Clausius-Clapeyron Equation Example Problem

Clausius Problem The Clausius-Clapeyron equation may be used to estimate vapor pressure as a function of temperature or to find the heat of the phase transition from the vapor pressures at two temperatures. The Clausius-Clapeyron equation is a related named for Rudolf Clausius and Benoit Emile Clapeyron. The equation describes the phase transition between two phases of matter that have the same composition. When graphed, the relationship between temperature and pressure of a liquid is a curve rather than a straight line. In the case of water, for example, vapor pressure increases much faster than temperature. The Clausius-Clapeyron equation gives the slope of the tangents to the curve. Clausius This example problem demonstrates how to use the Clausius-Clapeyron equation to predict the vapor pressure of a solution. Problem: The vapor pressure of 1-propanol is 10.0 torr at 14.7  °C. Calculate the vapor pressure at 52.8  °C.Given:Heat of vaporization of 1-propanol 47.2 kJ/mol Solution The Clausius-Clapeyron equation relates a solutions vapor pressures at different temperatures to the heat of vaporization. The Clausius-Clapeyron equation is expressed byln[PT1,vap/PT2,vap] (ΔHvap/R)[1/T2 - 1/T1]whereΔHvap is the enthalpy of vaporization of the solutionR is the ideal gas constant 0.008314 kJ/K ·molT1 and T2 are the absolute temperatures of the solution in KelvinPT1,vap and PT2,vap is the vapor pressure of the solution at temperature T1 and T2Step 1 - Convert  °C to KTK  °C 273.15T1 14.7  °C 273.15T1 287.85 KT2 52.8  °C 273.15T2 325.95 KStep 2 - Find PT2,vapln[10 torr/PT2,vap] (47.2 kJ/mol/0.008314 kJ/K ·mol)[1/325.95 K - 1/287.85 K]ln[10 torr/PT2,vap] 5677(-4.06 x 10-4)ln[10 torr/PT2,vap] -2.305take the antilog of both sides 10 torr/PT2,vap 0.997PT2,vap/10 torr 10.02PT2,vap 100.2 torr Answer: The vapor pressure of 1-propanol at 52.8  °C is 100.2 torr.

The Diversity of Over- and Under- Compounds

The Diversity of Over- and Under- Compounds The Diversity of Over- and Under- Compounds The Diversity of Over- and Under- Compounds By Mark Nichol Becoming familiar (or more familiar) with words beginning with over and under must include taking into account that these compounds can be both literal and figurative (or only figurative but rarely only literal) and can serve as various parts of speech. This post discusses some examples. Overboard has a literal meaning, referring to someone or something falling or being thrown from a ship or boat. (Board alludes to the wooden deck of a ship.) However, it also has the figurative sense of discarding an idea as if it were being thrown from a ship and of excessive enthusiasm; remarking that someone has gone overboard implies that the person is not on the firm footing of reality or sensibility. Similar, overthrow can be literal, as when describing an athlete throwing a ball too far, causing a teammate to be unable to catch it, as well as figurative, as with the sense of â€Å"defeat,† â€Å"depose,† or â€Å"upset.† Overhead originally meant, literally, what was above one’s head, but it also serves as a noun with several meanings: It can refer to a stroke that a player in a game of tennis or a similar sport makes over his or her head, to a ceiling in a marine vessel, or to basic business expenses that do not fall under the budget for a specific project. Overtime is the extra time after the regulated period of play in a competition (as to provide contestants with the opportunity to break a tie) or the standard workday or workweek (or, by extension, the pay for additional time spent working), but it can also refer, more casually, to when participants in a project work extra hours to complete it. Many words beginning with over-, such as overlook (which can mean both â€Å"provide a view from above† and â€Å"fail to see†) and overtake (â€Å"catch up to and pass†) are verbs, and some in which over is the second element of the compound are nouns transformed from verb phrases, including handover (â€Å"transfer†) â€Å"and takeover (â€Å"forced or otherwise hostile transfer of power†). Likewise, words beginning with under serve various grammatical functions. Underhand is an adjective referring to an action undertaken to avoid detection or to a motion made with the hand moving up from below the shoulder (and underhanded means â€Å"deceitful†), and as an adverb, it means â€Å"secretly† or â€Å"with an underhand motion.† Underline and underscore both denote a line inserted beneath one or more words to emphasize them but also serve as verbs with that literal meaning and with the figurative sense of emphasis. Understand is an outlier, in that it has only a figurative meaning; one does not use the word to refer to posing beneath something. (The Old English word for that action is undergestandan.) The sense is of standing close to or in the midst of something and thus being familiar with it, although under may stem not from the Old English preposition under but from the homonym related to the Latin word inter, meaning â€Å"between† (though the homonyms may be directly related). And though underworld once referred to Hades (as well as, occasionally, the earth, as being located beneath heaven), it came to refer to the lowest level in the social ladder and, by extension, the figurative collective of criminals, especially those in organized crime. Want to improve your English in five minutes a day? Get a subscription and start receiving our writing tips and exercises daily! Keep learning! Browse the Spelling category, check our popular posts, or choose a related post below:25 Subordinating ConjunctionsThat vs. WhichGrammar Review #1: Particles and Phrasal Verbs