# States of matter aggregation

The matter is present in the nature in three different States of matter aggregation: solid, liquid and gas. Solids have fixed shape and volume. Liquids have fixed volume, but its shape conforms to that of their container. Gases have no way or certain volume, adjusting in both cases their container. These two properties, shape and volume, which serve to distinguish the three states of aggregation, depend on the attractive forces between the constituent particles of matter and the relative ordering of said particles.

LAWS OF GASES

The volume, V, of any substance (solid, liquid or gaseous) is a function of the amount of substance that can be expressed in terms of number of moles, n, of the pressure, p, and temperature, T.

Boyle-Mariotte’s Law

“A constant temperature and a fixed mass of gas, the volume occupied is inversely proportional to the pressure.” Bioprofe |States of matter aggregation theory| 01

It is better known by the expression: Bioprofe |States of matter aggregation theory| 02

Where V is the volume occupied at pressure P, and the V´ the volume occupied at pressure P’.

Charles-Gay Lussac Law

“At constant pressure and for a fixed mass of gas, the volume occupied is directly proportional to the temperature”. Bioprofe |States of matter aggregation theory| 03

“At constant volume and for a fixed mass of gas, the pressure is directly proportional to the temperature”. Bioprofe |States of matter aggregation theory| 04

State Equation of ideal gases.

Boyle-Mariotte and Charles-Gay Lussac Laws can be combined into a single expression, thus obtaining a relationship between volume of a given mass of gas, pressure and temperature. Bioprofe |States of matter aggregation theory| 05 Bioprofe |States of matter aggregation theory| 06 Bioprofe |States of matter aggregation theory| 07

Dalton’s Law.

“The total pressure, p, exerted by a mixture of gases is equal to the sum of partial pressures, pI, that each gas would exert if it were only component in the same container”. Bioprofe |States of matter aggregation theory| 08

(p = total pressure of the mixture; pi = partial pressure of each gas xi = mole fraction of each gas).

Apparent molecular mass of a gas mixture, M: Bioprofe |States of matter aggregation theory| 09

(Mi = molecular mass of each gas; ni = number of moles of each gas; Vi = volume for each gas; V = volume of the mixture).

Kinetic energy of 1 mole of ideal gas: Bioprofe |States of matter aggregation theory| 10

SPEED MOLECULES

Mean square velocity gas: Bioprofe |States of matter aggregation theory| 11

Average speed of a gas: Bioprofe |States of matter aggregation theory| 12

Most likely gas velocity: Bioprofe |States of matter aggregation theory| 13

Relationship between the different speeds: Bioprofe |States of matter aggregation theory| 14

Graham’s Law:

“The gases diffusion or effusion speed, v, are inversely proportional to the square roots of their densities or molecular weights”. Bioprofe |States of matter aggregation theory| 15

REAL GASES

Van der Waals equation for 1 mole of gas: Bioprofe |States of matter aggregation theory| 17

(a / V2 = internal gas pressure; b = covolume).

Relationship between a, b and R and the constant criticism: Bioprofe |States of matter aggregation theory| 16

GIBBS PHASES RULE:

F + L = C + 2

(F = number of phases; L = number of freedom degrees; C = number of components).

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