Atomic Theory and Structure

The Atomic Theory

• Dalton's Atomic Theory (1803) states that elements are made of small particles called atoms.
• Atoms of a given element are identical in size, mass, and chemical properties, and are different from atoms of other elements.
• Compounds have atoms of >1 element, with the ratio of atoms being an integer or simple fraction.
• Chemical reactions involve the separation, combination, or rearrangement of atoms, not their creation or destruction.

The Structure of the Atom

• J.J. Thomson discovered the electron through the cathode ray tube experiment.
• Robert Millikan determined the charge and mass of an electron via the oil drop experiment.
• Electron charge: -1.6022 x 10^-19 C
• Electron mass: 9.1095 x 10^-28 g

Radioactivity

• Henri Becquerel, along with Marie and Pierre Curie, studied radioactivity.
• Radioactive substances decay and produce three types of rays.
• Alpha ($\alpha$) particles have a positive charge.
• Beta ($\beta$) particles have a negative charge.
• Gamma ($\gamma$) rays have no charge.

The Proton and the Nucleus

• J.J. Thomson proposed the "plum-pudding" model of the atom.
• Rutherford's experiment (1910) involved scattering alpha particles.
• Most alpha particles passed through undeflected, but some were deflected at large angles.
• The nuclear model states most of the atom is empty space.
• Most of the atom's mass is in the nucleus; a small region containing positively charged protons.

The Neutron

• James Chadwick discovered the neutron in 1932.
• Neutrons are electrically neutral particles found in the nucleus.
• A neutron's mass is slightly greater than a proton's mass.

Atomic Number, Mass Number and Isotopes

• Atomic number (Z) = number of protons in the nucleus of an element's atom.
• Mass number (A) = total number of protons and neutrons in an atom's nucleus.
• Isotopes are atoms with the same atomic number but different mass numbers.

Molecules and Ions

• A molecule is two or more atoms held together by chemical bonds.

Diatomic and Polyatomic Molecules

• Diatomic molecules contain only two atoms ($H_2$, $N_2$, $O_2$, $Br_2$, $HCl$, $CO$).
• Polyatomic molecules contain more than two atoms ($O_3$, $H_2O$, $NH_3$, $CH_4$).

Ion

• An ion is an atom or group of atoms with a net positive or negative charge.

Forming Cations and Anions

• Cations are ions with a positive charge, formed when an atom loses electrons (Na $\rightarrow$ $Na^+$ + $e^-$, Ca $\rightarrow$ $Ca^{2+}$ + $2e^-$, Al $\rightarrow$ $Al^{3+}$ + $3e^-$).
• Anions are ions with a negative charge, formed when an atom gains electrons (Cl + $e^-$ $\rightarrow$ $Cl^-$, O + $2e^-$ $\rightarrow$ $O^{2-}$, N + $3e^-$ $\rightarrow$ $N^{3-}$). Polyatomic ions include $OH^-$, $CN^-$, $NO_3^-$, $SO_4^{2-}$, $NH_4^+$.

Heat

• Heat is energy that flows between a system and its environment due to a temperature difference.

Units of Heat

• calorie (cal) is the heat needed to raise 1 gram of water from 14.5°C to 15.5°C.
• kilocalorie (kcal) is the heat needed to raise 1 kilogram of water from 14.5°C to 15.5°C.
• British thermal unit (BTU) is the heat needed to raise 1 pound of water from 63°F to 64°F.
• 1 cal = 4.186 J
• 1 kcal = 1000 cal = 4186 J
• 1 BTU = 252 cal = 1055 J

Specific Heat

• Specific heat (c) is the heat needed to change the temperature of a mass (m) of a substance by $\Delta T$: $Q = mc\Delta T$

Latent Heat

• Heat required to change the phase of a mass $m$ is $Q = mL$, where $L$ is latent heat.
• Latent heat of fusion ($L_f$) is the heat needed to change a solid to a liquid.
• Latent heat of vaporization ($L_v$) is the heat needed to change a liquid to a gas.

Work and Heat in Thermodynamic Processes

• Gas expansion from $V_i$ to $V_f$ has work done by the gas: $W = \int_{V_i}^{V_f} P dV$
• The work done is the area under the curve on a $P-V$ diagram.
• When pressure is constant, $W = P(V_f - V_i)$.

Thermodynamic Processes Types

• Adiabatic: No heat exchange (Q = 0).
• Isobaric: Constant pressure.
• Isovolumetric: Constant volume (W = 0).
• Isothermal: Constant temperature.

The First Law of Thermodynamics

• Change in internal energy $\Delta E_{\text{int}}$ of a system equals heat $Q$ added to the system minus work $W$ done by the system: $\Delta E_{\text{int}} = Q - W$

Applications of the First Law

• Cyclic processes return a system to its initial state; thus, $\Delta E_{\text{int}} = 0$, and $Q = W$.
• Free expansion is an adiabatic process where a gas expands into a vacuum, and $Q = 0$, $W = 0$, and $\Delta E_{\text{int}} = 0$.

Heat Transfer Methods

Conduction

• The rate of heat transfer: $P = kA \frac{T_H - T_C}{L}$, where k is thermal conductivity, A is area, L is thickness, $T_H$ is hot temperature, and $T_C$ is cold temperature

Convection

• Convection is heat transfer by the movement of a fluid.

Radiation

• The rate of heat transfer: $P = \sigma A e T^4$, where $\sigma$ is the Stefan-Boltzmann constant ($5.6696 \times 10^{-8} \mathrm{~W/m^2 \cdot K^4}$), A is surface area, e is emissivity, and T is temperature in Kelvin.

Second Law of Thermodynamics

Heat Engines

• Heat engines convert heat into work.
• Its thermal efficiency is: $e = \frac{W_{\text{net}}}{Q_H} = 1 - \frac{Q_C}{Q_H}$, where $W_{\text{net}}$ is net work, $Q_H$ is heat absorbed from the hot reservoir, and $Q_C$ is heat exhausted to the cold reservoir.

Refrigerators and Heat Pumps

• Refrigerators move heat from cold to hot.
• The coefficient of performance is $\mathrm{COP} = \frac{Q_C}{W} = \frac{Q_C}{Q_H - Q_C}$

Second Law Statements

• Kelvin-Planck statement declares it is impossible create a heat engine operating in a cycle, extracts heat, and performs equal work.
• Clausius statement declares it is impossible create a cyclical device transfers heat cold to hot without work.

Entropy

• Entropy is the measure of a system's disorder.
• Change in entropy $\Delta S$ during a reversible process is $\Delta S = \int_{i}^{f} \frac{dQ}{T}$.
• For a reversible isothermal process: $\Delta S = \frac{Q}{T}$.

Entropy and the Second Law

• The total entropy of an isolated system always increases ($ \Delta S_{\text{total}} \geq 0$).
• Entropy is related to the number of possible microscopic states of a system, described by $S = k_B \ln W$, where $k_B$ is the Boltzmann constant ($1.38 \times 10^{-23} \mathrm{~J/K}$) and W is the number of microscopic states.