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 014/015 : SEMESTER ACADEMIC SESSION 014/015 : SEMESTER SCES30 : KIMIA FIZIK II PHYSICAL CHEMISTRY II Jun 015 June 015 MASA : jam TIME : 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 9 soalan dalam 9 halaman yang dicetak) (This question paper consists of 9 questions on 9 printed pages)
BAHAGIAN A : KIMIA KUANTUM (50 MARKAH) SECTION A : QUANTUM CHEMISTRY (50 MARKS) Jawab DUA () soalan dalam Bahagian ini. Answer TWO () questions in this Section. 1. (a) Tuliskan nota pendek daripada dua topik yang berikut: Write a short note on two of the following topics: (i) (ii) (iii) (iv) Fungsigelombang Wavefunction Vektor momentum sudut (magnitud dan orientasi) bagi sesuatu elektron-p Angular momentum vector (magnitude and orientations) for a p-electron Persamaan eigenilai Eigenvalues equation Kaedah hampiran dalam mekanik kuantum Approximation methods in quantum mechanics (10 markah/marks) (b) Kesan fotoelektrik adalah asas spektroskopi fotoelektron. Satu foton cahaya-x yang jarak gelombangnya bernilai 150 pm (1 pm=10-1 m) menembusi ke bahagian dalam sesuatu atom dan menganjakkan elektron. Halaju elektron yang dikeluarkan ditentukan bernilai.14x10 7 ms -1. Hitungkan betapa kuat elektron ini terikat pada atom tersebut. The photoelectric effect is the basis of photoelectron spectroscopy. An x-ray photon of wavelength 150 pm (1 pm=10-1 m) plunges into the inner part of an atom and ejects electrons. The speed of the ejected electrons was determined and found to be.14x10 7 ms -1. Calculate how tightly was the electrons bound to the atom. (5 markah/marks) (c) Fungsigelombang bagi sesuatu zarah yang jisim m dihadkan bergerak dalam satu kotak berdimensi-satu dan berkepanjangan L, ialah The wavefunction for a particle of mass m confined to move in a one-dimensional box of length L is Ψ n = N sin ( nπx L ), n = 1,, /9
di mana N adalah satu pemalar penormalan. where N is a normalization constant. (i) Tunjukkan N= L, diberi Show that N=, given that L sin x dx = ¼ (x sin x). (ii) Tunjukkan tenaga yang dibenarkan bagi zarah ini adalah terkuantum, dan diberi oleh Show that the allowed energy for the particle is quantized, and is given by E n = n h 8mL. (10 markah/marks). (a) Tenaga bagi atom hidrogen pada keadaan dasar ialah -13.6 ev. Hitungkan tenaga bagi atom hidrogen apabila elektronnya telah diuja ke orbital atom s. The energy of hydrogen atom at the ground state is -13.6 ev. Calculate the energy of the hydrogen atom when its electron is excited to s atomic orbital. (3 markah/marks) (b) Berikan dua kesamaan dan dua perbezaan antara orbital 1s atom hidrogen dan orbital 1s atom helium. Give two similarities and two differences between 1s orbital of hydrogen atom and 1s orbital of helium atom. (4 markah/marks) (c) Tuliskan persamaan Schrodinger bagi atom helium. Terangkan mengapa persamaan ini tidak boleh diselesaikan secara langsung. Namakan dua kaedah hampiran yang boleh digunakan untuk menentukan tenaga dan fungsigelombang bagi atom helium. Write down the Schrodinger equation for helium atom. Explain why this equation cannot be solved exactly. Name two approximate methods which can be used to determine the energy and wavefunction for helium atom. (6 markah/marks) 3/9
(d) Yang mana fungsigelombang berikut mematuhi prinsip Pauli? Terangkan jawapan anda. Which of the following wavefunction satisfy the Pauli principle? Explain your answer. (i) (ii) (iii) (iv) 1s (1) 1s () (1) () + (1) () 1s (1) 1s () (1) () - (1) () 1s (1) 1s () (1) () 1s (1) 1s () (1) () (5 markah/marks) Jawab soalan (e) atau (f) Answer question (e) or (f) (e) Fungsigelombang yang menghuraikan sesuatu pengayun harmonik mempunyai bentuk The wavefunction describing a harmonic oscillator has the following form y v ( x) Nv exp ( ) Hv ( y), v = 0,1,,... x 1 y dan/and ( / mk) 4, di mana N v adalah satu pemalar penormalan, H v adalah polinomial Hermit, m adalah jisim satuan dan k adalah pemalar daya bagi pengayuan tersebut. where N v is the normalization constant, H v is the Hermite polynomials, m is the reduced mass and k is the force constant. Tunjukkan purata sesaran dari keseimbangan, x, bagi pengayun harmonik ini adalah sifar, iaitu, x =0, diberi Show that the averaged displacement from the equilibrium, x, for the oscillator is zero, i.e. x = 0, given that y H v (y) = v H v-1 (y) + H v+1 (y) / dan/and H v (y) H v (y) exp (-y ) dy = 0 jika/if v v. (7 markah/marks) 4/9
(f) Diberi fungsigelombang bagi sesuatu atom hidrogenik ialah Given that the wavefunction for a hydrogenic atom is 3 Z Z r ( r) exp( ), 3 a a di mana a adalah jejari Bohr, Z adalah nombor atom, dan r adalah jarak antara elektron dan nukleus. Hitungkan purata pemisahan antara elektron dan nukleus bagi atom hidrogen, diberi where a is the Bohr radius, Z is the number atom, and r is the distance between the electron and the nucleus. Calculate the average separation between the electron and the nucleus for hydrogen atom, given that n ax n! o x e d x, n = 0, 1,,... n 1 a (7 markah/marks) 5/9
Jawab SEMUA soalan dalam Bahagian ini. Answer ALL questions in this Section. BAHAGIAN B (5 MARKAH) SECTION B (5 MARKS) 3. Dalam tindakbalas pirolisis etana menghasilkan etelina kebiasaan melalui tindakbalas heterogenus mengunakan pemangkin pepejal dimana kadar tindakbalas diberi seperti berikut, In the pyrolysis reaction of ethane to produce ethylene is generally a heterogeneous reaction with solid catalysts with the rate of equation given as, d[ C dt H 6 ] ( k 1 k [ CH 3 ] k 4 [ H ])[ C Tindakbalas ini dilakukan pada suhu 700 900 K dan tekanan melebihi 0. bar. Ramal mekanisma tindakbalas. The reaction is carried out at 700 900 K and pressure above 0. bar. Predict the reaction mechanism. H 6 ] (5 markah/marks) 4. Satu tindakbalas telah dijalankan dalam larutan organik lengai pada suhu bilik. Progres tindakbalas diikuti mengunakan optik serapan pada 350 nm. Data berikut telah diperolehi. A reaction has been studied in an inert organic solvent at room temperature. The progress of reaction has been monitored by the optical absorption at 350 nm. The following data are obtained. t(s) 0 000 6000 10000 Abs 1.50 1.6 0.9 0.7 0.40 Anggapkan tertib pertama tindakbalas, kira pemalar tindakbalas. Assuming the reaction is first order, calculate the rate constant. (10 markah/marks) 6/9
5. Penguraian asetildehid pada suhu 518 0 C besar kemungkinan melibatkan hasil dari pelanggaran antara dua molekul acetildehid. Kepekatan acetildehid yang tinggal selepas setiap selang masa, [A], ialah tekanan asal (P 0 ) tolak P seperti yang tersenarai. Selesaikan [A] anda dan seterusnya tentukan pemalar kadar tindakbalas ini, The decomposition of acetaldehyde at 518 o C could probably involve as a result of collision between two acetaldehyde molecules. The concentration of acetaldehyde remaining after each interval of time, [A], is the original pressure (P 0 ) minus P as listed in the following table. Solve your [A] and subsequently determine the rate constant of this reaction. Masa, saat 0 4 105 4 480 840 Time, sec Tekanan, MPa 48.4 5.8 58.6 66.6 74.6 80.93 Pressure, MPa P, MPa 0 4.399 9.865 17.87 5.86 3.53 (10 markah/marks) 7/9
BAHAGIAN C (5 MARKAH) SECTION C (5 MARKS) Jawab mana-mana TIGA soalan dari (6-9) dalam Bahagian C. Setiap soalan mempunyai markah yang sama. Answer any THREE from questions (6-9) in Section C. Each question has equal mark. 6. Takrifkan satu sistem tertutup. Bagi sistem tertutup, tulis persamaan-persamaan termodinamik asas yang berhubung dengan fungsi keupayaan termodinamik, U, H, A dan G kepada pembolehubah semulajadi T, p, V dan S. Berikan juga persamaan-persamaan ini bagi sistem terbuka bila pertukaran jirim dibenarkan. Define a closed system. For a closed system, write the fundamental thermodynamic equations relating the important thermodynamic potential functions U, H, A and G to the natural variables, T, p, V and S. Give also these equations for an open system where mass exchange is allowed. 7. Pembentukan ethana melibatkan tindakbalas berikut: The formation of ethane involved the following reaction: C(s) + 3H (g) CH 3 CH 3 (g) Kira keupayaan kimia pada keadaan piawai bagi ethana, μ CH3. CH 3 (g) Calculate the standard state chemical potential for ethane, μ CH3. CH 3 (g) Di beri pada 98 K entalpi molar separa piawai bagi etana ialah, Given at 98 K the standard partial molar enthalpy of ethane is H CH 3 CH 3 (g) = 85 kj mol 1, Dan entropi-entropi absolut piawai bagi CH 3 CH 3 (g), C(s) dan H (g) ialah: And the standard absolute entropies of CH 3 CH 3 (g), C(s) and H (g) are: S CH 3 CH 3 (g) S C(s)(g) S H (g) = 9 J mol 1 K 1 = 6 J mol 1 K 1 = 131 J mol 1 K 1 8/9
8. Berikan persamaan-persamaan mentakrifkan pekali pengembangan termal ( ) dan pemampatan isoterma ( ). Guna persamaan in bagi menunjukan: Give the defining equations for the thermal expansion coefficient ( ) and isothermal compressibility ( ). Using these show that ( U V ) = α T p T 9. Gambar rajah fasa bagi satu molekul baru yang berkaitan dengan renol (sejenis dadah) diberikan di bawah. The phase diagram of a new molecule related to renol (a drug) is given below. Pada 300 K dan 1 bar, adakah molekul in gas, cecair atau pepejal? At 300K and 1 bar, is this molecule a gas, liquid or solid? Tekanan wap keseimbangan (p s ) bagi pepejal ini ialah, The equilibrium vapour pressure of the solid (p s ) is lnp s = 4000K T + 15 Guna persamaan Clapeyron bagi menganggar entalpi pemeluwapan H sub bagi molekul ini. Use the Clapeyron equation to approximate the enthalpy of sublimation H sub for this molecule. TAMAT END 9/9