Understanding Atoms, Molecules, and States of Matter
Atom
The matter consists of atoms. These consist of the nucleus and cortex. The core is formed by protons (p+) and neutrons (n). The crust consists of electrons (e–).
Ions
An atom can become an ion by electron gain or loss. If it gains electrons, it becomes an anion (negatively charged ion). If it loses electrons, it produces a cation (positively charged ion).
Atomic Number (Z)
The atomic number is the number of protons in the nucleus of an atom. It identifies the atoms of an element. This matches the number of electrons as the atom is neutral. It is represented by Z.
Mass Number (A)
The mass number is the total number of particles that form the core (number of protons + number of neutrons). It is denoted by A.
Isotopes
Isotopes are varieties of atoms of the same element (same Z) which differ in the number of neutrons (different A).
AX = Element Symbol
They are represented by X, where Z = atomic number
ZA = Mass number
Relative Atomic Mass of an Element (ar, u)
The relative atomic mass of an element is the weighted average of the masses of different isotopes that make up the item.
The atomic mass unit (u) is defined as one twelfth of the mass of carbon isotope -12.
Molecule
A molecule is a set of identical or different atoms that constitute the minimum amount of a substance that retains its chemical properties. The composition of a molecule is indicated by chemical formulas.
Molecular Mass (mr, u)
The molecular mass is the sum of the relative atomic masses of atoms in a molecule.
Molar Mass (m, g)
The mole is the amount of substance that contains 6.023 x %IMAGE_1% particles. This number is called Avogadro’s number (NA).
If the particles are atoms, the mass in grams of one mole numerically coincides with the atomic mass.
If the particles are molecules, the mass in grams of one mole (molar mass) coincides numerically with its molecular mass.
Empirical Formula
The empirical formula indicates the simplest ratio between the atoms of elements forming the molecule.
For example, the CH2O molecule has one carbon atom for every two hydrogen atoms and one oxygen.
Molecular Formula
The molecular formula indicates the number of atoms of each element present in the molecule. The molecular formula is a multiple of the empirical formula.
Molecular formula = n x Empirical formula
For example, the empirical formula CH2O corresponds to a molecular formula C2H4O2
C2H4O2 = 2 x (CH2O)
States of Matter
The properties of the three states of matter can be explained from the kinetic molecular theory. This theory postulates that all matter is made of particles that are constantly moving and colliding elastically (no kinetic energy is lost).
Solid State
Solids hold their own shape and constant volume. They are incompressible.
Their particles have virtually no mobility, are very close together, so they can only vibrate.
Liquid
Liquids have constant volume and it has little variation with temperature. They adapt to the shape of the container that contains them.
Their incompressibility is almost nil.
Their particles are close to each other but do not occupy fixed positions, as they have some mobility, which increases with temperature. They hit the walls of the container, exerting hydrostatic pressure.
Vapor Pressure of a Liquid
The vapor pressure of a liquid is the vapor pressure of a liquid in a closed container when equilibrium is achieved between the liquid and vapor at a given temperature.
At a given temperature, the vapor pressure gives an indication of the tendency of liquids to pass into a gaseous state. Depending on the value of the vapor pressure, they are said to be more or less volatile.
The SI unit is the pascal (Pa). Also used are the atmosphere (atm) and millimeter of mercury (Hg). The equivalences between these units are:
1.01 x 105 Pa = 1 atm = 760 mm Hg.
Gaseous
The gases adapt to the shape of the container and occupy its entire volume. Temperature changes cause significant changes in volume. They are easily compressible and have very low density.
The distance between the particles is much higher than in other states. The particles, whose volume is negligible compared to the total volume occupied by a gas, continuously move randomly in all directions without any attractive forces between them. They hit the walls of the container, exerting gas pressure.
The gases described are called ideal or perfect gases. Any real gas at low pressure conditions can be considered an ideal gas.
Rate of Diffusion
Molecular diffusion is the transport of material produced by the random motion of gas molecules.
According to the kinetic molecular theory, collisions between molecules are elastic, kinetic energy is not lost, 1/2mv2 = constant, and therefore, the gases with lower molecular mass are also faster and have faster diffusion.
Laws of the Gases
General Gas Law
The general law of ideal gases relates the variables pressure (p in Pa or atm), volume (V in L), and absolute temperature (T in K) in different states (1, 2, …) for the same mass of a given gas.
%IMAGE_2% (T = temperature in °C + 273)
If the transition from the initial state 1 to final state 2 is realized by maintaining a variable p, V, or T constant, expressions are obtained:
%IMAGE_3% AT constant V = Constant (Boyle’s Law)
%IMAGE_4% A constant p = Gay-Lussac’s Law
%IMAGE_5% Constant AV = Gay-Lussac’s Law
General Equation of Ideal Gas
The general equation of ideal gases relates the variables p, V, T with the quantity (number of moles) of a gas.
pV = nRT
where:
%IMAGE_6% R = The universal gas constant.
0.082 = 8.31 = 8.31
From the general equation of ideal gases, it can be assumed that equal volumes of different gases under the same conditions of temperature and pressure have the same number of moles and, therefore, the same number of molecules.
A gas is in normal condition (NC) when its temperature is 273 K (0 °C) and pressure 1.01 x %IMAGE_7% Pa (1 atm). Under these conditions, the volume occupied by a mole (molar volume, %IMAGE_8%) of any gas is 22.4 L.
Other expressions of the gas equation are:
pV = %IMAGE_9% RT where m = mass of gas (g)
M = molar mass of gas (g/mol)
p = %IMAGE_10% d = density (g/L)
Dalton’s Law
The total pressure (%IMAGE_11%) of a mixture of gases equals the sum of partial pressures (%IMAGE_12%) of all the gases forming the mixture.
%IMAGE_13% Dalton’s Law
The partial pressure exerted by each component of the mixture depends on the number of moles of gas that it represents of the total number of moles (mole fraction %IMAGE_14%).
%IMAGE_15%
The partial pressure of each component can also be obtained using the general equation of ideal gas, whereas the volume occupied by each component is the total volume of the container.
Changes in State
%IMAGE_16% Boiling is a form of vaporization that occurs throughout the entire mass of fluid at a characteristic temperature (boiling temperature). Evaporation occurs at all temperatures and is located on the surface of the liquid.
When the vapor pressure of the liquid equals the external pressure, boiling occurs. Therefore, the boiling temperature depends on external pressure. If atmospheric pressure decreases, the boiling temperature also decreases.
%IMAGE_17% In a pure substance, while there is a change of state process, the temperature remains unchanged and is characteristic of that substance.
How to Solve a Problem:
1. The problems of amount of substance (mol, molecules, etc.):
– Relations between obtaining mol/g of substance/particle number, using the molecular mass and Avogadro’s number.
– Based on initial data, applying the above relations as conversion factors.
2. The gas problems:
– Derive the equation that must be applied:
%IMAGE_18% For the same amount of gas under different conditions: General Gas Law.
%IMAGE_19% For one of the variables n, p, T, or V knowing three of them: general equation.
%IMAGE_20% To obtain or use the density (d) or molecular mass (M): %IMAGE_21%
%IMAGE_22% For partial pressures in gas mixtures: %IMAGE_23%
– Replace the variables by their numeric value and solve the equation.
3. The problems of empirical and molecular formulas:
%IMAGE_24% From the data (e.g., percentage composition), see data for each element.
%IMAGE_25% Divide each amount by the atomic mass of an element. Thus we get the number of moles of each element.
%IMAGE_26% Divide each amount obtained from the smallest one. Thus we get the simplest relationship integers. This is the ratio of the compound that are tied.
%IMAGE_27% With the above relationship, write the empirical formula.
%IMAGE_28% Calculate the molecular mass of the compound, if not provided by the sentence.
%IMAGE_29% Divide the molecular mass of the mass of the empirical formula. Multiply the empirical formula for the value obtained, we get the molecular formula.
4. To relate the moles to mass (g), use the molecular mass. To relate the number of moles to particles, use Avogadro’s number.
5. In the gas problems, you should always use the absolute temperature (K) and choose the appropriate R:
%IMAGE_30%
6. To calculate the partial pressures exerted by the gas mixture, each component is considered to occupy the total volume (no volume exists partially).
7. If in calculating the empirical formula, subscripts are obtained that do not approach a whole number, all subscripts must be changed by multiplying by the appropriate integer.
Item 2
Classification of Matter:
Mixtures and Solutions
Pure Substances:
Pure substances are those of fixed composition and constant properties and characteristics (temperature changes of state, vapor pressure, electrical conductivity, etc.). They can be separated into simpler substances by physical processes. Pure substances are classified into elements and compounds.