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Basic Chemistry applications

 

 

Error analysis is the study and evaluation of uncertainty in a scientific measurement. Experimental error is the inevitable uncertainty that is present in all measurements.

Significant figures:
Experimental errors should always be rounded to one significant figure.
The last significant figure in any answer should be of the same order of magnitude as the uncertainty. Lastly, in the absence of a specified absolute error, the error is assumed to be plus or minus 1 in the last digit.

Accuracy is the closeness of a result to the true value, and precision is the closeness of a set of results to each other. In other words it is the reproducibility of a certain result at more than 1 data point.

Random error comes from random circumstances such as thermal vibrations. Repeating the experiment can get rid of random error. Systematic error comes from flaws in design construction, calibration, operation, or interpretation of an experiment. Thus random error has to do with precision, and systematic error has to do with accuracy. Some examples of random error also include small errors in judgment by the experimenter. Examples of systematic error include instruments that are uncalibrated and procedural errors.

Error propagation is a way to see how the errors in 2 or more quantities propogate to cause further uncertainty in calculations.

When you add two quantities, the error in the sum is the sum of the absolute errors of the two components. When you multiply or divide, the relative error of the product or quotient is given by the sum of the individual relative errors.

Beer’s law: The amount of light absorbed by a colored solution is proportional to the concentration of the absorbing molecules. In graphic form, absorbance vs concentration will yield a linear slope for a fixed wavelength.

Molarity is moles solute divided by the volume of the solution. Molality is moles solute divided by the kg of solvent.  Weight percent is mass solute divided by mass solution x 100. Parts per hundred for weight percent means mass solute x100 divided by 100 grams solution. Volume percent is similar in that it is volume of solute divided by volume of solution times a hundred. Volume percent parts per 100 is simply volume solute x100 divided 100 ml of solution. Weight volume percent is mass solute divided by 100 ml solution x100%. Parts per million is mass solute in grams divided by the 10^6 grams solution. Parts per billion is the mass of solute in grams divided by 10^9 grams of solution.

Absorbance can be calculated by multiplying molar absorptivity times path length (in cm) times concentration, or by invoking the proportionality method: C1/C2 = A1/A2.

Acids and Bases:
Arrhenius definition – An acid is a substance that forms H+ ions in an aqueous solution. Water is necessary as the solvent in this case. An Arrhenius base is a substance that forms OH- ions in an aqueous solution. Again water is the solvent.

Bronsted-Lowry definition: An acid is a substance that donates protons (H+) to another polar substance. A base is a substance that accepts protons (H+) from another polar substance. Bronsted Lowry also predicts the presence of conjugate acids and bases. Each acid has a conjugate base, and each base has a conjugate acid.

Lewis definition: An acid is an electron pair accepter, and a base is an electron pair donator.

The ions of a strong acid completely dissociate, while the ions of a weak acid only partially dissociate.

The strength of an acid or base is given by the pH scale. pH = -log (concentration of H+).
Strong acids have low pH values, while strong bases have high pH values. pOH is defined as 14-pH. When doing pH calculations, the significant figures (sig figs) are only considered significant if they occur AFTER the decimal point. For example, 5.18 has 2 sig figs. The reason is due to the logarithm function. If the concentration of H+ has 2 sig figs, then the pH should have 2 digits in the decimal place.

Equivalents is the quantity of acid that yields 1 mol of H+ or the quantity of base that reacts with 1 mol H+.

When equivalent amounts react the following holds: NaVa=NbVb. Under these conditions, equivalents of acid = equivalents of base. This point is called the equivalence point since the equivalents of acid are the same as the equivalents of base. The equivalence point can be approximated by the end point, which shows a rapid pH change, or a color change due to the indicator.

Percent difference = absolute value of measured – actual, divided by actual, times 100.

Extensive depends on the amount present in a system, whereas intrinsic is independent to the size of a system.

Sodium tripolyphosphate, or STPP enhances the performance of the detergent by controlling the pH, and essentially it softens the water.

Rate laws can be determined by the stoichiometry of elementary reactions, but the overall rate reaction cannot be determined by the stoichiometry. The rate determining step is the elementary step that controls the overall rate of the reaction. The rate determining step is also the slowest step.

Vapor Pressure is the partial pressure of a vapor exerted over a liquid (measured at equilibrium). At equilibrium, the rate of molecules that leave the liquid state equals the rate of molecules that enter condense.

A volatile substance has a higher tendency to vaporize, where as a nonvolatile substance is less likely to vaporize.

Soaps and detergent are not the same thing despite being used for similar purposes. Hard water comes about from water with calcium and magnesium ions. Soft water lacks these calcium and magnesium ions. Most of detergent is sodium tripolyphosphate, or STPP. The phosphates in detergent also have negative environmental effects, such as eutrophication of lakes. The phosphate was wastewater (after washing) causes excessive growth of algae, which when dead, sink to the bottom and eat up oxygen. Thus there is a lack of oxygen for other fish and marine animals, which leads to death of marine life.
An acid is strong if it loses protons (H+) easily. Some examples of strong acids include HCl, HI, and HBr. Notice that the second ionic component is a halogen, from group VII. Strong acids have a large Ka value, which means that the position of equilibrium lies to the right. Also almost all the strong acid is ionized. On the other hand, all weak acids have very small Ka values, which means they do not ionize completely. While other halogens make strong acids, HF is not a strong acid, but a weak acid. Also interesting to note is that the conjugate acid of a strong base is a weak acid, and the conjugate base of strong acid is a weak base.  

Strong bases usually have hydroxide (OH). Some examples include LiOH, NaOH, KOH, RbOH, CsOH, and FrOH. Note that all of these are in group 1 combined with hydroxide. For group 2 strong bases include BE(OH)2, Mg(OH)2, Ca(OH)2, Sr(OH)2, Ba(OH)2, and Ra(OH)2. Elements such as bond polarity, anion stability, and bond strength also influence the strength of an acid or base. As for that conjugate base stability, the more resonance structures an acid has, the stronger the acid.

pH = -log([H+])
pH is only neutral when the concentration of H+ is equal to the concentration of hydroxide (OH-). pH =7 is only neutral when the temperature is 25 degrees Celsius. A solution can be neutral at pH values OTHER than 7.

When a common ion is added in a reaction, the equilibrium base concentration diminishes.

A buffer resists changes in pH if acid or base is added to a solution. It works if a solution contains a weak acid and its conjugate acid, or a weak base and its conjugate acid. If a solution has a weak acid and conjugate base, then if a base is added, the undissociated weak acid reacts with the added base. If an acid is added, then the conjugate base reacts with the added acid.  

A liquid can be boiled if the ambient pressure (in most cases the atmospheric pressure) is less than or equal to the vapor pressure. In other words when the vapor pressure is greater than the ambient pressure, a material will boil. At high altitudes, where the ambient pressure is lower than at sea level, the boiling point will occur at lower temperatures.

Two colligative properties are boiling point elevation and freezing point depression. These depend upon how well the solute in a solution lowers the vapor pressure.
The very presence of a solute in a solution raises the boiling point, because the solute also lowers the vapor pressure, which means a higher temperature is needed in order for boiling to occur. The key is that the solute lowers the vapor pressure of a solution.

Osmosis is the flow of solvent through a semi permeable membrane. The solute tends to block the passing through of solute. The solvent thus moves from lower to higher solute. This translates into the solvent always moving from dilute areas to more concentrated areas.

Osmotic pressure is defined as the product of molarity, ideal gas constant, and temperature.

The total energy in the universe is constant. Energy is always conserved, but it changes forms. For example, the kinetic energy of a car can change forms to thermal energy due to friction, or potential energy when the car is at an altitude relative to a reference point. Total energy is always conserved.

Thermodynamics is the study of heat and energy. Mostly it is concerned with macroscopic chemistry. Thermodynamics kicked off during the industrial revolution when a better understanding of heat and work were needed for increased efficiency and innovation. Thus heat and work were studied, and shown to be equivalent. James Joule in particular showed that work could be performed by a falling weight on a pulley, which would in turn heat up a solution by increasing its temperature.

More info on exergy, energy, and efficiency can be found here.

It is common knowledge that heat flows from hot to cold, but this only occurs until a thermal equilibrium is reached.

A system and its surroundings are together called the universe. Also important are intensive and extensive properties. The former involve properties that are independent of the quantity. Examples include temperature, pressure, and density. Extensive properties are dependent on the quantity present, and include moles, number of particles, volume, work, energy, and mass.

A state function depends only on the current state, whereas a path function DOES depend on that path taken. Path functions include heat and work, which depend on the paths.

The first law of thermodynamics: The change in internal energy is equal to the addition of heat and work. Essentially this translates to energy neither being created nor destroyed. In more general terms, the total energy of the universe is conserved, but energy can change forms.

Work and heat have sign conventions that have changed in recent years. If work is done ON a system, the work is positive. If the system performs work on the surroundings, then the work is negative. Conversely, heat added from the surroundings to the system is positive, whereas heat removed from the system TO the surroundings is negative.

If the change in temperature is 0, also known as isothermal, then the change in internal energy is also 0 due to E=3/2 RT. The first law of thermodynamics tells us that the change in internal energy is equal to q + W, but if change in internal energy is 0, then q=-W OR W=-q. The former means that the work a system does on the surroundings is equal to the heat provided by the surroundings. The converse is also true, if q=-W, then there is no change in temperature.

A reversible change is made if it is gradual. If the change is not gradual, then some work is lost, and the change is called irreversible.
Entropy is defined to be a state function, with the change in entropy equal to reversible heat divided by temperature in Kelvin.

Enthalpy is a state function. The change in enthalpy equals the change in internal energy plus pressure times change in volume. Also change in enthalpy can be shown to be heat at a constant pressure.

The change in enthalpy for any standard state element is zero.

Hess’s Law states that the enthalpy change for any reaction is equal to the sum of all individual product enthalpy changes minus the sum of all individual reactant enthalpy changes.

Spontaneous processes happen in the direction which has the maximum number of microstates (probabilities). High entropy also refers to a maximum number of microstates. Thus spontaneous processes are linked with larger entropies.

As time progresses the most random (highest entropy) arrangement is favored. This refutes common sense, since why would solids even exist? The answer lies in the minimization of energy through bonding forces in conjunction with a maximization of entropy.

Entropy is an extensive property.

Second law of thermodynamics – Entropy is constantly increasing until a maximum is reached at equilibrium. Equilibrium means the rate of forward reaction and backward reaction are equal, and that the concentrations are constant.

Spontaneous changes are only possible if the entropy of the system and surroundings are increasing.

Gibbs free energy is a state function. The change in Gibbs free energy is given by the change in enthalpy minus the product of temperature and change in entropy. If change in Gibbs free energy is negative, then the reaction is spontaneous.

The change in Gibb’s free energy for a system is also intertwined to the change in entropy in the universe. Consequently, if the entropy increases, then the change in gibbs free energy must decrease.

Unlike Gibb’s free energy or Enthalpy, entropy can be measured on an absolute scale as predicted by the 3rd law of thermodynamics: A perfectly ordered crystal at 0 Kelvin has absolute entropy of 0.

Kinetics: Orders cannot be determined by stoichiometry, rather they must be determined by experimentation.

Frequency factor is called Z, and involves the frequency of collisions. The steric factor is called P, and refers to the percent of molecules that have the correct orientation. The preexponential term in the Arrhenius equation is then equal to the product of Z and P.

Every elementary step has a rate equation that can be determined by the stoichiometry coefficients. Elementary steps can be classified as unimolecular, bimolecular, or termolecular. The list goes on, but termolecular rarely occurs. If there is just one reactant, the elementary reaction is termed unimolecular. If there are two reactants, the equation is termed bimolecular, and if there are three reactants, the reaction is termed termolecular.

The rate determining step is the slow step, and any molecule that does not come out in the overall reaction equation is called a reaction intermediate.

Catalysts increase the rate of reaction, ie make the reaction proceed faster. More specifically, catalysts have an effect on the preexponential and the activation energy in the Arrhenius equation.

 

A catalyst offers an additional pathway for a reaction to occur.  

 

          

2006 Philosophy Paradise