Heat Capacity

Heat Capacity
When a substance is heated, its change in temperature(∆T) is proportional to the quantity of heat energy it absorbs(q), thus:

q/∆T = constant

The value of this constant is different for each substance and is called that substance's 'heat capacity'.

Specific Heat Capacity
The specific heat capacity(c) of a substance is the amount of heat energy required to raise 1 gram of that substance by 1 degree kelvin.

c = q/(mass * ∆T)

Molar Heat Capacity
The molar heat capacity(C) of a substance is the amount of heat energy required to raise the temperature of 1 mole of that substance by 1 degree kelvin.

C = q/(moles * ∆T)

Units
Heat energy is in joules, temperature is in degrees kelvin, and mass is in grams, thus c has units of J/(K*g) and C has units of J/(K*mol).

Enthalpy

(See Energy first.)

What is enthalpy?
Enthalpy(H), or 'heat content,' is a variable that describes the thermodynamic potential(hence 'heat content') of a system.
The enthalpy of a system is defined as its internal energy plus the product of the pressure on it(P) and its volume(V).

H = E + PV

How is it used?
In many reactions the only type of work done is that of a newly formed gas expanding and pushing back the atmosphere. This is called PV work, and is equal to the product of the pressure of the atmosphere and the change in volume of the gas.

w = -P∆V

The value is negative because the gas(system) is doing work on, and thus losing energy to, the atmosphere(surroundings).

In reactions such as these, if the pressure is constant (as is most common) it is often more meaningful and convenient to examine the change in enthalpy of a system rather than the change in its internal energy. This is because by using enthalpy we can avoid having to consider PV (and thus all) work done by the system.
This is how:

H = E + PV

so at constant pressure

∆H = ∆E + P∆V

and since

∆E = q + w
&
w = -P∆V

we can see that

∆E = q - P∆V
& rearranging
q = ∆E + P∆V

so

∆H = q

As this is only true at constant pressure we write the above as

∆H = q_p

with _p effectively meaning 'at constant pressure'.

Thus to find the change in enthalpy of a system under these conditions, we only have to measure the heat transferred between the system and its surroundings.

Further
For reactions that involve little or no work, and thus where ∆E = q, knowing ∆H means knowing ∆E.

Energy

When we wish to observe a change in something we can describe that thing as a 'system'. Everything else relevant to our observations of that system is it's 'surroundings'.

-The internal energy(E) of a system is the sum of the potential and kinetic energies of all its particles.

When energy is transferred between a system and its surroundings it is always transferred in the form of work and/or heat.

-Heat(q) is the energy transferred between a system and its surroundings due to a difference in their temperatures.

-Work(w) is the energy transferred when a force moves an object.

A change in internal energy of a system will be equal to the energy transferred to/from its surroundings in the form of heat and/or work. This statement is described in the equation:

∆E = q+w

where ∆ = 'change in'.

q, w, and ∆E can have positive or negative values depending on whether the system is gaining or losing energy. (loss is -, gain is +)

The 'first law of thermodynamics' or the 'law of conservation of energy' states that the total amount of energy in the universe is constant, i.e. energy cannot be created or destroyed. Any change in the energy of a system is accompanied by an opposite change of equal magnitude in its surroundings, thus there is no net gain or loss of energy.

∆Euniverse = ∆Esystem + ∆Esurroundings = 0

Nuclear Charge

The nuclear charge, Z, of an atom's nucleus is the total charge of all the protons it contains (the same as its atomic number.) Lower orbital electrons can in effect "shield" higher orbital electrons from some of the positive charge of the nucleus, changing the Z that higher orbital electrons 'perceive'. Effective nuclear charge, Z_eff, is the net positive charge of the nucleus as perceived by an electron.

Periodic Table

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See also:
Periodic Table Trends