Cambridge A Level Chemistry 9701 — 2010 Oct/Nov Paper 3 · Variant 4

This document consists of 12 printed pages and 4 blank pages. DC (CW) 28188/3 © UCLES 2010 [Turn over * 1 8 6 3 3 0 7 0 2 5 * UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Advanced Subsidiary Level and Advanced Level READ THESE INSTRUCTIONS FIRST Write your Centre number, candidate number and name on all the work you hand in. Give details of the practical session and laboratory where appropriate, in the boxes provided. Write in dark blue or black pen. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. DO NOT WRITE IN ANY BARCODES. Answer all questions. You may lose marks if you do not show your working or if you do not use appropriate units. Use of a Data Booklet is unnecessary. Qualitative Analysis Notes are printed on pages 13 and 14. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. CHEMISTRY 9701/34 Advanced Practical Skills October/November 2010 2 hours Candidates answer on the Question Paper. Additional Materials: As listed in the Instructions to Supervisors Session Laboratory For Examiner’s Use 1 2 3 Total

2 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use There are three questions on this paper. Question 2 should not be the last question attempted. 1 FB 1 is an aqueous solution containing 21.50 g dm–3 of a mixture of iron(II) sulfate, FeSO4 and iron(III) sulfate, Fe2(SO4)3. FB 2 is an aqueous solution containing 2.00 g dm–3 potassium manganate(VII), KMnO4. In the presence of acid, the iron(II) sulfate is oxidised by potassium manganate(VII). 2KMnO4(aq) + 8H2SO4(aq) + 10FeSO4(aq) 5Fe2(SO4)3(aq) + 2MnSO4(aq) + K2SO4(aq) + 8H2O(l) (a) Method • Fill a burette with FB 2. • Pipette 25.0 cm3 of FB 1 into the conical flask. • Use a 25 cm3 measuring cylinder to add 10 cm3 of dilute sulfuric acid to the flask. • Place the flask on a white tile. • Carefully titrate with FB 2 until the first permanent pink colour is obtained. You should perform a rough titration. In the space below record your burette readings for this rough titration. The rough titre is … cm3. • Carry out as many accurate titrations as you think necessary to obtain consistent results. • Record in a suitable form below all of your burette readings and the volume of FB 2 added in each accurate titration. • Make certain any recorded results show the precision of your practical work. [7] I II III IV V VI VII

3 9701/34/O/N/10 © UCLES 2010 [Turn over For Examiner’s Use (b) From your accurate titration results obtain a suitable value to be used in your calculation. Show clearly how you have obtained this value. 25.0 cm3 of FB 1 required … cm3 of FB 2. [1] Calculations Show your working and appropriate significant figures in the final answer to each step of your calculations. (c) (i) Calculate the concentration, in mol dm–3, of the potassium manganate(VII) in FB 2. FB 2 contains 2.00 g dm–3 KMnO4. [Ar: O, 16.0; K, 39.1; Mn, 54.9] The concentration of potassium manganate(VII) in FB 2 is … mol dm–3. (ii) Calculate how many moles of KMnO4 were present in the volume calculated in (b). … mol of KMnO4. (iii) Calculate how many moles of iron(II) sulfate, FeSO4, reacted with the potassium manganate(VII) in (ii). 2KMnO4(aq) + 8H2SO4(aq) + 10FeSO4(aq) 5Fe2(SO4)3(aq) + 2MnSO4(aq) + K2SO4(aq) + 8H2O(l) … mol of FeSO4 reacted with the potassium manganate(VII). I II III IV V

4 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use (iv) Calculate the concentration, in mol dm–3 of FeSO4 in FB 1. The concentration of FeSO4 in FB 1 is … mol dm–3. (v) Calculate the concentration, in g dm–3, of FeSO4 in FB 1. [Ar: O, 16.0; S, 32.1; Fe, 55.8] FB 1 contains … g dm–3 of FeSO4. (vi) FB 1 is an aqueous solution containing 21.50 g dm–3 of FeSO4 and Fe2(SO4)3. Calculate the percentage, by mass, of FeSO4 in this mixture. The mixture contains … % FeSO4. [5] [Total: 13]

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6 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use 2 FB 3 is a mixture containing anhydrous sodium carbonate, Na2CO3, and sodium hydrogencarbonate, NaHCO3. When heated, sodium hydrogencarbonate decomposes. 2NaHCO3(s) Na2CO3(s) + CO2(g) + H2O(g) Anhydrous sodium carbonate does not decompose when heated. You are to determine if sodium hydrogencarbonate is the major component, by mass, of the mixture in FB 3. (a) Method – Read through the instructions before starting any practical work. • Weigh and record the mass of an empty boiling-tube. • Tip the contents of the tube labelled FB 3 into the weighed boiling-tube. Reweigh and record the mass of the boiling-tube and FB 3. • Gently heat the FB 3 in the boiling-tube for 2 minutes then heat strongly for a further 2 minutes. Take care not to lose any solid from the tube during heating. • Warm the upper parts of the boiling-tube to evaporate any water that may have condensed while heating the solid. • Place the hot tube on a heat-proof mat and leave to cool. • You are advised to continue with part (d) of this question or to start another question while the tube cools. • When cool, reweigh the boiling-tube and the residual sodium carbonate. • Reheat, cool and reweigh the tube until you are satisfied decomposition is complete. Results In an appropriate form, in the space below, record all of your balance readings, the mass of FB 3 heated, the mass of residual sodium carbonate and the mass loss on heating. [6] I II III IV V VI

7 9701/34/O/N/10 © UCLES 2010 [Turn over For Examiner’s Use Calculations Do not use your experimental results in part (i) (b) (i) Use the equation for the decomposition of NaHCO3 on heating to calculate the theoretical ratio mass of NaHCO3 mass loss on heating. 2NaHCO3(s) Na2CO3(s) + CO2(g) + H2O(g) [Mr: NaHCO3, 84.0; CO2, 44.0; H2O, 18.0] theoretical ratio = … (ii) Use the following expression to calculate the mass of NaHCO3 in the sample of FB 3 that was heated. theoretical ratio from b(i) × experimental mass loss from (a) mass of NaHCO3 = … g (iii) Tick the appropriate box in the table below. NaHCO3 is the major component, by mass, in FB 3 NaHCO3 is not the major component, by mass, in FB 3 Justify your answer with supporting evidence. … … [2]

8 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use (c) Do not carry out your suggestions. Suggest two ways in which you could show that sodium carbonate does not decompose on heating. (i) … … (ii) … … [2] (d) A student is asked to weigh, with maximum precision, a solid. The three balances available are: balance A, reading to 1 decimal place, balance B, reading to 2 decimal places, balance C, reading to 3 decimal places. The smallest division on a burette is 0.1 cm3. The maximum error in a single burette reading is ±0.05 cm3 Balance readings can be treated in the same way. Complete the following table. balance maximum error for a single balance reading / g maximum % error when weighing: A ± 9.0 g of solid = B ± 4.00 g of solid = C ± 0.500 g of solid = [2] [Total: 12]

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10 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use 3 FB 4, FB 5, FB 6 and FB 7 are aqueous solutions each containing one of the ions Al 3+, NH4 +, Mg2+, Mn2+. You will carry out the following tests on each of the solutions. At each stage of any test you are to record details of the following. • colour changes seen • the formation of any precipitate • the solubility of such precipitates in an excess of the reagent added Where gases are released they should be identified by a test, described in the appropriate place in your observations. You should indicate clearly at what stage in a test a change occurs. Marks are not given for chemical equations. No additional tests for ions present should be attempted. If any solution is warmed, a boiling-tube MUST be used. (a) Carry out the following tests. Record your observations in the spaces provided in the table. test observations FB 4 FB 5 FB 6 FB 7 (i) To 1 cm depth of solution in a test- tube add 1 cm depth of aqueous sodium hydroxide. Swirl the tube, then add a further 2 cm depth of aqueous sodium hydroxide. In tests (ii) and (iii) put a cross in any boxes where the test is not carried out. (ii) If a precipitate remains at the end of test (i) leave the test-tube and contents to stand for a few minutes. (iii) If no precipitate formed at all in test (i) tip the contents of the tube into a boiling-tube and warm gently. Care: heated solutions containing sodium hydroxide are liable to be ejected from the tube.

11 9701/34/O/N/10 © UCLES 2010 [Turn over For Examiner’s Use test observations FB 4 FB 5 FB 6 FB 7 (iv) To 1 cm depth of solution in a test- tube add 1 cm depth of aqueous ammonia. Swirl the tube, then add a further 2 cm depth of aqueous ammonia. [6] (b) Use the Qualitative Analysis Notes on page 13 to identify the cation present in each of the solutions. Complete the table below to identify each ion and to give supporting evidence from your observations. solution cation supporting evidence FB 4 FB 5 FB 6 FB 7 [4] Rinse and re-use test-tubes where possible. I II III IV V VI I II III IV

12 9701/34/O/N/10 © UCLES 2010 For Examiner’s Use (c) Carry out the following tests on the solution you have identified as containing Al 3+ ions and record your observations in the spaces provided. observation (i) Add aqueous sodium iodide (ii) Add dilute sulfuric acid Explain how your results confirm the presence of Al 3+ and eliminate any other ion. … … [1] (d) What other cation listed in the Qualitative Analysis Notes on page 13 would give similar results to Al 3+ in (a)? … [1] (e) Carry out the following tests and make careful observations of all that happens in each experiment. Complete the table. test observations (i) To 1 cm depth of aqueous silver nitrate in a test-tube add 1 cm depth of aqueous sodium chloride. Keep the tube for comparison with the observations in test (ii). (ii) Repeat test (i). To 1 cm depth of aqueous silver nitrate in a test-tube add 1 cm depth of aqueous sodium chloride, then Do not repeat your observations from test (i) add 1 cm depth of aqueous sodium iodide and shake the tube. [2] (f) Suggest an explanation for your observations when aqueous sodium iodide is added in test (e)(ii). … … … [1] [Total: 15]

13 9701/34/O/N/10 © UCLES 2010 [Turn over Qualitative Analysis Notes Key: [ ppt. = precipitate ] 1 Reactions of aqueous cations ion reaction with NaOH(aq) NH3(aq) aluminium, Al 3+(aq) white ppt. soluble in excess white ppt. insoluble in excess ammonium, NH4 +(aq) no ppt. ammonia produced on heating barium, Ba2+(aq) no ppt. (if reagents are pure) no ppt. calcium, Ca2+(aq) white ppt. with high [Ca2+(aq)] no ppt. chromium(III), Cr3+(aq) grey-green ppt. soluble in excess giving dark green solution grey-green ppt. insoluble in excess copper(II), Cu2+(aq) pale blue ppt. insoluble in excess blue ppt. soluble in excess giving dark blue solution iron(II), Fe2+(aq) green ppt. turning brown on contact with air insoluble in excess green ppt. turning brown on contact with air insoluble in excess iron(III), Fe3+(aq) red-brown ppt. insoluble in excess red-brown ppt. insoluble in excess lead(II), Pb2+(aq) white ppt. soluble in excess white ppt. insoluble in excess magnesium, Mg2+(aq) white ppt. insoluble in excess white ppt. insoluble in excess manganese(II), Mn2+(aq) off-white ppt. rapidly turning brown on contact with air insoluble in excess off-white ppt. rapidly turning brown on contact with air insoluble in excess zinc, Zn2+(aq) white ppt. soluble in excess white ppt. soluble in excess [Lead(II) ions can be distinguished from aluminium ions by the insolubility of lead(II) chloride.]

14 9701/34/O/N/10 © UCLES 2010 2 Reactions of anions ion reaction carbonate, CO3 2– CO2 liberated by dilute acids chromate(VI), CrO4 2– (aq) yellow solution turns orange with H+(aq); gives yellow ppt. with Ba2+(aq); gives bright yellow ppt. with Pb2+(aq) chloride, Cl– (aq) gives white ppt. with Ag+(aq) (soluble in NH3(aq)); gives white ppt. with Pb2+(aq) bromide, Br– (aq) gives cream ppt. with Ag+(aq) (partially soluble in NH3(aq)); gives white ppt. with Pb2+(aq) iodide, I– (aq) gives yellow ppt. with Ag+(aq) (insoluble in NH3(aq)); gives yellow ppt. with Pb2+(aq) nitrate, NO3 – (aq) NH3 liberated on heating with OH–(aq) and Al foil nitrite, NO2 – (aq) NH3 liberated on heating with OH–(aq) and Al foil; NO liberated by dilute acids (colourless NO → (pale) brown NO2 in air) sulfate, SO4 2– (aq) gives white ppt. with Ba2+(aq) or with Pb2+(aq) (insoluble in excess dilute strong acid) sulfite, SO3 2– (aq) SO2 liberated with dilute acids; gives white ppt. with Ba2+(aq) (soluble in excess dilute strong acid) 3 Tests for gases gas test and test result ammonia, NH3 turns damp red litmus paper blue carbon dioxide, CO2 gives a white ppt. with limewater (ppt. dissolves with excess CO2) chlorine, Cl2 bleaches damp litmus paper hydrogen, H2 “pops” with a lighted splint oxygen, O2 relights a glowing splint sulfur dioxide, SO2 turns acidified aqueous potassium dichromate(VI) from orange to green

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16 9701/34/O/N/10 © UCLES 2010 BLANK PAGE Permission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort has been made by the publisher (UCLES) to trace copyright holders, but if any items requiring clearance have unwittingly been included, the publisher will be pleased to make amends at the earliest possible opportunity. University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge Local Examinations Syndicate (UCLES), which is itself a department of the University of Cambridge.

UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS GCE Advanced Subsidiary Level and GCE Advanced Level MARK SCHEME for the October/November 2010 question paper for the guidance of teachers 9701 CHEMISTRY 9701/34 Paper 3 (Advanced Practical Skills), maximum raw mark 40 This mark scheme is published as an aid to teachers and candidates, to indicate the requirements of the examination. It shows the basis on which Examiners were instructed to award marks. It does not indicate the details of the discussions that took place at an Examiners’ meeting before marking began, which would have considered the acceptability of alternative answers. Mark schemes must be read in conjunction with the question papers and the report on the examination. • CIE will not enter into discussions or correspondence in connection with these mark schemes. CIE is publishing the mark schemes for the October/November 2010 question papers for most IGCSE, GCE Advanced Level and Advanced Subsidiary Level syllabuses and some Ordinary Level syllabuses.

Page 2 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 Question Sections Indicative material Mark 1 (a) PDO layout I Volume given for Rough titre and accurate titre details tabulated. 1 MMO Collection II In the correct spaces, records initial and final burette readings for Rough titre and; Initial and final burette readings and, volume of FB 2 added recorded for each accurate titre Headings should match readings. Do not award this mark if: 50(.00) is used as an initial burette reading; More than one final burette reading is 50.(00); Any burette reading is greater than 50.(00) 1 MMO Decisions III Has two uncorrected, accurate titres within 0.1 cm3 Do not award this mark if having performed two titres within 0.1 cm3 a further titration is performed which is more than 0.10 cm3 from the closer of the initial two titres, unless a fourth titration, within 0.1 cm3 of the third titration or of either of the pair has also been carried out. 1 PDO Recording IV All accurate burette readings (initial and final) recorded to nearest 0.05 cm3. Assessed on burette readings only. 1 MMO Quality V, VI and VII Round any burette readings to the nearest 0.05 cm3. Check and correct subtractions in the titre table. Select the “best” titre using the hierarchy: two identical; titres within 0.05 cm3, titres within 0.10 cm3 etc. Award V, VI and VII for a difference to Supervisor within 0.15 cm3 Award V and VI only for a difference of 0.15+ cm3 – 0.25 cm3 Award V only for a difference of 0.25+ cm3 – 0.40 cm3 If the selected “best” titres are > 0.40 cm3 apart, cancel one of the Q marks awarded. 3 [7]

Page 3 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 (b) ACE Interpretation Calculates the mean, correct to 2 decimal places (third decimal place rounded to the nearest 0.05 cm3) from any accurate titres within 0.20 cm3. A mean of exactly .x25 or .x75 is allowed but the candidate may round up or down to the nearest 0.05 cm3. If ALL burette readings are given to 1 decimal place then the mean can be given to 1 decimal place if numerically correct without rounding. Mean of 24.3 and 24.4 = 24.35 (✓) Mean of 24.3 and 24.4 = 24.4 () Titres to be used in calculating the mean must be clearly shown – in an expression or ticked in the titration table. 1 [1] (c) ACE Interpretation No additional factor/expression is allowed in any step If an answer, with no working, is given in any section allow if correct. I Uses 2.00/158.0 in step (i) and answer (i) × cand titre/1000 in step (ii) 1 PDO Display II Uses answer (ii) × 5 in step (iii) and answer (iii) × 1000/25 in step (iv) 1 III Uses answer (iv) × 151.9 in step (v), and answer (v) × 100/21.50 in step (vi) 1 IV Appropriate working shown in a minimum of four sections. 1 V 3 to 5 significant figures in final answers to all sections attempted – minimum of four final answers required 1 [5] [Total: 13]

Page 4 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 2 (a) PDO Layout I Records at least four different balance readings and at least one mass of solid/gas Accept 0.0(0X) g as the mass of the empty tube or a statement that the tube is tared. 1 PDO Recording II Gives all appropriate headings and units when recording results. Do not accept mass of empty tube as 0.0(00)g here unless tube is described as tared. (minimum of three pieces of information) 1 III All recorded balance readings consistent to at least 1 decimal place. (minimum of three balance readings) 1 MMO Decisions IV Evidence of reheating to “constant” mass. For balances reading to 1 d.p. two masses must be identical For 2 or 3 d.p. balances, two masses must be within 0.05 g 1 MMO Quality V and VI checks and corrects if necessary all subtractions in the results table. Calculate mass heated/mass of residue to 3 significant figures. Compare to supervisor standard or standard value of 1.40. Award V and VI for a difference up to 0.10 Award V only for a difference of 0.10+ to 0.20 Where a candidate repeats the experiment use cumulative masses of FB 3 and residue. Where masses of FB 3 and residue cannot be checked, accept candidate values to calculate the ratio. 2 [6] (b) ACE Interpretation ACE Conclusions (i) Calculates 2.71, (2.710, 2.7097) and (ii) Has: cand value in (i) x mass loss from table in (a) If no mass loss is recorded in the table, check the value used. (iii) Ticks the appropriate box for the experiment and makes some comparison between mass of NaHCO3 and the mass of FB 3 used If mass of NaHCO3 calculated in (ii) ≥ mass of FB 3, ignore any ticked box but award the mark for any statement that the mass is not possible. 1 1 [2]

Page 5 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 (c) ACE Improvements (i) No mass change with Na2CO3 (on heating). (ii) Evidence for no gas produced, e.g.: limewater unaffected, no gas collected in a gas syringe If there is reference to measuring mass and to measuring volume but the absence of change is not mentioned, award one of the two marks available. 1 1 [2] (d) ACE Interpretation Max errors of 0.05, 0.005 and 0.0005 respectively for balances A, B and C. Calculates: 1.11% error for balance A 0.25% error for balance B 0.20% error for balance C Allow ecf on % errors only if: (i) Max errors given are 0.1, 0.01 and 0.001 respectively for balances A, B and C and % errors are 2.22%, 0.50% and 0.40% (ii) All max errors are incorrect by a factor 10 e.g. 0. 5, 0. 05 and 0. 005. % errors are 11.1%, 2.5% and 2.0% 1 1 [2] [Total: 12]

Page 6 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 FB 4 is MnSO4(aq); FB 5 is MgSO4(aq); FB 6 is Al2(SO4)3(aq); FB 7 is (NH4)2SO4(aq) 3 (a) MMO Collection Give one mark for each of the following: I for FB 4 – tests (i) and (iv) II for FB 5 – tests (i) and (iv) III for FB 6 – tests (i) and (iv) IV for FB 7 – tests (i), (iii) and (iv) V Give one mark for any change/darkening of the initial precipitate in test (ii) for FB 4 to a qualified brown. The darkening may be described in test (i) or in test (iv) VI Describes the test on gas for ammonia in test (iii) for any solution that has no precipitate in either part test of (i) and is warmed. The test for ammonia is expected with FB 7 Do not award (VI) if the test is carried out with a solution in which a precipitate had formed at any stage or If a solution in which no precipitate is formed is not warmed with sodium hydroxide 1 1 1 1 1 1 [6] Results required with NaOH(aq) and NH3(aq) for the award of marks I to IV in 3(a) observations test FB 4 FB 5 FB 6 FB 7 (i) addition of NaOH off-white, pale brown, buff or beige precipitate Do not accept cream or equivalent colour precipitates white precipitate white precipitate No precipitate or no change Do not accept clear on its own as an observation; clear solution is acceptable further addition of NaOH precipitate insoluble precipitate insoluble precipitate soluble no precipitate or no change (may be left blank) (iii) warming solution with NaOH any reference to a gas being evolved or reference to red litmus turning blue (iv) addition of NH3 as NaOH as NaOH as NaOH as NaOH further addition of NH3 as NaOH as NaOH precipitate insoluble as NaOH

Page 7 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 (b) ACE Conclusions Do not accept any ion other than Mn2+, Mg2+, Al3+or NH4 + in any section. Marks I to III Ions must be correct, including charge, if a symbol has been given. – no ecf in this section. Award I only if one ion only is identified from correct observations. Award I and II if two ions only are identified from correct observations. Award I, II and III if all four cations are identified from correct observations. The 4th cation may be identified by elimination from incomplete supporting evidence. A deduction of Mn2+ is allowed from a cream ppt with NaOH(aq) and NH3(aq) IV Award this mark if the supporting evidence fits the ion identified and the practical performed for at least three of the four ions Allow ecf on ion order for mark IV. (Mg2+ and Al 3+ are most likely to be interchanged depending on “solubility in excess” observations. 1 1 1 1 [4] Minimum evidence required in observations for the ion identity marks I, II and III. In some cases, identification may be allowed from incomplete observations. There must, however, be no observations that are contrary to those expected with any “correctly” identified ion. The same criteria will be applied to “candidate’s supporting evidence in awarding mark IV. Candidates are not permitted to introduce (from the Qualitative Analysis Notes) supporting evidence that is not given in the observations. Mn2+ off-white precipitate with each reagent, or off-white precipitate turning brown with either of the reagents identification of the ion is allowed from an incorrect observation of a cream or yellow-white precipitate – one ion is known to be Mn2+ Mg2+ white precipitate, insoluble in (excess) NaOH Al 3+ white precipitate, soluble in (excess) NaOH NH4 + no precipitate/no change with either reagent or ammonia, alkaline gas or gas turning red litmus blue evolved

Page 8 Mark Scheme: Teachers’ version Syllabus Paper GCE A/AS LEVEL – October/November 2010 9701 34 © UCLES 2010 (c) MMO Collection Records no precipitate/no reaction with each of the reagents. 1 [1] (d) ACE Conclusions States that Pb2+/lead(II) would give similar results. Award this mark providing there are no contrary observations for the solution identified as containing Al 3+ 1 [1] (e) MMO Collection Records a white ppt in (i) Records a yellow precipitate or precipitate turning yellow in (ii). 1 1 [2] (f) ACE Conclusions Award one mark for any attempt to describe replacement of Cl by I in the ppt. 1 [1] [Total: 15]