed pressure varies directly with the quantity of gas. Equal volumes of gases, measured at the same temperature and pressure, contain equal numbers of molecules. Avogadro’s law thus predicts a directly proportional relation between the number of moles of a gas and its volume.

• **Gay-Lussac’s Law**: When different gases react with each other chemically to produce gaseous substances, then under the same condition of temperature and pressure, the volume of the reacting gases and product gases bear a simple ration among one another.

• **Avogadro’s hypothesis**: Under the same condition of pressure and temperature, equal volumes of all gases contain equal number of molecules.

• The molecular weight of an element or compound is the sum-total of the atomic weights of the atoms which constitute a molecule of the substance. Example: The molecular formula formula of nitric acid is HNO3; hence its molecular weight = H + N + 3 × O = 1 + 1 4 + 3 × 16 = 6• (taking atomic weight of hydrogen as 1).

• **Gram-Atomic Weight**: A quantity of any substance whose mass in grams is numerically equal to its atomic weight, is called its Gram-Atomic Weight.

• **Gram-Molecular Weight**: A quantity of any substance whose mass in grams is numerically equal to its molecular weight, is called its Gram-Molecular Weight or mole.

• Molecular volume occupied by a mole of any gas is called the gram-molecular volume or molar volume. On the basis of Avogadro’s hypothesis, the gram molecular volume of any gas at normal temperature and pressure is 22.4 litres.

• **Avogadro Number**: From Avogadro’s hypothesis, we know equal volume of all gases contain equal number of molecules at normal temperature and pressure. Also we know that at normal temperature and pressure one mole of any gas occupies 22.4 litres. Combining the two, we can say that that, gram- molecular volume of all gases contain equal number of molecules at normal temperature and pressure. This number is known as Avogadro Number and is equal to 6.06X1023.

• **The Gas Equation**: According to Boyle’s Law, the volume of a gas varies inversely as the pressure, temperature remaining constant, i.e., V “1/ P and according to Charles’ law, the volume of a gas varies directly as the absolute temperature, pressure remaining constant, i.e. V “T Both, these laws can

be combined as: The volume of a given mass of a gas varies inversely with the pressure and directly with the temperature. V “(1/ P)XT or V “T/P or (PXV)/T = K(constant). In other words, For a given mass of a gas, if the initial conditions are P1, V1, and T1, then the altered conditions are P2, V2, and T2. Thus, (P1X V1)/ T1 = (P2X V2)/ T2

• **The ideal gas equation of state**: If the variables P, V, T and n (the number of moles) have known values, then a gas is said to be in a definite state, meaning that all other physical properties of the gas are also defined. The relation between these state variables is known as an equation of state. By combining the expressions of Boyle’s, Charles’, and Avogadro’s laws (you should be able to do this!) we can write the very important ideal gas equation of state: PV= nRT, where the proportionality constant R is known as the gas constant. This is one of the few equations you must commit to memory in this course; you should also know the common value and units of R.

• An ideal gas is an imaginary gas that follows the gas laws and has 0 volume at 0 K i.e., the gas does not exist.