QUIZ 1 September 4, NAME: ACETONE Score: /10

Transcription

1 QUIZ 1 September 4, 2015 NAME: AETONE Score: /10 Be sure to show proper units in every case.] 1. (5 points) Draw structures for the following molecules to the right of each name. 2 N O O 2S p-aminobenzoic acid ydrogen sulfide Methane Naphthalene trans-butadiene 2. (5 points) In the table, indicate the proper best definition of each word or phrase in column A by inserting the proper number from column B: 9 Equilibrium Gas constant olumn A olumn B 1. A property proportional to the size of the system 2. A property independent of the size of the system 2 Intensive property 6 Surroundings 8 eat capacity. Fundamental constant of the universe, given as J K -1 mol -1 in SI units 4. Describing a macroscopic system in which the parts are observed to exchange energy over time 5. Statement of the zeroth law of thermodynamics 6. Everything in the universe except the system under study 7. Describing a multi-part system in which the parts exchange thermal energy through their boundaries 8. Measure of the amount of energy required to change the temperature of a substance by a given amount 9. The condition of a system for which no macroscopic change is observed

2 QUIZ 1 September 4, 2015 NAME: AETONE Score: /10. (10 points) For each entry on the left, given the derivative with respect to the independent variable indicated. (A, B,, and n are constants.) Function Derivative ff(tt) ee AA/TT2 dddd dddd 2AA TT ee AA/TT2 gg(ee) AA + BBEE 2 + EE dddd dddd 2BB EE EE 2 PPPP nnnnnn PP TT VV nnnn VV dd AA/TT2 ff(tt) ee llllll 2AA dddd TT h(xx) AA BB ddh dddd AAAA (BB ) 2

3 Fall, 2015(15F) QUIZ 2 September 11, 2015 NAME: BIPENYL Score: /20 [Show all work clearly. Be sure to show proper units and correct number of significant figures.] 1. (5 points) In Table 4.1 in the andbook, the van der Waals parameter, a, for 2O is about 150 times larger than the value of a for e. In one complete sentence, explain what this means about these two molecules. The intermolecular attraction between water molecules is much stronger than the intermolecular interaction between helium atoms. 2. (5 points) In the box, indicate the correct definition (from column B) of the words or phrases in column A. olumn A olumn B e Elastic collision a. Absolute temperature f Mole fraction of substance i b. Boltzmann s constant d Pressure c. elsius a Thermodynamic temperature scale d. Force per unit area g Zeroth Law e. No change in translational energy f. Pi/Ptotal g. Two systems in thermal equilibrium with a third system at temperature T are also in thermal equilibrium with each other.. (10 points) An athlete at high performance may inhale.75 liters of air at 1.00 atm and K. The inhaled air contains 0.5% water by volume and the exhaled air contains 6.2% by volume. For a respiration rate of 2 breaths per minute, how many moles of water are exhaled per minute through the lungs? V total L 6.84 L m This volume corresponds to a specific number of moles: P Vtotal ( Pa)( m ) n 0.280mole 1 RT J K K First, calculate the volume expelled per breath: V ( )(.75 L) L In 2 breaths, the expelled volume is: ( ) ( )( )

4 QUIZ September 18, 2015 NAME: ARBON TETRALORIDE Score: /20 1. (6 points) Using van der Waals constants, estimate the radius of a methane molecule, assuming that the molecule is a sphere. The van der Waals b for methane is m /mol. The excluded volume per molecule is therefore VV mmmmmmmmmmmmmmmm bb mm /mmmmmm mm /mmmmmmmmmmmmmmmm. This is the NN mmmmmmmmmmmmmmmm/mmmmmm point where two molecules just touch, so VV mmmmmmmmmmmmmmmm (2rr), where r is the radius of the molecule. Solving for the radius gives the size of the methane molecule: rr VV mmmmmmmmmmmmmmmm 8 ( mm ) 8 One may also use this equation, which is in the book: mm σσ bb (4/ mm /mmmmmm) 2ππNN 0 2ππ( mmmmmmmmmmmmmmmm/mmmmmm) 10 mm From this, one finds rr mm. Either method is counted correct. 2. (4 points) The one-dimensional speed distribution function is ff(vv xx ) 2mm eeeeee mmvv 2 xx, where the ππππππ 2kkkk symbols have their usual meaning. Derive an equation for the average speed, < vv xx > in one dimension. One merely does the integral: < vv xx > 0 ff(vv xx )vv xx ddvv xx 2mm ππππππ 0 vv xxexp mmvv 2 xx ddvv 2kkkk xx 2kkkk ππππ. (10 points) In the following, indicate which statements match the word or phrase in column A the best by putting the letter of it in the blank next to the answer. [There is only one best answer for each.] olumn A c Boyle temperature a. AAexp ( EE kkkk ) olumn B e ompression factor d ritical temperature b Gaussian a Boltzmann factor b. BBexp ( xx2 2σσ 2) c. For a van der Waals gas, aa RRRR d. ondition at which 0 and VV mm TT 2 PP 0 VV mm 2 TT e. PPVV mm RRRR

5 Fall, 2015(15F) QUIZ 4 September 25, 2015 NAME: DIOXANE Score: /20 1. (6 points) Suppose you draw a single card from a standard 52-card deck. (a) What is the probability of drawing an ace of any suit? There are four aces out of 52 cards, so the probability is PP (b) What is the probability of drawing the ace of hearts from a standard deck? There is only one ace of hearts, so the probability is PP (6 points) Determine the rms speed of Kr at K. uu kkkk mm RRRR MM ( JJ KK 1 mmmmmm 1 )( KK) kkkk mmmmmm mm ss 1. (4 points) For a particular system, the internal energy is given by the following equation: UU(TT, VV) UU 0 + AAAA + BBBB, where UU 0, AA, aaaaaa BB are constants independent of temperature and volume. Show that this is a mathematically acceptable form for U as a state function. [Show all work; explain.] One has to show the Maxwell relation: AA and TT (UU 0 + AAAA + BBBB) TT BB. But vv VV TT TT vv (UU 0 + AAAA + BBBB) vv 0. Similarly TT VV VV 0. These two crossed partial derivatives are equal, which is the requirement for an acceptable state function. 4. (4 points) elium gas is expanded from a molar volume of 22.4 liters to a molar volume of 44.8 liters against a constant external pressure of bar. ow much work does the amount of gas do in this process? The work done by the gas is ww PP eeeeee (VV 2 VV 1 ) PPPP ( mm mm ) 1.12 kkjj

6 QUIZ 5 October 9, 2015 NAME: FURAN Score: /20 1. (12 points) alculate the change in enthalpy of water when it is heated from room temperature ( K) to its normal boiling point (7.15 K), as accurately as you can KK mm PPPP dddd KK 7.17 KK TT TT TT KK TT 2 dddd JJ TT KK TT TT TT JJ KK ( ) ( ) ( ( ) ) JJ , JJ + 8,46.92 JJ 27, JJ + 7,105.9 JJ + 2, JJ 5, JJ But this is on a molar basis. The molar mass of water is gm, so one can find this on a weight basis by division: 5, JJ JJ gggg gggg TT 4 2. (8 points) For a gas that obeys the van der Waals equation of state, determine function of T, Vm, and the van der Waals constants. VV mm as a RRRR aa VV mm bb For a van der Waals gas, PP VV mm 2. Taking the derivative of this function gives VV mm RRRR VV mm bb aa VV2 RR mm VV VV VV mm mm bb 0 RR VV mm bb mm

7 QUIZ 6 October 16, 2015 NAME: GLYOSIDE Score: /20 1. (10 points) Assume that you have an ideal gas with a temperature-independent heat capacity, VVVV 5 RR. (a) Suppose that you carry 2.60 moles of this gas through a reversible expansion that 2 doubles the volume at constant temperature. What is the change in entropy? VV 2 VV 2 SS SS VV ddvv PP VV 1 TT TT ddvv nnnn 1 VV 1 VV VV dddd nnnn llll 2VV 1 VV 1 VV 1 2VV 1 (2.60)( JJ KK 1 ) ln(2) JJ KK 1 (b) Suppose that you carry the same amount of this gas through a process in which the temperature goes from the starting temperature of K to K, while holding the volume constant. What is the entropy change during that process? TT SS SS TT ddtt VV TT KK VV TT dddd KK nn 5RR 2 llll KK KK JJ KK 1 (2.60) ln(1.540) JJ KK 1 2. (10 points) Which of the following equations is/are correct, and which is/are incorrect? Mark an X in the appropriate box. (Graded right 0.5wrong; do not guess.) EQUATION orrect Incorrect θ θ P T P X θ θ S V P T T P X θ θ S V T T P X ds S S dt + dv T P V T X ( T, P) P θ V ( T ) + V T dp θ T P X P

8 Fall, 2015(15F) QUIZ 7 October 2, 2015 NAME: YDRAZINE Score: /20 1. (8 points) Using information in the andbook, calculate the molar entropy of fusion of water at its normal melting point. θθ From the andbook s Table 6.1, the information is: TT ff KK and ff,mm 6.01 kkkk mmmmmm 1 θθ By definition SS ff,mm θθ ff,mm TT ff JJ mmmmmm KK 22.0 JJ KK 1 mmmmmm 1 2. (8 points) onsider a reversible arnot engine using an ideal gas that operates between room temperature ( K) and K. (a) If one extracts exactly 1 kj of heat at K, how much work can the engine do? First calculate the ideal efficiency: εε TT hoooo TT cccccccc TT hoooo KK KK KK That determines how much of the heat is used as work: ww εε qq ( )(1 kkkk) JJ (b) Secondly, consider a arnot engine working between the same temperatures as in (a), except that it uses a van der Waals gas as the working fluid. What is the maximum work one can achieve from this engine for an input of exactly 1 kj? The ideal efficiency gives maximum work, so the maximum work is the same: J. (4 points) In each case, give the simplest requirement for spontaneity in terms of an inequality. onstant temperature and constant volume ( AA) TT,VV 0 onstant temperature and constant pressure ( GG) TT,PP 0

9 QUIZ 8 October 0, 2015 NAME: INDIGO Score: /20 1.(10 points) (a) Using data in your handbook, calculate the enthalpy of the dissociation of bromine at K by the reaction BBBB 2 (gg) 2 BBBB (gg) This is done using data for the various formation enthalpies in Table 5.8. θθ 2 ff mm θθ (BBBB) ff mm θθ (BBBB 2 ) 2(111.9 kkkk) 0.9 kkkk 19.8 kkkk (b) Also using data from your handbook, calculate the Gibbs free energy change for the same reaction at K. From the same data table, one can find the Gibbs energy change in an analogous manner: GG θθ 2 ff GG mm θθ (BBBB) ff GG mm θθ (BBBB 2 ) 2(82.4 kkkk).1 kkkk kkkk 2. (10 points) alculate the change in entropy when one mole of water is heated from K to K at a constant pressure of 1 bar. This calculation involves only a change in temperature so the change is calculated as follows: KK θθ SS mm SS mm θθ dddd KK PP 08.5 KK KK θθ PPPP (TT) TT dddd Substitution from Table 5.6 for the temperature-dependent heat capacity gives: SS mm θθ 08.5 KK KK cc 1 + cc 2 TT + cc TT 2 + cc 4 TT + cc 5 TT 2 dddd TT TT 2 cc 1 TT + cc 2 + cc TT + cc 4 TT 2 + TT 1 cc 5 TT dddd cc 1 llll TT 2 + cc TT 2 (TT 2 TT 1 ) + cc 1 2 (TT 2 2 TT 2 1 ) + cc 4 (TT 2 TT 1 ) cc TT TT 1 ( )llll ( ) ( ) + ( ) JJ KK(mmmmmm) JJ [ ] KK(mmmmmm) JJ KK(mmmmmm) Note that using a temperature-independent Pm in the simple equation gives a similar value, but the correct way of working the problem is to include all temperature-dependent terms. Using a temperature-independent heat capacity without explicitly saying why you assume temperature independence (in this case, because the temperature range is small) shows a lack of knowledge of the general usage of these equations.

10 QUIZ 9 November 1, 2015 NAME: KERATIN Score: /20 1. (10 points) A commonly studied reaction is the dimerization of NO2 to dinitrogen tetroxide in the gas phase: 2 NNNN 2 (gg) NN 2 OO 4 (gg) (a) Predict, by calculation, the equilibrium constant for this reaction at K. [Show all work.] First method from free energies of formation: GG θθ 99.8 kkkk 2(51. kkkk) 2.8 kkkk 2800 JJ KK aa ( KK) eeeeee JJ.09 KK ( KK) Second method from enthalpies of formation and Third-Law entropies: GG θθ θθ TT SS θθ 11.1 kkkk 2(.2 kkkk) ( KK) 04.4 JJ JJ 55. kkkk kkkk KK KK 2.9 kkkk KK aa ( KK) eeeepp Either method is considered correct JJ JJ KK ( KK).22, essentially the same number. (b) Assume that the pressures are sufficiently low that each component can be considered an ideal gas. Write a correct expression for Ka in terms of the partial pressure of each gas, Pi, and any other necessary parameters. [Define any symbols you use.] PP NN2 OO 4 KK aa 2 PP θθ PP NNNN2 where PP θθ is the standard pressure (in the case of data from Table 5.8, that is 1 bar). 2. (10 points) onsider the dimerization of NO2, as discussed in question 1. Assume that for practical purposes, both θ and S θ are temperature-independent. [This is an approximation, of course, and will lead to some errors, but may not be too bad.] Predict Ka for this reaction at 7.15 K, considering that approximation to be correct. [Show all work, including derivation of any intermediate quantities.] In this case, one may use the second method, as in question 1, because the enthalpy and entropy changes are independent of temperature: And GG θθ θθ TT SS θθ 55. kkkk (7.15 KK) JJ 10.0 kkkk KK KK aa (TT) eeeeee GGθθ RRRR KK aa(7.15 KK) eeeeee 1000 JJ JJ KK (7.15 KK)

11 QUIZ 10 November 20, 2015 NAME: LYSERGI AID Score: /20 1. (10 points) Ratcliffe and hao (anad. J. hem. Eng. 1969, 47, 148.) measured the properties of solutions of isopropanol (PP tttttttt) and n-decane (PP tttttttt). For a particular solution, the liquid had a mole fraction, XX 2, of and the total pressure over the solution, PP tttttttttt, was torr. They condensed the gas phase and measured that in gas, the n-decane gas-phase mole fraction was From these data, find the activities, aa ii, and activity coefficients, γγ ii, of isopropanol and n-decane, assuming a Raoult s law standard state. First calculate the partial pressures of the two components: PP 1 YY 1 PP tttttttttt (909.6 tttttttt) 882. tttttttt and PP 2 YY 2 PP tttttttttt 0.000(909.6 tttttttt) 27. tttttttt. The activity on the Raoult s Law scale is aa ii PP ii PP ii. Using the values in the problem, this formula gives: aa iiiiiiiiiiiiiiiiiiiiii and aa dddddddddddd At equilibrium, the activity of a component in the gas phase is equal to the activity in the liquid. So, we can calculate the activity coefficients from aa ii γγ ii XX ii. When one does that, the results are γγ iiiiiiiiiiiiiiiiiiiiii aa iiiiiiiirrrrrrrrrrrrrr XX iiiiiiiiiiiiiiiiiiiiii and γγ dddddddddddd aa dddddddddddd XX dddddddddddd (10 points) Below is a boiling point diagram for a solution of two materials, A and B. The abscissa is the mole fraction of component B. Insert the appropriate letter(s) in the blank space(s) next to phrases to indicate the appropriate region(s) or point(s) which those phrases describe. _(f) Boiling temperature of B _(e) Boiling temperature of A _(g) Azeotrope _(b) Liquid (c)(d)_ Liquid + vapor _(a) Vapor

12 QUIZ 11 December 4, 2015 NAME: MALEI ANYDRIDE Score: /20 1. (10 points) An aqueous solution containing calcium chloride freezes at -4. If you were to heat this solution until it boils, what would the temperature be? From Tables 7.5 and 7.6 in the andbook, one finds KK bb KK kkkk/mmmmmm and KK ff KK kkkk/mmmmmm. Since the molality is constant in the two processes: θθ bb mm θθ ff KK bb KK ff KK ence, θθ bb bb θθ KK ff (4 KK) KK. ff Normally, water boils at 100, so this solution boils at (10 points) The enry s Law constant for N2 in water is bar at K, on the mole fraction scale. At equilibrium at this temperature, how many moles of N2 are dissolved in 1 kg of water with a nitrogen overpressure of 0.79 bar? Because the solution is in the dilute limit, one may assume the activity coefficient is 1. Therefore, PP NN bbaaaa XX NN2 kk bbbbbb The molar mass of water is MM 2( gg) gg gg In one kilogram of water, there are 1000 gg nn 2 OO mmmmmm gg Then, from the definition of mole fraction in a binary solution XX NN nn NN2 nn 1 XX 2 OO NN ( mmmmmm) mmmmmm