Avogadro’s law

Avogadro’s law, a statement that under the same conditions of temperature and pressure, equal volumes of different gases contain an equal number of molecules. This empirical relation can be derived from the kinetic theory of gases under the assumption of a perfect (ideal) gas. The law is approximately valid for real gases at sufficiently low pressures and high temperatures.

The specific number of molecules in one gram-mole of a substance, defined as the molecular weight in grams, is 6.02214129 × 10²³, a quantity called Avogadro’s number, or the Avogadro constant. For example, the molecular weight of oxygen is 32.00, so that one gram-mole of oxygen has a mass of 32.00 grams and contains 6.02214129 × 10²³ molecules.

The volume occupied by one gram-mole of gas is about 22.4 L at standard temperature and pressure (0°C, 1 atmosphere) and is the same for all gases, according to Avogadro’s law. It called molar volume of gas.

The law was first proposed in 1811 by Amedeo Avogadro, a professor of higher physics at the University of Turin for many years, but it was not generally accepted until after 1858, when an Italian chemist, Stanislao Cannizzaro, constructed a logical system of chemistry based on it.

From the Avogadro's law follows an important consequence: the mass ratio of equal volumes of the two different gases is constant for these gases. This constant is called the relative density of the gas and marked D. Because the molar volumes of all gases are identical, the ratio of the molar masses of each pair of gases is also equal to this constant:

where М₁ and М₂ – molar masses of two gaseous substances.

Basic gas laws.

Boyle's law (sometimes referred to as the Boyle–Mariotte law): at constant temperature the volume of a gas is inversely proportional to its pressure.

T = const

Inverse proportionality occurs when one variable gets larger by the same factor as another gets smaller.

Charles’s Law: at constant volume the pressure of a gas is directly proportional to its temperature.

V = const

Charles defined a new temperature scale in which the lowest possible temperature is 0^оС absolute, corresponding to -273.15 ^оС This temperature is called absolute zero.

The symbol T is used for absolute temperature, and t is used for Celsius temperature:

T = t + 273.15

Temperatures of approximately 0.000001 K have been produced in laboratories, but 0 K has never been reached.

Gay-Lussac's Law: at constant pressure the volume of a gas is directly proportional to its temperature.

P = const

A temperature of 0^оC and a pressure of 1.00 atm (760 mm Hg, 101.3 kPa) constitute a set of conditions for a gas often called standard temperature and pressure (abbreviated STP).

Combined gas law.

The combined gas law is a gas law that combines Charles's law, Boyle's law, and Gay-Lussac's law. There is no official founder for this law; it is merely an amalgamation of the three previously discovered laws. These laws each relate one thermodynamic variable to another mathematically while holding everything else constant. The combined gas law clearly states that: the ratio between the pressure-volume product and the temperature of a system remains constant. This can be stated mathematically as

where:

P is the pressure

V is the volume

T is the temperature measured in kelvin

k is a constant (with units of energy divided by temperature).

For comparing the same substance under two different sets of conditions, the law can be written as:

The addition of Avogadro's law to the combined gas law yields the ideal gas law. If five of these quantities are given, the sixth may be calculated. Temperatures must be expressed in kelvins, and the units of pressure and of volume must be the same on both sides of the equation.

Ideal gas law.

The ideal gas law is the equation of state of a hypothetical ideal gas. It is a good approximation to the behavior of many gases under many conditions, although it has several limitations. It was first stated by Émile Clapeyron in 1834 as a combination of Boyle's law and Charles's law. The ideal gas law is often introduced in its common form:

PV = nRT

where

P is the absolute pressure of the gas,

V is the volume of the gas,

n is the amount of substance of gas (measured in moles),

R is the ideal, or universal, gas constant, and

T is the absolute temperature of the gas.

This equation is called ideal gas law equation.

In SI units, P is measured in pascals (Pa), V is measured in cubic metres (m³), n is measured in moles, and T in Kelvin (273.15 Kelvin = 0.00 degrees Celsius). R has the value 8.314 J·K⁻¹·mol⁻¹ or 0.08206 L·atm·mol⁻¹·K⁻¹ or ≈ 2 calories if using pressure in standard atmospheres (atm) instead of pascals, and volume in liters instead of cubic metres.

How much gas is present could be specified by giving the mass instead of the chemical amount of gas. Therefore, an alternative form of the ideal gas law may be useful. The chemical amount (n) (in moles) is equal to the mass (m) (in grams) divided by the molar mass (M) (in grams per mole):

By replacing n with m/M,

and subsequently introducing density ρ = m/V, we get:

Dalton’s Law of Partial Pressures.

A mixture of gases follows the same laws as a gas composed of only one substance. Dalton’s law of partial pressures enables us to consider the properties of each component of a gas mixture.

In a mixture of gases, each gas has a partial pressure which is the hypothetical pressure of that gas if it alone occupied the volume of the gas mixture at the same temperature (The pressures of the individual components of a mixture are called partial pressures). The total pressure of an ideal gas mixture is the sum of the partial pressures of each individual gas in the mixture.

In chemistry and physics, Dalton's law (also called Dalton's law of partial pressures) states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases.

This empirical law was observed by John Dalton in 1801 and is related to the ideal gas laws. Mathematically, the pressure of a mixture of non-reactive gases can be defined as the summation: P_total = p₁ + p₂ + …+ p_n, where p₁, p_2, …, p_n represent the partial pressure of each component.

30. Nomenclature of Aromatic Compounds

For molecules having alkyl groups or other simple substituents attached to the benzene ring benzene is used as the parent name and the attached groups are named in alphabetical order before it.

If more than one substituent is attached to the benzene ring, their locations are specified by numbers. The lowest possible numbers are used and the substituents are named in alphabetical order.

When only two substituents are present the prefixes ortho-, meta- and para are used in place of 1,2-, 1,3- and 1,4- respectively.

Ortho-, meta- and para- are generally abbreviated to o-, m- and p- in most cases.

Benzene and derivatives of benzene

Benzene derivatives have from one to six substituents attached to the central benzene core. Examples of benzene compounds with just one substituent are phenol, which carries a hydroxyl group, and toluene with a methyl group. When there is more than one substituent present on the ring, their spatial relationship becomes important for which the arene substitution patterns ortho, meta, and para are devised. For example, three isomers exist for cresol because the methyl group and the hydroxyl group can be placed next to each other (ortho), one position removed from each other (meta), or two positions removed from each other (para). Xylenol has two methyl groups in addition to the hydroxyl group, and, for this structure, 6 isomers exist.