JF Physial Chemistry 010-011. JF CH 1101: Introdution to Physial Chemistry. Dr Mike Lyons. Shool of Chemistry Trinity College Dublin. melyons@td.ie A ompendium of past examination questions set on Physial Chemistry on the JF Chemistry paper and problem sheets assoiated with CH1101 Physial Chemistry (Lyons). This booklet has been produed to provide JF Chemistry students with a full seletion of problems in basi Physial Chemistry set by the author over the last few years. These problems have appeared in the Annual, and the Supplemental examination papers in Chemistry set by the Examination Board of the Shool of Chemistry, University of Dublin, Trinity College. They are made available to Trinity JF Chemistry students to assist them in their revision of the basi Physial Chemistry letures on properties of Gases, Thermodynamis, Equilibria and Eletrohemistry delivered by Dr Lyons in the first semester to students taking CH 1101. I hope that you will find it a useful self learning and revision aid. Mike Lyons 1 September 010
JF Chemistry Module CH1101. 009 MCQ Semister 1 Test 1. Consider the synthesis of ammonia whih proeeds aording to the following reation: ½ N (g) + 3/ H (g) NH 3 (g). If the standard hange in Gibbs energy for the reation is given by Δ r G 0 = - 16,370 J mol -1 at T = 98 then the equilibrium onstant for the reation is: (a) 7.38 x 10 (Answer) (b) 7.38 x 10 - () 0.1 (d) 100 (e) there is insuffiient data supplied to answer the question. You may assume that the gas onstant R = 8.314 J mol -1-1.. In air at 98 whih gas has the lowest average root mean square speed? (a) H O(g) ; (b) CO (g) (Answer) ; () CO(g) ; (d) Ne(g) ; (e) CH 4 (g). 3. For ideal gases whih of the following statements are orret? i. At onstant temperature, the volume of a fixed mass of gas is proportional to the external pressure. ii. iii. iv. At onstant external pressure and temperature, when 1L of N reats with L of O, L of NO are formed At a given temperature and external pressure, equal volumes of any ideal gas ontain the same number of moleules At a given temperature, the moleules in any ideal gas have the same average veloity v. At a given pressure and temperature, the mean-free path of a gas is independent of the volume of the ontaining vessel a) (ii) and (iii) b) (i), (iii) and (v) ) (ii) and (iii)
d) (ii) and (v) e) (ii), (iii) and (v) (Answer) Setion A Long Questions 009 Annual (a) (b) Briefly disuss the onept of ph as applied to aqueous solutions paying attention to its definition and measurement. Draw the shape expeted for the titration urve expeted for a titration of a strong aid by a strong base and between a weak aid and a strong base. You should desribe features of interest assoiated with eah of these titration urves. Consider the titration of 100 ml of 0.1 M aeti aid with 0.1 M NaOH. (i) What is the ph of the solution when 90 ml of 0.1 M NaOH has been added to 100 ml of 0.1 M aeti aid. (ii) Determine the ph at the equivalene point. (iii) What is the ph after 110 ml of 0.1 M NaOH has been added. Supplemental (a) (b) () (d) Define the terms oxidation, redution, galvani ell, eletrolysis ell. Desribe using a suitable example, with a labelled diagram and pertinent hemial equations, how a fuel ell operates. Derive and state the relationship between the hange in Gibbs free energy ΔG and the open iruit ell potential E ell. Calulate the equilibrium onstant at 98 for the reation Fe s Cd aq Fe aq Cd s + + ( ) + ( ) ( ) + ( ) given that the standard redution potentials are E 0 (Cd +,Cd)= -0.40 V and E 0 (Fe +,Fe) =- 0.44 V. Is the reation strongly produt favoured?
Setion B MCQ 009 Annual 1. Consider the following reation: N (g)+3h (g) NH (g). At 3 equilibrium at a ertain temperature the onentrations of NH3 (g), H (g) and N (g) are 0.94 M, 1.60 M and 0.5 M respetively. The numerial value of the equilibrium onstant for the reation is: (a) 0.415 ; (b) 1.13; () 1.06; (d) 0.664; (e) 1.7. Corret answer: a.. Calulate the onentration of OH - ion for an aqueous solution with a ph of 9.45. Note that the ion produt of water w = 1 x 10-14. (a) 1.8 x 10-10 M ; (b) 1.0 x 10-14 M ; ().8 x 10-5 M ; (d) 0.35 M ; (e) 3.5 x 10-10 M. Corret answer: 3. A buffer ontains equal onentrations of a weak aid HA and its onjugate base A -. If the value of A for the weak aid is 1.0 x 10-9, what is the ph of the buffer? (a) 9.0 ; (b) 5.0 ; () 1.0; (d) 13.0 ; (e) 7.0. Corret answer: a. 4. If the standard potential E 0 is 0.56 V at 98 for the ell reation: Cr O ( aq) + 6Fe (aq)+14h (aq) Cr (aq)+6fe (aq)+7h O(l) alulat + + 3+ 3+ 7 e the equilibrium onstant for the reation. (a) 6. x 10 56 ; (b) 37.8 ; ().9 x 10 9 ; (d).5 x 10 8 ; (e) 1.4 x 10 3. Corret answer: a. Supplemental 1. Consider the reation: N (g)+3h (g) NH (g). If the standard 3 molar free energy of formation of NH3(g) at 98 is 16.45 kj mol -1, alulate the equilibrium onstant for this reation at 98. (a) 3.6 x 10 - ; (b) 1.66 x 10-3 ; () 5.6 x 10-14 ; (d) 1.71 x 10-6 ; (e).9 x 10-7. Corret answer: d.. The ph of 0.1 M CH 3 COOH is.87. What is the value of A for CH 3 COOH? (a) 1.3 x 10-3 ; (b) 1.8 x 10-6 ;() 1.8 x 10-5 ; (d) 0.037; (e).7 x 10-6. Corret answer:. 3. The onjugate base of HSO - 4 is: (a) OH - ; (b) SO - 4 ; () H SO 4 ; (d) HSO - 4 (e) H O. Corret answer: b.
+ 4. The standard potential of the Ag Ag redox ouple is + 0.80 V and the standard potential of the ell + + Fe(s)Fe (aq) Ag (aq)ag(s)is + 1.4 V. What is the standard potential of the + Fe Fe redox ouple? (a).04 V ; (b) 0.44 V; ().04 V ; (d) + 0.44 V ; (e) 0.88 V. Corret answer: b.
JF Chemistry Module CH 1101 010. Dr Mike Lyons Setion A Long Questions 010. Annual. 1. Answer either : part (a) and part (b) or part () and part (d). a. What is the internal energy U and the enthalpy H of a system? Write down an expression for the First Law of Thermodynamis whih relates the hange in internal energy of a system to the work done on the system and the heat absorbed by the system. Hene derive a relationship between the hange in internal energy ΔU and the hange in enthalpy ΔH of a system. b. A gas absorbs 300 J of heat and at the same time expands by 1 dm 3 against a onstant pressure of 1 atm. What is the hange in internal energy ΔU and hange in enthalpy ΔH of the system.. Define the term heat apaity and briefly desribe using a labelled diagram and any equations where pertinent how the bomb alorimeter an be used to measure the hange in internal energy of ombustion of a material. d. Inside in a bomb alorimeter, 1.0 g of otane C 8 H 18 ombusts in oxygen to form arbon dioxide and water aording to the expression CH + 5/ O 8CO + 9HO. The temperature was 8 18 observed to rise from 5.00 to 33.0 C. The alorimeter ontained 100 g of water (speifi heat apaity of water = 4.184 Jg -1-1 ) and the heat apaity of the bomb is 837 J -1. Calulate the internal energy of ombustion of otane.. Answer all parts. (a) Briefly explain using speifi examples and learly labelled diagrams how a Galvani (Voltai) ell and how a Polymer Membrane Eletrolyte (PEM) fuel ell operates. (b) The net reation that ours in a voltai ell is + + Zn() s + Ag ( aq) Zn ( aq) + Ag() s. Write down the half reations that our at the anode and athode. If the standard
redution potentials at 98 are E 0 (Ag +,Ag)=0.799V and () E 0 (Zn +,Zn) = - 0.763V, alulate the voltage developed by the ell, the hange in reation Gibbs energy ΔG 0 and the equilibrium onstant for the ell reation. Is the reation strongly produt favoured? Consider a galvani ell involving the following half-reations: Ni + (aq) + e - Ni(s), E 0 (Ni +,Ni) = - 0.5 V; Cr 3+ (aq) + 3e - Cr(s), E 0 (Cr 3+,Cr) = - 0.74 V. Calulate the ell potential observed at a temperature of 98 when [Ni + ] = 1.0 x 10-4 M and [Cr 3+ ] =.0 x 10-3 M. Supplemental 010. 1. (a) (b) A strip of magnesium metal of mass 1.5 g is dropped into a beaker of dilute hydrohlori aid. Given that the Mg is the limiting reatant, alulate the work done by the system as a result of the reation. The atmospheri pressure is 1 atm and the temperature is 93.. If the enthalpy of ombustion of solid itri aid is 1986 kj mol-1, alulate the heat liberated when 10 g of solid itri aid undergoes total ombustion at 98 : (i) at onstant pressure, (ii) at onstant volume. Note: itri aid has formula C6H8O7. The molar mass M = 19 g mol-1. Total ombustion means reation with O and onversion to CO and HO.. Answer four parts. (a) What do you understand by the terms weak aid and solution ph? Provide an example of a weak aid and indiate the way that the aid strength of a weak aid an be quantified. (b) Calulate the ph of a 5.0 x 10 - M NaOH solution given the information that w = 1.0 x 10-14. () Calulate the H 3 O + ion onentration and the ph of a 0.003 M Ba(OH) solution assuming that the ion produt w = 1.0 x 10-14. (d) Derive an expression for the ph of an aqueous solution of weak aid HA of onentration and having an aid dissoiation
onstant A. If A is assumed to be very small derive an approximate expression for the solution ph mentioning any approximations whih you make. (e) Use the theoretial results derived in part (d) to alulate the ph of a weak aid solution of onentration 0.1 M and having an aid dissoiation onstant A = 3.5 x 10-8. Setion B MCQ. Annual. 1. Whih of the following graphs does not give a straight line for an ideal gas? (a) V versus T, (b) T versus P, () P versus 1/V, (d) n versus 1/T, (e) n versus 1/P. (orret answer option (e)).. Whih of the following statements is always true for an ideal gas? (a) If the temperature and volume of a gas both inrease at onstant pressure, the amount of gas must also inrease. (b) If the pressure inreases and the temperature dereases for a onstant amount of gas, the volume must derease. () If the volume and the amount of gas both derease at onstant temperature, the pressure must derease. (Corret answer option (b)). 3. A solution has a hydrogen ion onentration of 0.001 M. Whih of the following statements are orret? (i) The solution ph is 3.0. (ii) The solution is aidi. (iii) The hydroxide ion onentration is 1.0 x 10-11. Note that w = 10-14. (a) All statements are orret. (b) (i) only. () (i) and (ii) only. (d) (iii) only. (e) None of the statements are orret. (Corret answer option (a)). 4. Given that a (aeti aid) = 1.80 x 10-5 and W = 1.0 x 10-14 then the ph of an 0.89 M solution of sodium aetate is : (a) 9.35, (b) 7.0, () 5.0, (d) 13.0 and (e) 3.0. (Option (a) is orret).
5. The Galvani ell + + Cu Cu ( aq) Ag ( aq) Ag is based on the following + + ell reation: Ag ( aq) + Cu( s) Ag( s) + Cu ( aq). Note that T = 98 and the standard eletrode potentials are 0 E ( Cu +, Cu) = 0.34V and 0 + E ( Ag, Ag) = 0.80V. Whih of the following statements are orret? (i) The silver eletrode is the athode and the opper eletrode is the anode. (ii) Two moles of eletrons flow through the external iruit from anode to athode when the ell operates. (iii) The observed ell potential is 0.46 V. (iv) The hange in Gibbs energy for the ell reation is -88,766 J mol (a) All statements are orret. (b) (i) only. () (i) and (ii) only. (d) (iii) and (iv) only. (e) None of the statements are orret. (Option (a) is orret). 6. Whih of the following statements pertaining to ideal gases are orret? (i) The average kineti energy of a gas moleule is proportional to the absolute temperature T of the gas sample. (ii) The ratio of the veloities by whih two different types of ideal gas v m moleules A and B move is given by A = B where m and v vb ma denote the mass and veloity of the moleules. (iii) The average veloity of a H moleule at 73 is 000 ms -1 if the average veloity of an O moleule at this temperature is 500 ms -1. (iv) The heavier the gas moleule is the quiker it travels through the ontainer. (a) All statements are orret. (b) (i), (ii) and (iii) are orret. () (iv) is orret. (d) (iii) is orret. (e) None of the statements are orret. (Option (b) is orret). -1.
7. Whih of the following is the orret expression for the equilibrium onstant for the reation: NO( g) NO( g) + O( g) (a) [ NO ] [ NO][ O ] =, (b) [ NO][ O ] [ ] NO =, () [ NO ] [ NO] [ O ] =, (d) [ NO] [ O ] [ NO ] =, (e) = [ NO] [ O ] [ NO ] (Option (d) is orret). Supplemental. 1. Whih of the following graphs does not give a straight line for an ideal gas? (a) P versus V, (b) P versus T, () V versus T, (d) Average kineti energy vs T, (e) P versus n. (orret answer option (a)).. The equilibrium onstant for the reation of hydrogen gas and ethene to produe ethane under ertain onditions is 9.8 x 10 18. H (g) + C H 4 (g) C H 6 (g) = 9.8 x 10 18. What is the equilibrium onstant for the following reation C H 6 (g) H (g) + C H 4 (g) under the same onditions? (a) 9.8 x 10 18. (b) 4.9 x 10 18. () 1.9 x 10 19. (d) 9.8 x 10-18. (e) 1.0 x 10-19. (Corret answer : option (e)). 3. The thermodynami equilibrium onstant for the following reation SO (g) + O (g) SO 3 (g) is 0.15 at 17 C. Whih of the following statements are true? (i) The reation is strongly produt favoured. (ii) The reation is reatant favoured. (iii) The hange in Gibbs energy is negative. (iv) The hange in Gibbs energy is 3.66 kj mol -1. (a) All statements are orret. (b) (i) is orret. () (ii) and (iv) are orret. (d) (iii) is orret. (e) None of the statements are orret. (Corret option : answer ()).
4. Whih of the following statements pertaining to aids and bases are orret? (i) Aids are speies whih aept protons. (ii) Aid solutions have a ph value greater than 7. (iii) bases are speies whih donate protons. (iv) The ph of a base solution is less than 7. (v) The weaker the Bronsted Lowry aid the stronger is the onjugate base. (a) All statements are orret. (b) None of the statements are orret. () (i) and (ii) are orret. (d) (v) is orret. (e) (iii) and (iv) are orret. (Corret answer: option (d)). 5. The Galvani ell Zn Zn + ( aq) Cu + ( aq) Cu is based on the + + following ell reation: Cu ( aq) + Zn( s) Cu( s) + Zn ( aq). Note that T = 98 and the standard eletrode potentials are 0 E ( Cu +, Cu) = 0.34V 0 and E ( Zn +, Zn) = 0.76V. Whih of the following statements are orret? (i) The opper eletrode is the athode and the zin eletrode is the anode. (ii) Two moles of eletrons flow through the external iruit from anode to athode when the ell operates. (iii) The observed ell potential is 1.10 V. (iv) The hange in Gibbs energy for the ell reation is -1,300 J mol -1. (a) All statements are orret. (b) (i) only. () (i) and (ii) only. (d) (iii) and (iv) only. (e) None of the statements are orret. (Option (a) is orret). 6. Whih of the following is the orret expression for the equilibrium onstant for the reation: A( g) B( g) + C( g) (a) [ A] [ B][ C] =, (b) [ B][ C] [ A] =, () [ A] [ B] [ C] =,
(d) [ B] [ C] [ A] =, (e) [ B] [ O ] [ A] =. (Corret option = (d)). 7. On the spae shuttle, the arbon dioxide produed by the astronauts is handled by an environmental ontrol system that utilizes the following reation.. If the standard hange in enthalpy and entropy for the reation are H = -138.4 kj and S = -139 J/, then the standard hange in Gibbs energy G at 98 for this reation is : (a) 4.13 x 10 4 kj. (b) -135 kj. () 180 kj. (d) 97.0 kj. (Corret answer option (d)).
JF Chemistry Module CH1101. Dr Mike Lyons, Shool of Chemistry, Trinity College Dublin. Email: melyons@td.ie Problem Sheet 1. Introdution to Physial Chemistry: Gas Laws and Chemial Thermodynamis. 1. A 1x10 3 L steel storage tank ontains 88.5 kg of methane CH 4. If the temperature of the gas is 98 determine the pressure inside the tank.. A sample of helium gas is held at onstant temperature inside a ylinder of volume 0.80 L, where a piston exerts a pressure of 1.5 x 10 5 Pa. If the external pressure on the piston is inreased to.1 x 10 5 Pa, what will the new volume of the gas be? 3. Calulate the work done by a system in whih a reation results in the formation of 1 mol CO gas at 98 and 100 kpa. Assume that CO behaves as an ideal gas. 4. Calulate the work done when 1 mol Ar gas onfined in a ylinder of volume 1 dm3 at 98 expands isothermally and reversibly to dm3. 5. A strip of magnesium metal of mass 1.5 g is dropped into a beaker of dilute hydrohlori aid. Given that the Mg is the limiting reatant, alulate the work done by the system as a result of the reation. The atmospheri pressure is 1 atm and the temperature is 93..
6. A system absorbs 300 J of heat and at the same time expands by 1 dm3 against a onstant pressure of 1 atm. Determine the hange in internal energy and enthalpy in the system. Note that 1 atm = 1.013 x 105 Nm-. 7. If the enthalpy of ombustion of solid itri aid is 1986 kj mol-1, alulate the heat liberated when 10 g of solid itri aid undergoes total ombustion at 98 : (i) at onstant pressure, (ii) at onstant volume. Note: itri aid has formula C6H8O7. The molar mass M = 19 g mol-1. Total ombustion means reation with O and onversion to CO and HO. Problem Sheet. Introdution to Physial Chemistry: Gas Laws and Chemial Thermodynamis. 1. Calulate the mole fration of N, O and Ar in dry air at sea level, given that 100g of air onsists of 75.5 g of N, 3. g O and 1.3 g Ar.. Determine the mean free path of oxygen moleules in a sample of oxygen at SATP (98, 1 bar) given that the ollision ross setion of oxygen is = 0.4 nm. 3. In an experiment to measure the heat released by the ombustion of a sample of nutrient, the ompound was burned in a alorimeter and the temperature was observed to rise by 3. C. When a urrent of 1.3 A from a 1 V soure flows through a heater in the same alorimeter for a time of 156 s, the temperature rose by 4.47 C. What is the heat released by the ombustion reation?
4. Show that the differene in molar heat apaities for a perfet gas is given by: C C = R. Pm, V, m 5. Ethanol C H 5 OH is brought to the boil at 1 atm. When an eletri urrent of 0.68 A from a 1 V supply is passed for 500s through a heating oil immersed in the boiling liquid, it is found that the temperature remains onstant but 4.33 g of ethanol is vaporized. What is the enthalpy of vaporization of ethanol at its boiling point at 1 atm? 6. The standard enthalpy of formation of gaseous water at 98 is - 41.8 kj mol -1. Estimate its value at 373. Note that the molar heat apaities at onstant pressure for H O(g), H (g) and O (g) are 33.58 J -1 mol -1, 8.84 J -1 mol -1, and 9.37 J -1 mol -1 respetively. 7. Calulate the hange in molar entropy when a sample of hydrogen gas expands isothermally to twie its initial volume. 8. Calulate the hange in molar entropy when hydrogen gas is heated from 93 to 303 at onstant volume. The molar heat apaity at onstant volume for hydrogen is.44 J -1 mol -1. 9. Suppose a ertain small bird has a mass of 30g. what is the minimum mass of gluose that it must onsume to fly to a branh 10 m above the ground? The hange in Gibbs energy the oxidation of 1 mol gluose (C 6 H 1 O 6 ) to arbon dioxide and water vapour at 98 is 88 kj. 10. Estimate the omposition of a solution in whih two isomers A and B are in equilibrium A B at 37 C assuming that Δ r G 0 = -. kjmol -1.
11. Calulate the equilibrium onstant of the reation N (g)+3h (g) NH 3 (g) at 98 given that the hange in standard Gibbs energy for the reation is 3.90 kjmol -1. 1. Suppose that in an industrial proess N at 1.00 bar is mixed with H at 3.00 bar and the two gases are allowed to ome to equilibrium with the produt ammonia in a reator at onstant volume in the presene of a atalyst. At the temperature of the reation it has been determined experimentally that the equilibrium onstant = 977. What are the partial pressures of the three gases at equilibrium? Problem Sheet 3. Chemial Equilibria and Eletrohemistry 1. a. What do you understand by the terms weak aid and solution ph? Provide an example of a weak aid and indiate the way that the aid strength of a weak aid an be quantified. b. Calulate the ph of a 5.0 x 10 - M NaOH solution given the information that w = 1.0 x 10-14.. Calulate the H 3 O + ion onentration and the ph of a 0.003 M Ba(OH) solution assuming that the ion produt w = 1.0 x 10-14. d. Derive an expression for the ph of an aqueous solution of weak aid HA of onentration and having an aid dissoiation onstant A. If A is assumed to be very small derive an approximate expression for the solution ph mentioning any approximations whih you make.
e. Use the theoretial results derived in part to alulate the ph of a weak aid solution of onentration 0.1 M and having an aid dissoiation onstant A = 3.5 x 10-8. f. Explain using hemial equations where pertinent, the observation that the ph of an aqueous sodium aetate solution is alkaline whereas the ph of an ammonium hloride solution is aidi. g. Explain using an example how a buffer solution works and derive an expression for the ph of a buffer solution ontaining a weak aid HA and its onjugate base A -. Use this expression to alulate the ph of a solution ontaining 0.75 M lati aid ( A = 1.4 x 10-4 ) and 0.5 M sodium latate.. a. What do you understand by the terms equilibrium onstant and reation quotient Q. b. Derive an expression whih relates the hange in reation Gibbs energy ΔG to the equilibrium onstant and the reation quotient Q aording to: G RTln Q Δ =. Indiate how this expression may be used to relate the sign of ΔG (and hene to the question of whether the reation ours in a spontaneous or non spontaneous manner) to the relative magnitudes of Q and.. The standard hange in Gibbs energy for a hemial reation at a temperature of 98 is 150 kj mol -1. Determine the equilibrium onstant of the reation. d. The following equation N( g) + O( g) NO( g) desribes the formation of NO whih ontributes to air pollution whenever a fuel is burnt in air in a losed ontainer at a high temperature as in a gasoline engine. At 1500 the equilibrium onstant = 1 x 10-5. Suppose that a sample
of air has [N ] = 0.80 mol dm -3 and [O ] = 0.0 mol dm -3 before any reation ours. Calulate the equilibrium onentrations of reatants and produts after the mixture has been heated to 1500. 3. a. Briefly explain using speifi examples and learly labelled diagrams how a Galvani (Voltai) ell and how a Polymer Membrane Eletrolyte (PEM) fuel ell operates. b. The net reation that ours in a voltai ell is + + Zn() s + Ag ( aq) Zn ( aq) + Ag() s. Write down the half reations that our at the anode and athode. If the standard redution potentials at 98 are E 0 (Ag +,Ag)=0.799V and E 0 (Zn +,Zn) = - 0.763V, alulate the voltage developed by the ell, the hange in reation Gibbs energy ΔG 0 and the equilibrium onstant for the ell reation. Is the reation strongly produt favoured?. Consider a galvani ell involving the following halfreations: Ni + (aq) + e - Ni(s), E 0 (Ni +,Ni) = - 0.5 V; Cr 3+ (aq) + 3e - Cr(s), E 0 (Cr 3+,Cr) = - 0.74 V. Calulate the ell potential observed at a temperature of 98 when [Ni + ] = 1.0 x 10-4 M and [Cr 3+ ] =.0 x 10-3 M. d. In a large number of samples of water in whih the opper ion onentration is expeted to be quite small, the [Cu + ] was measured using an eletrohemial ell. This setup onsisted of a silver eletrode dipping into a 1.0 M solution of AgNO 3, whih was onneted by a salt bridge to a seond ompartment ontaining a opper eletrode. The opper ompartment was then filled with one water sample after another and the ell potential was measured for eah sample. In the analysis of one partiular sample the ell potential at 98 was measured as 0.6 V, with the opper eletrode being the anode. What was the
onentration of Cu + ion in this sample. Note that the relevant redution potentials are E 0 (Cu +, Cu) = 0.34 V and E 0 (Ag +, Ag) = 0.80 V. e. What mass of opper is deposited on the athode of an eletrolyti ell if an eletri urrentof A is passed through a solution of CuSO 4 for a period of 0 min.