General Chemistry

Hello! This blog will cover what my college calls principles of general chemistry. It will cover 1. Equilibrium, 2. Thermodynamics, 3. Kinetics, and 4. Quantum Chem. I will make list of tags soon so everyone can go back and forth between things. Hope you...

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Third Law of Thermodynamics

The third law of thermodynamics states that S = 0 at 0 K. This means that at 0 K, the coldest possible temperature (the temperature of 0 molecular movement), molecules have no entropy. Interestingly, by transitive property, this also means that at 0 K all substances are perfect crystalline structures! I’ll be real though, the third law is definitely the least useful for study of thermo.

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Second Law of Thermodynamics

The second law of thermodynamics, also called the entropy principle, states that in a closed system, the change in entropy for any reaction will be greater than or equal to 0. Entropy, abbreviated S, is a measure of the amount of disorder in a system. What this means is that all reactions either tend toward disorder or cause disorder in their thermal reservoirs. Some rules for S:

1) State function

2) Units of energy/temperature, usually Joules/Kelvin

3) Extensive

4) Change in S_wt. is always 0, so that means a rising level of order in a reactive system will necessarily lead to a rise in disorder in the thermal reservoir.

5) Change in S_theta = (change in energy of theta) / Temperature

The consequences of the second law are huge. The second law means that no machine can ever be 100% efficient, it means that the conversion of thermal to mechanical energy is less efficient than conversion of mechanical to thermal energy.

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Bond dissociation enthalpies

The inverse of enthalpies of formation, bond dissociation enthalpy DH is defined as the average energy it takes to break 1 mol of bonds in a given substance. Change in H can be calculated via DH in the same way by reversing the reactant and product sides. 

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Enthalpies of formation

Hess’s Law states that energy change for a chemical reaction equals the sum of energy changes for the set of reactions that equal the overall reaction. From this, we get an important equation:

change in H = sum of Hf*n_p - sum of Hf*n_r

Where n_p is the stoichiometric coefficient of each product and n_r is the same for reactants, and Hf is the enthalpy of formation, a constant for each substance that is equal to the enthalpy change in the reaction that creates it. From this definition we get two rules for Hf:

1) Hf=0 for elements in their most stable state (for example, while O [elemental oxygen] has an Hf > 0, O_2 has an Hf=0)

2) Hf for a compound is the enthalpy change for the reaction in which 1 mol of the compound is made from the stable state elements that make it up

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Enthalpy

Enthalpy is defined as the sum of the change in energy in the reactive system and the change in pressure on the reactive system. Thus, it also defined as the negative of the change in energy in the thermal reservoir. Enthalpy, importantly, is just a function. It has no qualitative definition beyond its mathematical one. Enthalpy is commonly abbreviated H. Features of enthalpy: 

1) H is an energy function

2) H is a state function (not dependent on path)

3) H is extensive (scales with size of system)

4) H takes into account wt., so that doesn’t need to be tracked

5) For processes NOT involving gases, change in H is effectively equal to change in energy in sigma.

6) Change in H is negative in exothermic reactions and positive in endothermic reactions. 

7) The sign of change in H is the same as the sign of change in sigma (i.e. if one is negative so will the other one be, etc.)

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First Law of Thermodynamics

The first law of thermodynamics, also called the energy principle, states that change in sigma + change in theta + change in wt. is always equal to 0. This is also called the law of conservation of energy, and it is never violated. This allows us to track energy movement. Looking at each part:

change in theta = m*c*T, where m is mass, c is specific heat (a constant for each material reflecting how much energy it takes to change the material’s temperature by 1 K), and T is change in temperature 

change in wt. = m*g*h, where m is mass, g is the gravitational constant (9.89 on earth) and h is change in height

NOTE that the first law can be applied to basically anything that happens, if there is no chemical reaction going on then sigma = 0 and you proceed. For example, if a 3g penny falls 25 cm into a 100 mL beaker of water (c = 4.18 J/K for water), the temperature of the water will rise by 1.8 x 10^-5 K. Of course, conversions from mechanical to thermal energy are often small, but the principle remains.

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Thermodynamic systems

Thermodynamics is the science of energy transfer. It is based around 3 laws which govern a specific view of chemical reactions, a view called the prototypical system. The prototypical system is composed of three parts:

sigma (can’t do greek letters), the reactive system, which is where the actual chemistry happens

theta, the thermal reservoir, which exchanges thermal energy with sigma

wt., the weight system, which exchanges mechanical energy with sigma, usually via volume changes. In open systems, wt. is the atmosphere

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End of Equilibrium Unit!

That was part 1/4, Thermodynamics coming up next, send me q’s if you have any!

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Polyprotic Acids and Bases

Some acids and bases dissociate by a more complex mechanism (see kinetics unit for explanation of mechanisms). Certain molecules have more than 1 acidic proton. Take, for example, Phosphoric Acid, H_3PO_4, where all 3 hydrogens may be donated. HOWEVER each additional proton is able to create less H_3O+ than the last. Polyprotic acids, as these are called, follow the following formula (though numbers may differ):

1) H_3A + H_2O --> H_2A- + H_3O+

2) H_2A- + H_2O --> HA^-2 + H_3O+, where K_a1 > K_a2

3) HA^2- + H_2O --> A^3- + H_3O+, where K_a1 > K_a2 > K_a3

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Interactions between strong and weak acids and bases

We define a strong acid as one that completely dissociates in solution, such that if we take a strong acid like Hydrochloric (HCl), we can assume that 0.1 M HCl means 0.1 M H_3O+. Weak acids are ones where this is not true, but there is a scale of weak acids, some dissociating more than others. The same can be said for strong and weak bases, replacing H_3O+ with OH-. The extent to which a weak acid or base dissociates is dependent on its equilibrium. For example, take acetic acid, a weak acid HOAc with K_a = 1.8 x 10^-5 M that produces conjugate base OAc-:

K_a = ([OAc-][H_3O+])/[HOAc] = 1.8 x 10^-5

We also know from stoichiometry that there is a 1 to 1 correlation between these species. From that we can determine that [H_3O+] = 1.34 x 10^-3 M. This gives us pH = 2.87 and that 1.34% of Acetic acid molecules have dissociated.

Acid - base combinations

1) Strong + strong: Because strong acids and bases dissociate completely, combining them is simply the inverse of the auto-protolysis of water, and thus K_eq = 1/K_w

2) Strong acid + weak base: follow the general equation 

H_3O+ (aq) + A- (aq) --> HA + H_2O, where K_eq = 1/K_a

Similarly, strong base + weak acid follows the equation

OH- (aq) + HA --> A- + H_2O, where K_eq = 1/K_b

3) Weak acid + weak base: No reaction

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Acids and Bases

Acids and bases are one of the most important classes of chemicals in terms of talking about equilibrium. There are several definitions that differ only slightly, but for the purposes of this course we will define them by the Bronsted-Lowry Definition: an acid is a proton donor, a base is a proton acceptor. Note that an H+ ion is a proton, the words will be used interchangeably (since if you take the electron off a hydrogen atom you are left with a proton). SO some properties of acids, bases, and acid base reactions:

1) The general form of an acid reaction is 

HA (aq) + H_2O (l) --> H_3O+ (aq) + A- (aq)

Where HA is the formula for the acid (all acids have at least 1 hydrogen, as they must donate it to be an acid), H_3O+ is Hydronium, and A- is the acid’s conjugate base, a specific base which will be present in some concentration after an acid dissociation reaction has reached equilibrium. Acids definitionally produce Hydronium.

Acid equilibriums can be described by the constant K_a, or the acid dissociation constant, defined as 

K_a = ([H_3O+][A-])/[HA]

2) The general form of a base reaction (or alkaline reaction) is

A- (aq) + H_2O (l) --> HA (aq) + OH- (aq)

Where A- is the base, HA is the conjugate acid, and OH- is Hydroxide. In the same way that acids definitionally produce Hydronium, bases definitionally produce Hydroxide. The equilibrium described here can be defined by the base dissociation constant K_b, defined as 

K_b = ([HA][OH-])/[A-]

3) Auto-protolysis of water: in neutral water, the random molecular interactions that occur in any liquid sometimes cause water molecules to exchange protons. The reaction

2H_2O (l) --> H_3O+ (aq) + OH- (aq)

Occurs in neutral water with an equilibrium K_w = 10^-14 M @ room temperature. This provides the general equilibrium statement for acid-base relationships, since

[H_3O+]*[OH-] = K_w and thus in neutral H_2O [H_3O+] = [OH-] = 10^-7 M

This gives us the basis for the pH scale, which is how we judge the strength of an acidic or basic solution. The p function is defined as 

p(x) = - log_10 (x) and pH is defined as p (H_3O+) thus pH = -log_10 (H_3O+)

Because from auto-protolysis pH + pOH = 14, we get the scale you may be familiar with from high school chem, wherein pH > 7 is alkaline and pH < 7 is acidic. 

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Solubility

Solubility, the ability of a species do dissolve in a liquid or aqueous solution, is quantifiable by equilibriums. Dissolution is a chemical reaction with the general formula

Solid (c) --> cation (aq) + anion (aq)

Taking the equilibrium expression of this gives us

K = ([cation][anion]) since pure solids are not involved in equilibria

Here we use K_sp, called the solubility product constant, instead of the equilibrium constant K_eq, but otherwise it is the same concept. If Q < K_sp, the solid will dissolve. If Q > K_sp, the solid either does not dissolve, or, if it previously already had, it precipitates out. If Q = K_sp, the solution is saturated, which is a kind of equilibrium wherein the maximum amount of solute has been dissolved in the solvent. 

Common Ion Effect

Using equilibriums to chart solubilities explains a phenomenon called the common ion effect, wherein a solution already containing one ion that the solid will dissociate into causes the solid’s solubitity product constant to lower. For example, if you dissolve table salt (NaCl), it dissociates into Cl- and Na+. If you dissolve it in a chloride solution, as in water that already has Cl- ions in it, you will be able to dissolve less salt. 

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LeChatelier’s Principle

LeChatelier’s principle states qualitatively that when a system at equilibrium experiences an environmental stress that pushes it away from equilibrium, the reaction will shift in a way that partially offsets that stress. From a quantitative perspective, this means that if you chart concentrations of reactants vs. products, the system will take the shortest path back to the equilibrium line. Some notes on stresses:

1) Pressure stress: raising the pressure on a system causes the reaction to favor the side with FEWER moles of gas

2) Volume stress: diluting a system causes the reaction to favor the side with more moles of species. 

3) Thermal stress: understanding this requires a brief definition. As you probably know from Chem 101, an endothermic reaction is one that creates heat, an exothermic reaction uses heat from its surroundings, thus leaving them colder. We will use this definition again in the thermo unit, but for now we must redefine these terms as they relate to equilibrium: an endothermic reaction is one where as temperature increases, so does K_eq. An exothermic reaction is one where as temperature increases, K_eq decreases. Thus, raising temperature causes endothermic reactions to shift right and exothermic reactions to shift left.

Side fact, this is why you can dissolve more things in hot water than cold!

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Quantifying equilibrium

A simple equation exists to quantify equilibrium called the Law of Mass Action. It states that for the reaction 

aA + bB --> cC + dD

the equilibrium can be quantified as 

K_eq = ([C^c][D^d])/([A^a][B^b])

Where [x] is the concentration of the species in aqueous solution or the partial pressure of the species if it is a gas. NOTE that pure solids and liquids are not counted in equilibrium expressions. 

The same expression, but replacing K_eq with the reaction quotient Q, is a way to determine how close to equilibrium a reaction is. If Q<K, the reaction shifts to the right (creates more products), if Q>K, the reaction shifts to the left (creates more reactants). 

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Equilibrium definition and rules

Equilibrium in chemistry is a concept applied to all reactions. Every reaction is dynamic, meaning that equations, like this possibly familiar one

6CO_2 + 6H_2O --> C_6H_12O_6 + 6O_2

are actually not entirely accurate, since chemical reactions don’t simply go from reactants to products, but rather back and forth. So, in the above, carbon dioxide and water are not simply mixing to form glucose and oxygen, but rather in a system of carbon dioxide, water, glucose, and oxygen, the system reaches equilibrium with a high concentration of glucose and oxygen and a low concentration of carbon dioxide and water. Thus, in a reaction between multiple species, we can define equilibrium as based on the concentrations of each species when the reaction has reached a point where the NET change in concentrations is 0. So, for example, if you took the reaction 

H_2 + I_2 --> 2HI

and start with 1 mol of H_2 and 1 mol of I_2: Hydrogen and iodine are constantly mixing and matching and forming Hydrogen Iodide, which is constantly breaking apart into Hydrogen and Iodine again. Equilibrium is the point at which you have 0.22 mol H_2, 0.22 mol I_2, and 1.56 mol HI, and at this point ALL THAT MIXING AND MATCHING IS STILL GOING ON but the NET change is 0, so if you look at the concentrations at any random point they may be different from the above, but over any length of time the average concentrations will be what you see above. 

SO, thats the definition, now some rules about equilibrium

1) It is not static, but dynamic (kind of a restatement of above). 2) It is a state function, which means it is independent of path, meaning that how a reaction gets to equilibrium has no effect on its equilibrium state. 3) It is independent of scale. So in the above reaction, if you had 2 mol of H_2 and 2 mol of I_2 to start, you would end with 0.44 mol H_2, 0.44 mol I_2, and 3.12 mol HI; the ratios are the same. 4) Equilibrium is dependent on temperature and pressure. 5) time to equilibrium varies based on the reaction.

[babewegotchemistry]

List of Topics

Hey all! So this is gonna get updated a whole lot in the next 2-3 weeks as I prepare for finals, so heres whats gonna be explained, each unit tagged with its title so you can find it easier

1. Equilibrium

2. Thermodynamics

3. Kinetics

4. Quantum chem

The tags won’t all be active for a few days but heres the master post, i’ll tag all of them below and ill repost this from time to time. Enjoy!