Jawab soalan mengikut arahan yang diberikan dalam setiap bahagian. Questions should be answered according to the instructions given in each section.

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1 UNIVERSITI MALAYA UNIVERSITY OF MALAYA PEPERIKSAAN IJAZAH SARJANA MUDA SAINS EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE PEPERIKSAAN IJAZAH SARJANA MUDA SAINS DENGAN PENDIDIKAN EXAMINATION FOR THE DEGREE OF BACHELOR OF SCIENCE WITH EDUCATION SESI AKADEMIK 2014/2015 : SEMESTER 1 ACADEMIC SESSION 2014/2015 : SEMESTER 1 SCES3130 : KIMIA FIZIK III PHYSICAL CHEMISTRY III Disember 2014/Januari 2015 December 2014/January 2015 Masa : 2 jam Time : 2 hours ARAHAN KEPADA CALON : INSTRUCTIONS TO CANDIDATES : Kertas soalan ini mengandungi Bahagian A, B dan C. This paper consists of Section A, B and C. Jawab soalan mengikut arahan yang diberikan dalam setiap bahagian. Questions should be answered according to the instructions given in each section. (Kertas soalan ini mengandungi 10 soalan dalam 11 halaman yang dicetak) (This question paper consists of 10 questions on 11 printed pages)

2 BAHAGIAN A (25MARKAH) SECTION A (25 MARKS) Jawab semua soalan. Simbol yang digunakan mempunyai maksud yang sama seperti diberikan dalam kuliah. 1. (a) Struktur di bawah merupakan unit ulangan bagi polimer komersial nilon-6, digunakan secara luas sebagai gentian dengan sifat mekanik yang kuat. Jika jisim purata nombor molekul suatu sampel itu adalah 500,000, kirakan purata darjah pempolimeran sampel itu. The structure below represents the repeating unit of a commercial nylon-6, Which is widely used as fiber of high mechanical strength. If the number average molecular weight of a polymer sample is 500,000, calculate the average degree of polymerization. NH (CH 2 ) 5 C O (4 markah/marks) (b) Suatu molekul polietilena mempunyai jisim molekul relatif Bentuk makromolekul itu boleh diwakili dengan model rambang koil. Sudut tetrahedron karbon adalah dan jarak ikatan C-C = nm, unit ulangan polietilena -CH 2 -CH 2 -, kirakan A polyethylene molecule has relative molecular weight of The structure of the macromolecule can be represented by the random coil model. Given the carbon tetrahedral angle of and the bond length of C-C being nm, the repeating unit -CH 2 -CH 2 -., calculate (i) (ii) (iii) panjang kontour rantai polimer itu the contour length of the polymer chain jarak hujung-ke-hujung punca-purata-kuasadua the root mean square end-to-end distance jarak pusat gravity ke segmen rantai punca-purata-kuasadua root-mean-square center of gravity to chain segment distance. (6 markah/marks) 2/11

3 2. (a) Diberi parameter keterlarutan bagi toluena dan sikloheksanon adalah masing-masing 18.2 dan 19.5 J 1/2 cm -3/2. Gunakan persamaan Hildebrand, kirakan jumlah perubahan haba apabila 500 cm 3 toluena dicampurkan dengan 500 cm 3 sikloheksanon. Bolehkah toluene larut dalam sikloheksanon? Given the solubility parameters for toluene and cyclohexanone are 18.2 dan 19.5 J 1/2 cm -3/2 respectively. Use the Hildebrand equation and calculate the total heat change when 500 cm 3 toluene is mixed with 500 cm 3 cyclohexanone. Can toluene dissolve in cyclohexanone? (b) Tulis nota pendek bagi salah satu (1) topik berikut. Write short note on one of the following topic. (i) (ii) Prinsip kromatografi telapan gel The working principle of gel permeation chromatography. M w dapat penghubungan lebih baik daripada M n kepada sifat mekanik sesuatu makromolekul. M w can correlate better than M n to the mechanical properties of a macromolecule. (c) Pilih satu (1) topik daripada yang berikut. Choose one of the following topic. (i) (ii) Bincangkan perbezaan utama antara lateks getah asli dan suatu lateks sinthetik. Discuss the main differences between natural rubber latex and a synthetic latex. Huraikan secara ringkas kegunaan lateks getah asli dalam industri. Describe briefly the uses of natural rubber latex in industry. 3/11

4 Jawab semua soalan dalam bahagian ini Answer all questions in this part. BAHAGIAN B (30 MARKAH) SECTION B (30 MARKS) 3. Pertimbangkan satu sistem tidak degenerat yang telah diusik yang mana tidak boleh diselesaikan secara tepat, persamaan Schrödinger tidak bersandar masa boleh ditulis sebagai berikut: Consider a non-degenerate perturbed system which is unsolvable exactly, its timeindependent Schrödinger can be written as follows: dimana where H ψ n = E n ψ n ψ n = ψ n (0) + λψ n (1) + λ 2 ψ n (2) + + λ k ψ n (k) +, E n = E n (0) + λe n (1) + λ 2 E n (2) + + λ k E n (k) +. ψ n (k) dan En (k) adalah pembetulan peringkat ke-k bagi fungsi gelombang dan tenaga. λ adalah satu parameter berjulat 0 ke 1. ψ n (k) and En (k) are the k-th order correction to the wave function and energy. λ is a parameter ranging from 0 to 1. (a) (b) (c) Tuliskan ψ n bila mana pengusikan ditutup. Write ψ n when the perturbation is turned off. Apakah nilai untuk k supaya ψ n akan menghampiri nilai tepat? What is the value for k so that ψ n will approach the exact value? Jika tenaga tidak diusik adalah x a.u. dan ψ n (0) H ψ n (0) dτ = 0.5x a.u. di mana H adalah pengusikan, tuliskan tenaga diusik dalam x dalam a.u.dengan menggunakan pembetulan peringkat pertama bila mana pengusikan dibuka secara penuh. If the unperturbed energy is x a.u. and ψ n (0) H ψ n (0) dτ = 0.5x a.u. where H is the perturbation, write the perturbed energy in terms of x in a.u. using the first order correction when the perturbation is fully turned on. (6 markah/marks) 4/11

5 4. Diagram paras tenaga bagi keadaan elektronik teruja pertama He ditunjukkan di bawah. The energy level diagram for the first excited electronic state of He is shown below. Energy (cm -1 ) (a) Pilih cuma satu daripada tiga orbital p. Kemudian, tuliskan secara lengkap fungsi-fungsi gelombang keadaan 1 P and 3 P. Apakah asas fizikal fungsifungsi gelombang ditulis seperti dalam bentuk-bentuk tersebut? Choose only one out of three p orbitals. Then, write explicity the correct zerothorder wave functions to represent 1 P and 3 P states. What is the physical basis the wave functions were written like in those forms? (b) Tuliskan semua kemungkinan nilai-nilai M dan M S untuk keadaan 3 P. Dengan menetapkan M J = 2, lukiskan satu gambarajah vektor bagi menunjukkan korelasi di antara tiga vektor momentum sudut L, S dan J dengan menggunakan nilai-nilai M dan M S tersebut. Write all possible values of M and M S for the 3 P state. Fixing M J = 2, draw a vector diagram to show a correlation between three angular momentum vectors L, S and J using the values of M and M S. (c) Apakah degenerasi bagi 3 P 2? Bagaimana degenerasi berkenaan boleh dihilangkan? What is the degeneracy of 3 P 2? How the degeneracy can be removed? (12 markah/marks) 5/11

6 5. Lengkungan tenaga keupayaan untuk beberapa keadaan elektronik H 2 + ditunjukkan di bawah. The energy level diagram for the first excited electronic state of He is shown below. 6/11

7 (a) Namakan penghampiran yang diguna yang membawa kepada pembentukan lengkungan tenaga keupayaan. Apakah asas fizikal penghampiran tersebut? Name the approximation used which leads to the construction of the potential energy curves. What is the physical basis of the approximation? (b) (c) (d) Keadaan pengujaan pertama H 2 + ditanda oleh dua simbol yang bersamaan bagi mewakili orbital molekul (MO) H 2 +. Dalam asas fizikal apakah simbol berkenaan ditentukan? The first excited state of H 2 + is denoted by two equivalent symbols to represent the molecular orbital (MO) of H 2 +. In what physical basis the symbol was determined? Lukis orbital-orbital yang mewakili kombinasi linear orbital atom (LCAO) bagi membentuk MO keadaan pengujaan kedua H 2 +. Draw orbitals to represent the linear combination of atomic orbital (LCAO) to form the MO in the second excited state of H 2 +. Bincangkan semua simetri terlibat dalam MO yang dilukis dalam 3(c). Discuss all the symmetry involved in the MO drawn in 3(c). (12 markah/marks) 7/11

8 BAHAGIAN C (45 MARKAH) SECTION C (45 MARKS) Jawab SEMUA soalan. Answer ALL questions. Mekanik Statistik/Statistical Mechanics 6. Takrifkan kuantiti-kuantiti tersebut: Define the following quantities (i) (ii) Fungsi sekatan secara umumnya dari segi tenaga dan kedegeneratan, dan hubungan di antara fungsi sekatan molekul dan sistem. The partition function in general in terms of the energy levels and degeneracies, and the relationship between the molecular and system partition functions. Taburan kuantum Boltzmann, dari segi tahap tenaga dan kedegeneratan dan fungsi sekatan. The quantum Boltzmann distribution, in terms of the energy level and degeneracies and partition function. m 7. Apakah makna p i dalam ungkapan entropi S = k i=1 p i ln p i? Tentukan kebarangkalian mana-mana keadaan dalam sistem yang mempunyai jumlah keadaan N yang sama kebarangkaliannya bagi setiap keadaan. Dalam sistem seperti ini apakah had entropinya apabila N? m What is the meaning of p i in the expression for the entropy S = k i=1 p i ln p i? Determine the probability of any given state in an N state system with equiprobable occurrence of any one state. In such a system what is the limit of the entropy as N? 8/11

9 8. Ungkapkan tenaga β = k B T dalam unit cm -1 apabila T = 298 K. Satu anggaran memberikan pemalar keseimbangan K p untuk tindak balas penceraian Express the energy β = k B T in cm -1 units when T = 298 K. One approximation gives the equilibrium constant K p of a dissociation reaction X 2 (g) 2X(g) (1) pada tekanan piawai Pa mengikut ungkapan at the standard state pressure at Pa according to the expression K p = ( g 2 o,x ) ( RT 3 g o,x2 N A P o) (Λ X 2 6 Λ ) 1 exp( βε X q R q D ) V Komen secara ringkas idea-idea utama yang boleh digunakan untuk mendapatkan ungkapan di atas. Untuk tindak balas penceraian I 2 pada T=298 K yang diberi oleh (1) di atas, data di bawah boleh didapati: Comment briefly the main ideas that could have been used to derive the above For the I 2 dissociation reaction at T=298 K given in (1) above the following data is available: g o,i = 4, g o,i2 = 1, Λ I = m, Λ I 2 = m, q R = 2770, q V = 1.58, ε D = 2770cm -1. Tentukan K p dari data. Determine K p from the data. Dari data termokimia pada T=298 K, ΔG f o I 2 (g) (kj mol -1 ) = 19.3, ΔG f o I (g) (kj mol -1 ) = 70.2, tentukan K p dari perhubungan ΔG o = RT ln K dan bandingkan keputusan- keputusan dari dua kaedah tersebut untuk pemalar keseimbangan. From the thermochemical data at T= 298 K, Δ G f o I 2 (g) (kj mol -1 ) = 19.3, ΔG f o I (g) (kj mol -1 ) = 70.2, determine K p from the relation ΔG o = RT ln K and compare the two results for the equilibrium constant. (15 markah/marks) 9/11

10 Kinetik/Kinetics: 9. Untuk tindak balas umum dwimolekul For the general bimolecular reaction A + B C(Prod.) Teori Eyring kadar tindak balas mutlak memberi rupa pemalar tindak balas sebagai The Eyring theory of absolute reaction rates give the form of the reaction rate constant as k r = kt h K = kt h f f A f B exp( E 0 /(RT)). (2) Terangkan secara ringkas setiap istilah yang muncul dalam persamaan ini. Explain briefly each term that appears in this equation. 10. Tindak balas dalam larutan boleh digambarkan oleh langkah-langkah berikut dengan pemalar kadar tindak balas yang ditunjukkan sebagai superskrip arah anak panah Reactions in solution can be described by the following steps with the rate constants indicated in superscripts of the direction arrow A + B k d AB AB AB k r A + B k p P (3)..(4).(5) Tunjukkan dengan kegunaan hipotesis keadaan mantap bahawa kadar tindak balas keseluruhan R ialah Show using the steady state hypothesis that the overall rate R is R = k pk d k r +k p [A][B]. (6) Dari teori,memperingatkan bahawa k d = 4πN a (r A +r B )D AB, dan ungkapan pembauran diberi oleh D AB = D A + D B untuk spesies dengan jejari r A dan r B 10/11

11 masing-masing. Untuk tindak balas kawalan pembauran, mengapa kadar tindak balas keseluruhan diberiolehr = k d [A][B]? From theory, recall k d = 4πN a (r A +r B )D AB, and the diffusion term is given by D AB = D A + D B for species with radii r A and r B respectively, and D X is the diffusion constant for species X. For a diffusion controlled reaction, why is the overall rate given by R = k d [A][B]? Pada suhu 298 K dan ph 7.4, pekali resapan untuk hemoglobin dan oksigen adalah D H = cm 2 s -1 dan D O2 = cm 2 s -1 masing-masing dengan jejari sepadannya r H = 35 A dan r O2 = 2.0 A. Kadar tindakbalas keseluruhan dwimolekul dari eksperimen untuk penambatan hemoglobin ke O 2 ialah M -1 s -1. Adakah tindakbalas ini tindak balas kawalan pembauran? At temperature 298 K and ph 7.4, the diffusion coefficients for hemoglobin and oxygen are respectively D H = cm 2 s -1 and D O2 = cm 2 s -1 with corresponding radii r H = 35 A and r O2 = 2.0 A. The overall experimental bimolecular rate constant for binding of hemoglobin to O 2 is M -1 s -1. Is this reaction diffusion-controlled? (k B = JK -1, R = JK 1 mol 1, h = Js, N A = mol 1, A = m) (15 markah/marks) TAMAT END 11/11

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