lecture notes a: limiting reagents and thermodynamics...

Chemistry 09-106: Modern Chemistry II Carnegie Mellon University

Lecture Notes A: Thermodynamics I Distributed on: Wednesday, January 12, 2005 of 10

Lecture Notes A: Limiting Reagents and Thermodynamics I

Concept test: A tool set consists of 5 wrenches, 4 screwdrivers, and 2 pliers. A manufacturer has 18 wrenches, 12 screwdrivers, and 8 pliers. How many sets can be assembled? a) 2 b) 3 c) 4 d) 5



1) Limiting Reagents: approach 1 30ml of 0.20 M salicylic acid is mixed with 25 ml of 0.14 M acetic anhydride. What compounds are present at the end of the reaction and what are their concentrations? 2 salicylic acid + acetic anhydride aspirin It is convenient to re-write this with abbreviations: 2 SA + AH ASP

0.200.030 0.0060molesmoles SA l moles SAl

= =

0.140.025 0.0035molesmoles AH l moles AHl

= =

If SA is the limiting reagent:

10.0060 0.00302mole ASPmoles ASP moles SA moles ASPmole SA

= =

If AH is the limiting reagent:

10.0035 0.00351mole ASPmoles ASP moles AH moles ASPmole AH

= =

So SA is the limiting reagent and 0.0030 moles ASP are produced by the reaction. The concentration of ASP is then: The concentration of AH remaining after the reaction is:



2) Limiting Reagents: approach 2 30ml of 0.20 M salicylic acid is mixed with 25ml of 0.14 M acetic anhydride. What compounds are present at the end of the reaction and what are their concentrations? 2 salicylic acid + acetic anhydride aspirin First, we consider the effects of the dilution to determine the concentrations before the reaction occurs:

initial initial final finalC V C V= or initialfinal initial

final

VC CV

=

SA : 0.20M

=

AH : 0.14M

=

2 SA + AH ASP initial: change: final:

2 SA + AH ASP initial: change: final:



Definitions

Thermodynamic state Consider a box containing a gas, such as is shown on http://intro.chem.okstate.edu/1314F00/Laboratory/GLP.htm There are about 1023 atoms in a macroscopic sample of a gas. To completely specify the microscopic state of a system, you would need to specify the position and velocity of each of these atoms. Yet, we know from experience that it only takes a few variables to uniquely specify the state of the gas, for example: P, V and T.

This is the difference between the detailed microscopic state of a system and the macroscopic THERMODYNAMIC state of a system.

Detailed microscopic description Thermodynamic description Position and velocity of all molecules (1023 molecules)

A few macroscopic variables For instance in PV=nRT, we assume “state” of the system is captured by: V: volume of the container n: number of particles in the container P: average* force exerted on walls of container T: average* kinetic energy of the particles

*average: Pressure and Temperature describe averaged properties of the gas. Temperature: the energy stored in the motion of the 1023 “internal” degrees of freedom. Statistical mechanics is the field that connects the microscopic description to the thermodynamic description: Historical side note: Boltzmann showed that the ideal gas law (PV=nRT) could be obtained by picturing the gas as containing “atoms” bouncing around via Newton’s laws. The ideal gas law is independent of the size (mass) of the atom, so Mach and most European scientists rejected Boltzmann’s atomic hypothesis: For a great book on Boltzmann’s life and his debates with Mach, see “Boltzmanns Atom: The Great Debate That Launched A Revolution In Physics” by David Lindley (ISBN: 0684851865)



3) The First Law of Thermodynamics ∆E = q + w E = internal energy of the system Two ways to change the energy of system: exchange heat with the surroundings (heat flows in response to a temperature difference)

do work on the system, or have the system do work on the surroundings (by changing a macroscopic variable, such as V)

q = heat positive when heat is transfered to the system (gains energy from surroundings) negative when heat is lost from the system (loses energy to the surroundings) w = work positive when work is done on the system (gains energy from surroundings) negative when the system does work (loses energy to the surroundings)

Units of heat and work

1 cal = 4.184 J 1 nutritional calorie = 1000 cal

Concept

The flame on the right is turned on, which heats up the gas causing it to expand. The piston is connected to a drive train that causes a car to move. The signs of q and w for the gas in the cylinder are:

a) q + w + b) q + w - c) q - w + d) q - w -



4) Pressure-volume work A gas expanding against a constant external pressure. Amount of work = (external force acting on a body) * (distance through which the force acts) Problem

A cylinder containing an ideal gas has an initial volume of 1.00 liters, and an initial temperature of 25oC.

It is heated to 300oC. What is the work done on the system (w) in both joules and calories?

Pext=1atm

Pext=1atmInitial State Final State

Flame

V = 1.00 l ; T=25oCT = 300oC

∆h

Pext

Pext



5) Other types of work Work is energy given to or extracted from a system by changing one of the macroscopic variables, Stretch a rubber band Magnetic work Electrical work for biological membrane

6) Heat and heat capacity For a constant volume process, qv = n Cv (Tfinal-Tinitial) = n Cv ∆T n = number of moles of the substance being heated Cv = molar heat capacity specific heat capacity is heat capacity per gram (instead of per mole) The specific heat capacity of water is Cv = 1cal/(g oK)



Problem In the movie “Back to the Future”, a DeLorian car is transformed into a time machine. To travel through time, the car must be powered with 1.21 GigaWatts of energy. They get this amount of power from a bolt of lightning. Suppose the time machine malfunctioned, and instead of this energy going to time travel, it went to heat. Estimate the temperature of the car after this unfortunate accident. Car: We will model as 500 kg of Fe, with a heat capacity of Cv(iron) = 0.45 J/(g oK). Heat: Assume a lightning stroke with a power of 1.21 GigaWatts (1.21x109 J/s) lasts for 120 microseconds (120x10-6 s) [source: ftp://nofc.forestry.ca/pub/fire/docs/ltg.faq] Concept Suppose that instead of the energy going into the entire car, it went only into the flux capacitor (which we will model as a 50 g block of iron). What is the temperature of the flux capacitor after being hit with the lightning bolt considered above?

a) 364oK b) 940oK c) 6700oK d) 64300oK



Problem Pioneers used to heat their coffee by placing an iron poker from the fire directly into the coffee. If a cup initially held 0.50 l of coffee at 20oC, what would be the final temperature of the coffee when a 500g iron poker at 800oC was placed in it? (Assume no heat is lost to the surroundings during the process). The density of water is 1g/ml. Cv(iron) = 0.45 J/(g oK).



Problem In making a scotch and water, you mix 4 liquid ounces of ice-cold water (0oC) with 1 liquid ounce of alcohol at (25oC). What is the final temperature of the mixture (assuming the heat capacity of water is the same as that of alcohol)? Concept The heat capacity of alcohol is actually less than that of water. What effect will the use of the correct heat capacity for alcohol have on the temperature obtained above.

a) The temperature will be the same. b) The temperature will be smaller than that obtained above. c) The temperature will be larger than that obtained above. d) Not enough information is given to answer this question.

lecture notes a: limiting reagents and thermodynamics...

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