Law of conservation of mass: matter can neither be created nor destroyed in a chemical reaction; the total mass of reactants equals the total mass of products. Law of definite proportions: a given chemical compound always contains the same elements combined in the same fixed proportion by mass, irrespective of its source or method of preparation.

Molar mass of CO2 = 12 + 2(16) = 44 g/mol. Number of moles = given mass / molar mass = 11 / 44 = 0.25 mol.

n = m / M

Number of molecules = 0.25 x 6.022 x 10^23 = 1.506 x 10^23 molecules. Each CO2 molecule has 3 atoms (1 C + 2 O), so number of atoms = 3 x 1.506 x 10^23 = 4.52 x 10^23 atoms.

N = n x N_A

One mole is the amount of a substance that contains as many elementary entities (atoms, molecules, ions) as there are atoms in exactly 12 g of carbon-12. This number of entities is Avogadro's number, N_A = 6.022 x 10^23 mol^-1.

1 mol = 6.022 x 10^23 particles

Divide each percentage by atomic mass: C = 24.27/12 = 2.02, H = 4.07/1 = 4.07, Cl = 71.65/35.5 = 2.02. Divide by the smallest (2.02): C = 1, H = 2, Cl = 1. Empirical formula = CH2Cl (empirical mass = 12 + 2 + 35.5 = 49.5). n = molar mass / empirical mass = 98.96/49.5 = 2. Molecular formula = C2H4Cl2.

n = molar mass / empirical formula mass

Molarity (M) is the number of moles of solute dissolved per litre of solution; unit mol/L (or M). Molality (m) is the number of moles of solute dissolved per kilogram of solvent; unit mol/kg (or m). Molality is independent of temperature since it uses mass, whereas molarity changes with temperature because volume changes.

M = n_solute / V(L); m = n_solute / mass_solvent(kg)

Molar mass of NaOH = 23 + 16 + 1 = 40 g/mol. Moles of NaOH = 5/40 = 0.125 mol. Volume = 450 mL = 0.450 L. Molarity = 0.125 / 0.450 = 0.278 M (approximately 0.28 M).

M = n / V(L)

Moles of H2 = 3/2 = 1.5 mol; moles of O2 = 29/32 = 0.906 mol. From the equation, 2 mol H2 need 1 mol O2. For 1.5 mol H2, O2 required = 0.75 mol, but 0.906 mol O2 is available, so O2 is in excess and H2 is the limiting reagent. Water formed = moles of H2 (since 2H2 -> 2H2O) = 1.5 mol = 1.5 x 18 = 27 g.

mass = moles x molar mass

Mole fraction of a component = number of moles of that component / total number of moles of all components in the solution; it is dimensionless and the sum of mole fractions equals 1. Mass percent of a component = (mass of the component / total mass of solution) x 100.

x_A = n_A / n_total; mass% = (mass component / total mass) x 100

1) The electron revolves around the nucleus only in certain fixed circular orbits of definite energy called stationary states, without radiating energy. 2) Angular momentum of the electron is quantised: mvr = nh/2pi, where n = 1, 2, 3... 3) Energy is emitted or absorbed only when an electron jumps from one orbit to another, and the energy difference equals hv (delta E = E2 - E1 = h v).

mvr = nh/2pi ; delta E = h v

Wavelength = 4000 Angstrom = 4000 x 10^-10 m = 4 x 10^-7 m. Energy E = hc/lambda = (6.626 x 10^-34 x 3 x 10^8) / (4 x 10^-7) = 1.988 x 10^-25 / 4 x 10^-7 = 4.97 x 10^-19 J.

E = hc / lambda

For a hydrogen atom, r_n = n^2 x r_1. For n = 3: r_3 = 3^2 x 0.529 = 9 x 0.529 = 4.761 Angstrom.

r_n = n^2 x r_1

It is impossible to determine simultaneously and with absolute accuracy both the position and the momentum (or velocity) of a microscopic particle such as an electron. The product of the uncertainties in position (delta x) and momentum (delta p) is at least of the order of h/4pi.

delta x . delta p >= h / 4pi

de Broglie wavelength lambda = h / (m v) = (6.626 x 10^-34) / (9.1 x 10^-31 x 2.05 x 10^7). Denominator = 1.866 x 10^-23. lambda = 3.55 x 10^-11 m = 0.355 Angstrom.

lambda = h / (m v)

1) Principal quantum number (n): gives the main energy level/shell and size of the orbital (n = 1, 2, 3...). 2) Azimuthal (angular momentum) quantum number (l): gives the subshell and shape of the orbital (l = 0 to n-1, i.e. s, p, d, f). 3) Magnetic quantum number (m_l): gives the orientation of the orbital in space (m_l = -l to +l). 4) Spin quantum number (m_s): gives the direction of electron spin (+1/2 or -1/2).

l = 0 to (n-1); m_l = -l ... +l

Cr (Z = 24): [Ar] 3d5 4s1 (not 3d4 4s2). Cu (Z = 29): [Ar] 3d10 4s1 (not 3d9 4s2). One 4s electron shifts to 3d because exactly half-filled (3d5) and completely filled (3d10) subshells have extra stability due to symmetrical distribution of electrons and greater exchange energy.

Wave number (nu bar) = R (1/n1^2 - 1/n2^2) = 1.097 x 10^7 (1/2^2 - 1/3^2) = 1.097 x 10^7 (1/4 - 1/9) = 1.097 x 10^7 x (5/36) = 1.523 x 10^6 m^-1. This is the H-alpha line of the Balmer series.

nu bar = R (1/n1^2 - 1/n2^2)

Pauli's exclusion principle: no two electrons in an atom can have the same set of all four quantum numbers; an orbital can hold at most two electrons with opposite spins. Hund's rule of maximum multiplicity: electron pairing in orbitals of the same subshell (degenerate orbitals) does not occur until each orbital is singly occupied, and all singly filled orbitals have parallel spin.

Aufbau principle: in the ground state of an atom, electrons are filled into orbitals in order of increasing energy, i.e. the lowest energy orbital is filled first. (n + l) rule: the orbital with the lower (n + l) value has lower energy and is filled first; if two orbitals have the same (n + l) value, the one with the lower n is filled first (e.g. 4s (n+l=4) is filled before 3d (n+l=5)).

energy order by increasing (n + l)

Modern periodic law: the physical and chemical properties of elements are a periodic function of their atomic numbers. Mendeleev's law was based on atomic mass, whereas the modern law is based on atomic number (number of protons), which removed anomalies such as the position of argon and potassium.