1 2004 AP CHEMISTRY FREE-RESPONSE QUESTIONS 6. An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes. When the switch is clsed, the mass f the Sn electrde increases. The half-reactins are shwn belw. Sn 2+ (aq) + 2 e Sn(s) E = 0.14 V X 3+ (aq) + 3 e X(s) E =? (a) In the diagram abve, label the electrde that is the cathde. Justify yur answer. (b) In the diagram abve, draw an arrw indicating the directin f the electrn flw in the external circuit when the switch is clsed. (c) If the standard cell ptential, X 3+ /X electrde? (d) Identify metal X., is V, what is the standard reductin ptential, in vlts, fr the (e) Write a balanced net-inic equatin fr the verall chemical reactin ccurring in the cell. (f) In the cell, the cncentratin f Sn 2+ is changed frm 1.0 M t 0.50 M, and the cncentratin f X 3+ is changed frm 1.0 M t 0.10 M. (i) Substitute all the apprpriate values fr determining the cell ptential, (D nt d any calculatins.) (ii) On the basis f yur respnse in part (f) (i), will the cell ptential, equal t the riginal? Justify yur answer. E cell E cell, int the Nernst equatin., be greater than, less than, r 11 GO ON TO THE NEXT PAGE.
2 AP CHEMISTRY 2004 SCORING GUIDELINES Questin 6 An electrchemical cell is cnstructed with an pen switch, as shwn in the diagram abve. A strip f Sn and a strip f an unknwn metal, X, are used as electrdes. When the switch is clsed, the mass f the Sn electrde increases. The half-reactins are shwn belw. Sn 2+ (aq) + 2 e Sn(s) E = 0.14 V X 3+ (aq) + 3 e X(s) E =? (a) In the diagram abve, label the electrde that is the cathde. Justify yur answer. The Sn (tin) electrde is the cathde. The increase in mass indicates that reductin ccurs at the Sn electrde: Sn 2+ (aq) + 2 e Sn(s) Reductin ccurs at the cathde. 1 pint fr identifying Sn as the cathde 1 pint fr reasning based n increase in mass (b) In the diagram abve, draw an arrw indicating the directin f the electrn flw in the external circuit when the switch is clsed. Diagram shuld have arrw shwing electrns flwing frm the ande twards the cathde. 1 pint fr crrect directin f electrn flw 14
3 AP CHEMISTRY 2004 SCORING GUIDELINES (c) If the standard cell ptential, electrde? Questin 6 (cnt ), is V, what is the standard reductin ptential, in vlts, fr the X 3+ /X = Ecathde Eande V = 0.14 V Eande Eande = 0.74 V 1 pint fr crrect ptential with crrect sign (d) Identify metal X. Cr 1 pint fr crrect metal (e) Write a balanced net-inic equatin fr the verall chemical reactin ccurring in the cell. 3 Sn Cr 3 Sn + 2 Cr 3+ 1 pint fr crrectly balanced net-inic equatin (f) In the cell, the cncentratin f Sn 2+ is changed frm 1.0 M t 0.50 M, and the cncentratin f X 3+ is changed frm 1.0 M t 0.10 M. (i) Substitute all the apprpriate values fr determining the cell ptential, nt d any calculatins.) E cell, int the Nernst equatin. (D E cell = [Cr ] lg 2+ 3 n [Sn ] E cell = V [0.10] lg 6 [0.50] pint fr using 1 pint fr using n = 6 = V 1 pint fr substituting crrectly int the Q expressin based n the equatin in part (e) (ii) On the basis f yur respnse in part (f) (i), will the cell ptential, r equal t the riginal? Justify yur answer. E cell, be greater than, less than, E cell will be greater (mre psitive). Since the Q rati is a number less than 1, the lg f the rati will be negative. A negative times a negative is psitive. Thus, [0.10] lg increases E 3 cell 6 [0.50] 1 pint fr the crrect predictin with an explanatin based n Q 15
6 AP CHEMISTRY 2004 SCORING COMMENTARY Questin 6 Sample: 6A Scre: 10 This respnse earns a perfect scre f 10 pints: 2 pints fr part (a), 1 pint fr part (b), 1 pint fr part (c), 1 pint fr part (d), 1 pint fr part (e), 3 pints fr part (f)(i), and 1 pint fr part (f)(ii). In part (f)(ii), the explanatin f the change in vltage is clear and lgical. Sample: 6B Scre: 8 The pint is nt earned in part (d) fr the identificatin f aluminum as metal X. Nte that full credit is earned in part (e) even thugh aluminum is used in the equatin instead f irn, because this respnse is cnsistent with the incrrect answer given in part (c), and the stichimetry is crrect. Only 2 ut f 3 pints are earned in part (f)(i) because the Q term is incrrect. Full credit is earned in part (f)(ii) because the answer is cnsistent with the incrrect answer given in part (f)(ii). Sample: 6C Scre: 7 This respnse cntains three cmmn errrs. The pint is nt earned in part (c) because the standard reductin ptential shuld be negative. Only 1 ut f 3 pints is earned in part (f)(i) because 0.74 V is used in the Nernst equatin instead f 0.60 V, and the expnents are nt included in the Q term. Visit apcentral.cllegebard.cm (fr AP prfessinals) and (fr students and parents). 7
7 2004 Θ&Α Questin 6 What was the intent f this questin? The required essay was designed t assess students knwledge f electrchemistry and t integrate a variety f chemical principles. Students were expected t identify the cathde in a galvanic cell, t calculate a reductin ptential, and t use the Nernst equatin t determine the effects f changes in cncentratin. Hw well did students perfrm n this questin? It was apparent that many students were familiar with the material. The mean scre fr this questin was 4.1 ut f a pssible 10 pints. There were many perfect scres. The parts f the questin mst frequently answered crrectly were the identificatin f the cathde, the electrn flw, and the identificatin f the metal. The least frequently earned pints were calculating the reductin ptential and interpreting the vltage after cncentratin changes. What were cmmn student errrs r missins? Part (a): Mst students earned pints fr identificatin f the cathde. The mst cmmn errrs included the fllwing: Students mislabeled the ande and cathde. Students cnfused standard line ntatin with psitin f the half cells (ande-left and cathderight). Students identified the electrde as the slutin r the cntainer rather than the metal. Students failed t recgnize that the mass gain was due t Sn 2+ plating ut as Sn metal and incrrectly reasned that it was due t the mvement f electrns int the cathde. Part (b): Mst students earned the pint fr prperly shwing the electrn flw. The mst cmmn errr was representing the electrn flw thrugh the salt bridge r traveling in sme type f cmplete circuit using the salt bridge. Part (c): The mst cmmn errr ccurred when students gave an xidatin ptential f V fr Cr metal instead f a reductin ptential fr Cr 3+. Anther cmmn errr was t cmbine the data imprperly as = 0.60 V 0.14 V = 0.46 V. Part (d): Mst students were able t identify Cr as metal X regardless f the answer btained in Part (c). Thse nt identifying Cr mst ften chse Fe r sme ther metal knwn t pssess a 3+ xidatin state. Many students incrrectly identified Cr 3+ as the metal. Part (e): The mst cmmn mistake was failure t balance mass and charge. Sme students failed t remve spectatr ins, and sme failed t remve free electrns. 9
8 Part (f)(i): Many students did nt include expnents frm the balanced equatin when substituting fr Q. Sme were unable t select the Nernst equatin and ften chse G = RTlnK r G = nfe. Students ften substituted the ttal f the slutin mlarities rather than the number f electrns transferred; sme substituted in the reductin ptential value frm Part (c) instead f the cell ptential. Part (f)(ii): Many students incrrectly reasned that anything subtracted wuld reduce the vltage, withut recgnitin that ln Q was a negative value. Many incrrectly simplified that when the cncentratin decreases, the vltage decreases. Parts (f)(i) and (f)(ii) were frequently mitted, even when students had earned all pints in Parts (a) thrugh (e). Based n yur experience f student respnses at the AP Reading, what message wuld yu like t send t teachers that might help them t imprve the perfrmance f their students n the exam? Be sure t include a thrugh unit n electrchemistry. Have students draw, label, calculate, and make bservatins fr galvanic cells and electrlytic cells. Have students prperly identify ande and cathde and write half-cell reactins fr each. Make sure that students have the pprtunity t describe the flw f electrns and what is actually taking place in each type f cell. Many students had the miscnceptin that electrns were being pushed and pulled frm ne cell t anther r that prtns and electrns were exchanging places, thus accunting fr the mass change. Students shuld have the pprtunity t perfrm an electrchemical cell lab and measure vltages. Encurage students t read and answer all parts f each questin. Encurage mathematical reasning, sign, and magnitude, when dealing with questins invlving frmulas. Substantial partial credit is earned n this type f questin fr reasning based n an equatin r an answer btained in the previus part(s) f the questin. Make use f the Nernst equatin t calculate the E fr a galvanic cell. Encurage students t fully establish equatins befre making substitutins. Ensure that students understand what each quantity in an equatin represents. Fr example, it is nt enugh t understand that n is the number f mles if there is n cmprehensin f what this value actually represents. Questin 7 What was the intent f this questin? This was a brad questin designed t assess students understanding f chemical principles related t intermlecular frces, mlecular gemetry, and the structure f matter. Hw well did students perfrm n this questin? This was a chice questin, selected by apprximately 40 percent f the students. The mean scre was 2.4 ut f a pssible eight pints. Respnses were quite varied. Mst pints were earned fr mlecular gemetry. Understanding f the variety and terminlgy f intermlecular frces and the relatinship t the bserved prperties f matter (phase, melting pint, slubility) was generally weaker. 10