Archive for April 2002

Determining the Percentage of Acetic Acid in Vinegar by Titration

April 17, 2002

I. Purpose
The purpose of this lab was to determine the percentage of acetic acid in vinegar by titration. We did this by adding sodium hydroxide to the vinegar until the acetic acid was neutralized and using an indicator to show this end point. We measured the amount of vinegar and sodium hydroxide used and converted the moles of sodium hydroxide used to moles of acetic acid. Then we divided the mass of acetic acid by the mass of vinegar to obtain the mass percentage of acetic acid.

II. Procedure
1. Fill one Beral pipet with vinegar and another with standardized NaOH. Weigh and record the mass of each.
2. Add 5 drops of vinegar solution to one well of a 24 well reaction plate or very small flask or beaker. Reweigh the vinegar pipet and record its new mass.
3. Add one drop of phenolphthalein to the well.
4. Add drops of NaOH solution to the well until one changes the vinegar solution to a pink color that does not disappear when mixed.
5. Reweigh the NaOH pipet and record its mass.
6. Repeat the procedure two more times. Carefully record the pipets’ mass before and after. If containers are reused, rinse out the previous titrants before each new procedure.

III. Observations
Adding phenolphthalein to vinegar produced no visible changes. Oftentimes, when NaOH was added, the solution turned pink; however, the color disappeared after the solution was stirred. Finally, a single drop of NaOH neutralized the acetic acid and permanently turned the solution pink.

IV. Equations and Chemical Formulas
Acid-Base Neutralization: NaOH + HC2H3O2 -> NaC2H3O2 + H2O
Mol = Volume * Molarity
Mol NaOH Used: Grams NaOH Used * Density NaOH * Molarity NaOH
Molarity of Vinegar: Moles HC2H3O2 / Liters of Vinegar Used
Mass of Vinegar Used: (Mass of Vinegar Pipet Before) – (Grams of Vinegar Pipet After)
Mass of NaOH Used: (Mass of NaOH Pipet Before) – (Mass of NaOH Pipet After)
Mol HC2H3O2: Mol NaOH
Grams HC2H3O2: Mol HC2H3O2 * Molar Mass HC2H3O2
% HC2H3O2 in Vinegar: Mass of HC2H3O2 / Mass of Vinegar * 100
Density NaOH: 1 g/mL
Density Vinegar: 1 g/mL

V. Data and Calculations
Category Trial 1 Trial 2 Trial 3
Grams of Vinegar Pipet Before 3.77g 3.62g 3.45g
Grams of Vinegar Pipet After 3.61g 3.46g 3.32g
Grams of NaOH Pipet Before 3.92g 3.22g 3.72g
Grams of NaOH Pipet After 2.54g 1.94g 2.56g

Category Trial 1 Trial 2 Trial 3
Grams of Vinegar Used 0.16g
(3.77g – 3.61g) 0.16g
(3.62g – 3.46g) 0.13g
(3.45g – 3.32g)
Volume of Vinegar Used 0.00016L
(0.16g * 1g/mL * 1L/1000mL 0.00016L
(0.16g * 1g/mL * 1L/1000mL) 0.00013L
(0.13g * 1g/mL * 1L/1000mL)
Grams of NaOH Used 1.38g
(3.92g – 2.54g) 1.28g
(3.22g – 1.94g) 1.16g
(3.72g – 2.56g)
Mol NaOH Used 0.000138 mol
(1.38g * 1g/mL * 1L/1000mL * 1mol/10L) 0.000128 mol
(1.28g * 1g/mL * 1L/1000mL * 1mol/10L) 0.000116 mol
(1.16g * 1g/mL * 1L/1000mL * 1mol/10L)
Mol HC2H3O2 0.000138 mol
1 mol HC2H3O2
1 mol NaOH 0.000128 mol
1 mol HC2H3O2
1 mol NaOH 0.000116 mol
1 mol HC2H3O2
1 mol NaOH
Grams HC2H3O2 0.00828g
(0.000138 mol * 60g/mol) 0.00768g
(0.000128 mol * 60g/mol) 0.00696g
(0.000116 mol * 60g/mol)
% HC2H3O2 in Vinegar 5.18%
(0.00828g HC2H3O2 / 0.16g Vinegar) 5.35%
(0.00768g HC2H3O2 / 0.13g Vinegar) 5.17%
(0.00696g HC2H3O2 / 0.15g Vinegar)
Average % HC2H3O2 in Vinegar 5.2%
5.18% + 5.35% + 5.17%
Molarity of Vinegar 0.86M
(0.000138 mol HC2H3O2 / 0.00016L vinegar used) 0.8M
(0.000128 mol HC2H3O2 / 0.00016L vinegar used) 0.89M
(0.000116 mol HC2H3O2 / 0.00013L vinegar used)
Average Molarity of Vinegar 0.85M
0.86M + 008M + 0.89 M

VI. Summary
The purpose of this experiment was to find the percentage of acetic acid in vinegar by titration. We titrated acetic acid and sodium hydroxide, using phenolphthalein as a catalyst, and determined the amount to be 5.1%.
This experiment was very simple and easy to perform, but since the measurements had to be so precise and the endpoint of the solution could be reached at any time, the experiment required the utmost precision. If our accuracy is ruined, the fault is mine because I added the drops of sodium hydroxide drops to the vinegar. Though I do not know the accuracy of our experiment, I believe that we were successful. We worked together and achieved our desired result. What more could be asked of three smashing young chemists?


April 16, 2002

Acoustics is the study of the creation, transmission, and reception of sound.  The word acoustics also refers to the quality of sound as heard or transmitted in a room or concert hall.  Conic sections are often used in acoustics to amplify sound.

Vibrating objects produce sound.  As the object moves outward, it compresses the surrounding medium; the region of compression is called a condensation.  As the object then moves inward, the medium expands into the space previously occupied by the object.  This region is called a rarefaction.  As the object continues to move outward and inward, a series of condensations and rarefactions leave the object.  These series are sound waves.  Sound waves move outward from the object in all directions.

When sound waves in one medium strike a large object of another medium, some of the sound usually reflects off the new medium’s surface, and some refracts into the new medium.  The speed of sound in the new medium helps determine the amount of reflection off new medium’s surface.  When sound refracts, its speed and direction change.  If sound waves travel slower in the second medium, the waves refract towards the “normal,” an imaginary line perpendicular to the boundary between mediums.  If sound travels faster in the second medium, the waves will refract away from the normal.

Sound waves bend toward a region of slower speed.  For example, sound carries farther at night than during a sunny day because sound favors cooler temperatures.  During the day, air near the ground is warmer than the air above, so sound refracts away from it.  At night, air near the ground is cooler than the air above, so the sound bends toward it and travels across it for a greater distance.

Acoustics is most often used in the reflection and refraction of sound.  Acoustics is used for ultrasound and monitoring earthquakes.  Federally supported research on long-range underwater communication in World War II led to sonar and ultrasound techniques.  With sonar, ships “see” other vessels, map the ocean floor, identify mines, and isolate spots for oil drilling with acoustics.  Ultrasound is used to monitor pregnancies, image the inside of the body, stop internal bleeding, and destroy kidney stones.

Architectural acoustics involve making rooms and buildings quiet and providing good conditions for listening to speech and music.  It is an important part of the planning and construction of auditoriums, churches, halls, libraries, music rooms, and so on.  Various factors affect the acoustical quality of a room, including the size and shape of the room, the ability of the ceiling, walls and floor to keep out unwanted sound, and furnishings made of sound-absorbing materials, like carpets, drapes, and upholstered furniture.

Another factor is the room’s reflection of sound.  Sounds made by a speaker or musical instrument bounce back and forth against the surfaces of the room.  These reflections of sound make up its reverberation.  The reverberation time of a room is the time it takes for a sound to fade to one-millionth of its original energy.  Reverberations should last about one second in a speech auditorium and two seconds in a music hall.  If a strong reflection reaches a listener’s ear more than 1/20 of a second after the arrival of the direct sound, or else the listener will hear an echo.  Echoes should be avoided.

Acoustics have many other fields.  In sonochemistry, sound waves create high-energy bubbles in liquids.  When these bubbles heat and cool, they speed up chemical reactions for the creation of pharmaceuticals.  Defects in airplanes, bridges, and pipelines can be identified by sound waves.  Since sound waves can change pressure and temperature in gases, thermo-acoustic refrigerators can cool objects while being good to the environment.

Other areas of acoustics are environmental acoustics (controlling noise pollution), physiological acoustics (hearing sound), psychological acoustics (interpreting sound), musical acoustics (instruments and voices producing sound), and speech communication (producing and hearing speech).  Acoustics also encompasses sound waves we cannot hear, such as infrasound (too low) and ultrasound (too high.)  Sound waves within the earth and underwater are also outside human hearing and merit study.

Conic sections are often used in acoustics to amplify sound.  Orchestra shells, for example, have a parabolic shape.  A parabola is the set of all points equidistant from a fixed point and fixed line; it is shaped like a wave.  When a wave hits a parabola, it reflects towards the focus.  The orchestra’s sound reflects off the shell and back onto the audience.  This amplifies the orchestra’s sound.  The same principle is applied to enhance musical instruments.  String instruments are built with parabolas in their shape; when sound is made, it bounces off these parabolas and back into the focus, the sound post.

An ellipse, the set of all points equidistant from two fixed points (foci), is also key in acoustics.  When a line is drawn from the focus of an ellipse, it bounces off the side of the ellipse and touches the other focus.  This property is used in the lithiopter, a device that destroys kidney stones.  With this device, scientists fire shockwaves from one focus of an ellipse to destroy kidney stones at the other.

This property is also used in elliptical ceilings.  When sound is made at one focus of an ellipse, it bounces off the ceiling and reaches the other focus.  Thus, a person at one focus can even hear a whisper from the person at the other focus.  The most famous whisper gallery may be St. Paul’s Cathedral, built by the mathematician Sir Christopher Wren.

Some believe that Benjamin Franklin discovered this property at the Rotunda of the Capital Building, and he would stand at one focus to easily hear sound from the other focus, even in a crowded room.  Others credit John Quincy Adams.  While he was a member of the U. S. House of Representatives, he positioned his desk at one focus of the elliptical ceiling at the Capitol’s Statutory Hall and eavesdropped on private conversations of house members at the other focus.

The uses of acoustics are many, and conic sections are invariably important to them.  Research continues on how acoustics can be used to benefit humanity, and, as in the lithiopter, conic sections will be very important to the cause.  This “mathematical magic” can improve our lives for years to come.

Review of Thomas More’s “Utopia”

April 1, 2002

Few political science titles as more famous as Saint Sir Thomas More’s Utopia. Utopia, in the vein of Plato’s Republic, is a book about the ideal commonwealth. It is described by a fictitious explorer of this fictitious place named Raphael Hythloday. The book was very popular among humanists and is still read today, almost 500 years after its publication in 1516.

More’s Humanist Background
Thomas More was a prominent British humanist. His Latin teachers John Holt, William Grocyn, and John Colet, greatly influenced him when he was a student. He served as the Dean of St. Paul’s Cathedral and founded the first humanist grammar school in England. In 1499, he made the acquaintance of the Dutch humanist Erasmus.

He translated Greek poems and four short works by the Greek ironist Lucian, who is alluded to a few times in Utopia. More used Greek and Latin compounds to create several of the book’s names, including utopia (ou (not) + topos (place) = “no place”) and Hythloday (“expert in nonsense”). He also wrote a declamation of Lucian’s Tyrannicide, a large number of Latin epigrams, and an unfinished history of King Richard III (considered by some the main source of Shakespeare’s play) and translated a biography of the fifteenth century Italian philosopher Pico della Mirandola. With this record, it is easy to see why humanists looked forward to Utopia and wrote letters vouching for its publication.

Book I
Book I, actually written after Book II, introduces the narrator, Rafael Hythloday, and the characters of Thomas More and Peter Giles. These characters discuss the current state of England and whether a philosopher could do well in a King’s Council. While not addressing Utopia directly, the first book gives us a sharper sense of our source of information, Hythloday, and provides a sketch of England for comparison with Utopia.

The story opens with a brief account of Sir Thomas More’s trade mission to Flanders and his acquaintance with the classical scholar Peter Giles. The historical Giles was an intimate of Erasmus regarding practical affairs and was city clerk of Antwerp. As clerk of Antwerp, a major trade center, he was deeply involved with cosmopolitan shipping and commerce. The story switches from fact to fiction when Giles introduces More to Raphael Hythloday. Hythloday is a noted Portuguese sailor; he is brave and wise and served on three of Amerigo Vespucci’s voyages before becoming an explorer himself. Hythloday gives More and Giles clear, astute descriptions of the places he has visited.

More suggests that Hythloday join a king’s council in order to aid him with his vast stores of knowledge and wisdom. Hythloday refuses, saying that the king would only want to do things that strengthened his own self interest, rather than the kingdom’s, and the other council members would help the king find ways to be bad; hence, Hythloday’s voice would be quashed in the power struggle, so his efforts would be in vain. More then suggests Hythloday try to make the bad behavior of the rest of the court less bad; Hythloday dismisses this idea as absurd, a compromise of his principles, and altogether unwise. The debate ends there, probably because the author likely didn’t know the right course of action, either: he wrote this book when he had just been asked to join King Henry VIII’s council.

More then treats the problem of theft. Hythloday feels that the death penalty is useless in dealing with thieves, and as long as thieves are hungry, they will steal, regardless of consequences. He feels the cause of theft is the pride, sloth, and greed of the upper classes: by hoarding private property for themselves, hiring useless servants who are qualified to do nothing but steal when they are fired, and keeping standing armies whose soldiers rob when there is no war to fight, the rich make theft inevitable. Hythloday says he would rather use the societal system of the Polylerites (polus = “much”, leros = “nonsense”; ite = “the people of”: “the people of much nonsense”). They use thieves as slave workers and give restitution to the victimized party rather than the Crown. The possibility of revolt is neutralized by government rewards for snitching on conspiracies.

Hythloday says when he presented this idea to British noblemen, they soundly rejected it until Cardinal Morton supported him; afterward, they agreed with it wholeheartedly. Hythloday says this is final proof that a king would not need his counsel.

Hythloday then declares that whenever money is present in a commonwealth, the state will not be governed happily. More replies that without the possibility of gain, the people would become slovenly and the commonwealth would fall apart; Hythloday says that it is not so with the Utopians, who are governed fairly with few laws. More and Giles press Hythloday for more information about Utopia, and he responds to them in kind with the monologue that consists Book II.

Book II
Book II’s model is the ideal-commonwealth exercise pioneered by Plato. More described almost every aspect of his city in lucid detail; it is so detailed, in fact, that many of his readers believed Utopia was real and credited Raphael Hythloday, not Thomas More, with its discovery.

Utopia, like Great Britain, is an island with the sea as its natural protector; the tides, currents, and barriers are so dangerous that only Utopian sailors can navigate them, and then only by using certain landmarks.

There are fifty-four city-states on the island, matching the fifty-three counties plus London in the England and Wales of More’s time. The cities are “identical in language, customs, institutions, and laws”. They are all spacious; the nearest distance between towns is given as twenty-four miles, and the most remote are still within a day’s walking distance from their neighboring towns. The capital, Amaurot, is almost identical to London in geography. The houses are built in a block pattern and are all exactly the same, so that a man will not rebuild a house for the sake of cosmetic improvement. Each house has a garden in the backyard. The streets are twenty feed wide, which was lavish in More’s time.

Each town is allowed 6,000 households, generally made up of blood relations, with between ten and sixteen adults. The number of children is not regulated. Excess households are moved to colonies. Every thirty households elects a syphogrant. Over every ten syphogrants resides a tranibor. (Syphogrant could mean “warden of the sty” and tranibor “master eater”, puns referring to England’s Inns of Court.) The 200 syphogrants are brought together to elect the prince. They hold a secret ballot, and the prince rules for life unless suspected of tyranny. The other elected officials are chosen annually. The tranibors consult with the prince every other day, and more if necessary, to discuss affairs of state. They also settle disputes between private parties; there are few of those, and they are resolved as quickly as possible. Two different syphogrants are invited to the chamber for each meeting. No government measure is passed until it has been discussed in the senate for three days, and no one is allowed to give his opinion about it on the first day; that way, no one will recklessly give an erroneous opinion the first day and feel honor-bound to continue to support that opinion thereafter.

Farming is the one job that all men and women do, without exception. They are trained for it throughout childhood, and each person spends a two-year term in the farms some time during adulthood. Each person learns a particular trade; women usually take less labor-intensive jobs than men. The Utopians do not have lawyers; people represent themselves in the courts, as there are few laws anyway: adultery is the only crime for which there is a specific punishment. Sons are usually trained in their fathers’ crafts, but if one wishes to take up a different class, he can move to another family to train under a man of that occupation.

There is no private property, so government officials work hard so that no one will be idle. Six hours per day are devoted to work, rather than the eight of our time or sun-up to sun-down labor of More’s. This can be afforded because everyone works, unlike in More’s time or our own in which one of the two spouses, the priests and religious, the “gentlemen” and nobility, the retainers (servants and members of the standing army), and idle beggars do not work. Since all are employed, and no one in a useless job (in contrast to today’s society, example, in which professional athletes earn millions of dollars each), their standard of living is supported with much less work. The other hours of the day are given to each man’s discretion, as long as they are passed in a useful activity and not in sloth.

Dinner is eaten at the public houses, with preparation of food cycled between households. First consideration is given to the sick. The young and old are mixed together with the oldest starting the table conversation. Children up to marriageable age wait on the table or stand by in absolute silence. Each supper opens with a brief reading on a moral topic. No family ever lacks for food.

To keep order, personal freedom is greatly restricted. Speaking about politics outside the political forum is a capital offense, so as to restrict conspiracies. A man needs permission from his wife and father to travel to another place; if he is there over three days, he must practice his craft in that city.

The Utopians despite war and find many reasons to avoid it. They give bribes of gold and silver to avoid it; they have huge amounts of these natural resources but consider them useless. They usually hire foreign mercenaries, the Zapoletes, to fight for them; they throw these people into the heat of the battle for exorbitant rewards and would not mind if they were wiped off the face of the Earth. They offer ransom for the capture or murder of their enemies’ leaders; in so doing, they stoke suspicion of treason among the enemy ranks. They always send a hit squad to eliminate their enemy’s general. They take prisoners of war as slaves. While their tactics are deceptive and “unfair” by English standards, they are expedient, and when choosing between honor and expediency, the Utopians always select the latter.

The Utopians’ religion is theistic; they do not question the immortality of the soul but feel that if a man wants to cheapen himself by believing his soul is mortal, he can do so. They believe that pleasure is the most desirable part of life, and there are pleasures of the body, mind, and soul. Good health is valued. They follow Epicurus’s philosophy that when choosing between pleasures, one should select a greater one over a lesser one and should avoid pleasures that would lead to pain.

Though the majority of Utopians are non-Christian, they generally follow the Christian moral code, as it provides the greatest pleasures and discourages the pleasures spiked with pain. Many Utopians have embraced the Catholic faith brought to them from abroad and are eagerly awaiting the arrival of a priest to give them the Sacraments.

The Utopians tolerate all other religions and hold a weekly deist prayer service for those of all faiths in addition to allowing each to practice its own specific religious customs. People who do not desire pleasure are also tolerated, but the Utopians wonder why a man would deliberately choose to give himself misery.

In summation, the Utopian society is rather good, though there are some prices to be paid for their social equality (such as the restriction of freedom), and they are somewhat harsh to people from foreign countries. Thomas More says “meantime, while I can hardly agree with everything he [Hythloday] said (though he is a man of unquestionable learning and enormous experience of human affairs), yet I freely confess that in the Utopian commonwealth there are many features that in our own societies I would like rather than expect to see.” I agree. Many of the policies of the Utopians would be quite an improvement over our own; I especially like their simple legal system and sympathy toward religion. More’s Utopia is a relevant book even today.