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 2016/2017 : SEMESTER 1 ACADEMIC SESSION 2016/2017 : SEMESTER 1
SCES2230/SIC2003 : KIMIA FIZIK II
PHYSICAL CHEMISTRY II
Dis 2016/Jan 2017 MASA : 3 jam
Dec 2016/Jan 2017 TIME : 3 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 8 soalan dalam 11 halaman yang dicetak) (This question paper consists of 8 questions on 11 printed pages)
2/11 BAHAGIAN A (50 MARKAH)
SECTION A (50 MARKS) Jawab SEMUA soalan.
Answer ALL questions.
Beberapa maklumat berguna Some useful information
1 eV = 1.602 x 10-19 J
Cas elektrik/ Electric charge = 1.602 x 10-19 C
Jisim rehat elektron/ Electron rest mass, 𝑚𝑒 = 9.11 x 10-31 kg Pemalar Planck/ Planck constant, = 6.626 x 10-34 J.s Pemalar Rydberg / Rydberg constant, 𝑅 = 109,678 cm-1
Pemalar anjakan Wein/ Wien's displacement constant, w = 2.90 x 10-3 m.K 𝑇̂ = − ℏ2
2𝑚 𝑑2 𝑑𝑥2 𝜓𝑛(𝑥) = (2
𝑙)
1/2
sin (𝑛𝜋𝑥 𝑙 ) 𝜓𝑣(𝑥) = 1
(2𝑣𝑣!)(𝛼 𝜋)
1/4
𝑒−𝛼𝑥2/2𝐻𝑣(𝛼1/2𝑥), 𝛼 = (𝑘𝜇 ℏ2)
1/2
𝑧𝐻𝑛(𝑧) = 𝑛𝐻𝑛−1(𝑧) +1
2𝐻𝑛+1(𝑧), 𝐻0 = 1, 𝐻1 = 2𝑧
1. Soalan 1(a) – 1(d) seperti di bawah adalah berkenaan asal-usul mekanik kuantum.
Questions 1(a) – 1(d) as below are about the origin of quantum mechanics.
(a) Teori radiasi jasad hitam diguna secara kerap dalam astronomi bagi menganggar suhu permukaan bintang-bintang. Gambarajah 1 menunjukkan spektrum elektromagnet matahari diukur pada bahagian atas atmosfera:
The theory of blackbody radiation is used regularly in astronomy to estimate the surface temperatures of stars. Figure 1 shows the electromagnetic spectrum of the sun measured at the earth’s upper atmosphere:
3/11 Gambarajah 1
Figure 1
Anggar suhu permukaan matahari.
Estimate the surface temperature of the sun.
(2 markah/marks) (b) Apabila litium diradiasikan dengan cahaya, didapati keupayaan berhenti adalah 1.83 V untuk = 3000 Å dan 0.80 V untuk = 4000 Å. Kira pemalar Planck.
When lithium is irradiated with light, one finds a stopping potential of 1.83 V for
= 3000 Å and 0.80 V for = 4000 Å. Calculate Planck’s constant.
(3 markah/marks) (c) Gambarajah 2 menunjukkan spektrum sinaran atom hidrogen dalam
kawasan nampak dan ultraungu.
Figure 2 shows the emission spectrum of the hydrogen atom in the visible and the near ultraviolet region.
4/11 Gambarajah 2
Figure 2
Mengguna rumus Balmer, kira panjang gelombang jalur pertama bagi kawasan nampak spektrum atom hidrogen. Adakah keputusan anda bersetuju dengan jalur spektrum?
Using Balmer’s formula, calculate the wavelength of the first line of the visible region of the hydrogen atomic spectrum. Does your result agree with the line spectrum?
(3 markah/marks)
(d) Diberi radius satu elektron dalam orbit Bohr pertama adalah 5.29 x 10-11 m. Mempertimbangkan keadaan pengkuantuman Bohr, kira
halaju satu elektron dalam orbit Bohr pertama.
Given the radius of an electron in the first Bohr orbit is 5.29 x 10-11 m.
Considering the Bohr quantization condition, calculate the velocity of an electron in the first Bohr orbit.
(2 markah/marks) 2. Soalan 2(a) – 2(g) seperti di bawah adalah berkenaan prinsip-prinsip asas
mekanik kuantum dan beberapa aplikasi mudah.
Questions 2(a) – 2(g) as below are about the general principles of quantum mechanics and its some simple applications.
(a) Mengguna fungsi 𝑓(𝑥) dan g(𝑥), tentukan samada operator √ adalah linear atau bukan linear.
Using functions 𝑓(𝑥) and g(𝑥), determine whether operator √ is linear or nonlinear.
(3 markah/marks)
5/11 (b) Tunjukkan bahawa 𝑒𝛼𝑥 adalah satu fungsi eigen bagi operator tenaga
kinetik, dimana 𝛼 adalah satu pemalar. Apakah nilai eigen?
Show that 𝑒𝛼𝑥 is an eigenfunction of the kinetic energy operator, where 𝛼 is a constant. What is the eigenvalue?
(3 markah/marks) (c) Buktikan bahawa operator tenaga kinetik adalah Hermitian. Mengapa operator mekanik kuantum bagi tenaga kinetik diperlukan sebagai Hermitian?
Prove that the kinetic energy operator is Hermitian. Why is the quantum mechanical operator of the kinetic energy required to be Hermitian?
[∫ 𝑢(𝑥)𝑑𝑣(𝑥)
𝑑𝑥 𝑑𝑥 = [𝑢(𝑥)𝑣(𝑥)]𝑎𝑏− ∫ 𝑣(𝑥)𝑑𝑢(𝑥) 𝑑𝑥 𝑑𝑥
𝑏 𝑎 𝑏
𝑎
]
(5 markah/marks) (d) Buktikan bahawa
Show that
〈𝑥〉 =𝑎 2
untuk semua keadaan bagi satu zarah dalam kotak satu dimensi dengan panjang 𝑎. Adakah keputusan ini boleh diterima secara fizikalnya?
for all states of a particle in a one-dimensional box of length 𝑎. Is this result physically reasonable?
[∫ 𝑢 sin2𝑏𝑢 𝑑𝑢 =𝑢2 4 − 𝑢
4𝑏sin 2𝑏𝑢 − 1
8𝑏2cos 2𝑏𝑢 + 𝐶]
(5 markah/marks) (e) Kira kebarangkalian bahawa untuk semua keadaan bagi satu zarah dalam
kotak satu dimensi dengan panjang 𝑎 di jumpai di antara 0 dan 𝑎/2.
Calculate the probability that for all states of a particle in a one-dimensional box of length 𝑎 is found to be between 0 and 𝑎/2.
[∫ sin2𝑏𝑢 𝑑𝑢 =𝑢 2− 1
4𝑏sin 2𝑏𝑢 + 𝐶]
(4 markah/marks)
6/11 (f) Tunjukkan bahawa fungsi gelombang bagi keadaan pengujaan pertama
pengayun harmonik adalah dinormalkan.
Show that the wave function of the first excited state of a harmonic oscillator is normalized.
[∫ 𝑥2𝑛𝑒−𝑏𝑢2𝑑𝑢
∞ 0
= 1 ∙ 3 ⋯ (2𝑛 − 1)
2𝑛+1 ( 𝜋
𝑏2𝑛+1)
1/2
, 𝑏 > 0, 𝑛 = 1, 2, 3, . . . ]
(5 markah/marks) (g) Pertimbangkan satu pengayun harmonik dua dimensi yang mempunyai
tenaga keupayaan
Consider a two-dimensional harmonic oscillator whose potential energy is
𝑉(𝑥, 𝑦) =1
2𝑘𝑥𝑥2+1 2𝑘𝑦𝑦2.
Terbitkan paras-paras tenaga bagi sistem ini dari segi frekuensi (𝜈𝑥 dan 𝜈𝑦), nombor kuantum (𝑣𝑥 dan 𝑣𝑦) dan .
Derive the energy levels of this system in terms of frequency (𝜈𝑥 and 𝜈𝑦), quantum number (𝑣𝑥 and 𝑣𝑦) and .
(3 markah/marks) 3. Soalan 3(a) – 3(c) seperti di bawah adalah berkenaan atom-atom semacam
hidrogen.
Questions 3(a) – 3(c) as below are about the hydrogenlike atoms.
(a) Mengguna fungsi 𝑌𝑙𝑚(𝜃, 𝜙), tentukan samada operator 𝐿̂2 dan 𝐿̂𝑧 berulang- alik atau tidak. Berdasarkan keputusan ini, bolehkan magnitude dan salah satu komponen momentum sudut ditentukan secara serentak dengan ketepatan tak terhingga?
Using function 𝑌𝑙𝑚(𝜃, 𝜙), determine whether the operators 𝐿̂2 and 𝐿̂𝑧 commute or do not commute. Based on this result, can the magnitude and one the component of angular momentum be determined simultaneously with infinite precision?
(4 markah/marks)
7/11 (b) Dapatkan magnitude vektor momentum sudut spin dan komponen-
komponen vektornya bagi satu elektron. Lakar satu gambarajah yang mewakili orientasi vektor-vektor ini.
Find the magnitude of the spin angular momentum vector and its corresponding vector components for an electron. Draw a diagram to represent the orientation of the vectors.
(4 markah/marks) (c) Diberi orbital 2𝑝±1 sebagai
Given 2𝑝±1 orbitals as
𝜓2𝑝±1(𝑟, 𝜃, 𝜙) = 1 8𝜋1/2(𝑍
𝑎)
5/2
𝑟𝑒−𝑍𝑟/2𝑎 sin 𝜃 𝑒±𝑖𝜙, terbitkan orbital semacam hidrogen 2𝑝𝑥 sebagai 𝜓2𝑝𝑥. derive the real hydrogenlike orbital 2𝑝𝑥 as 𝜓2𝑝𝑥.
[𝑒±𝑖𝜙 = cos 𝜙 ± 𝑖 sin 𝜙]
(4 markah/marks)
8/11 BAHAGIAN B (25 MARKAH)
SECTION B (25 MARKS) Jawab SEMUA soalan.
Answer ALL questions.
4. Kinetik tindak balas enzim boleh digambarkan menggunakan mekanisme Michaelis-Menten. Jika S mewakili molekul substrat dan E adalah enzim maka bentuk yang mudah untuk mekanisme Michaelis-Menten adalah:
The kinetics of many enzyme reactions may be described in terms of the Michaelis- Menten mechanism. If S represents the substrate molecule and E is the enzyme then a simple form of the Michaelis-Menten mechanism is:
di mana ES mewakili kompleks enzim / substrat. Kadar tindak balas R diberikan oleh R = k2 [ES].
where ES represents the enzyme/substrate complex. The reaction rate R is given by R = k2 [ES].
(a) Gunakan penghampiran keadaan mantap untuk menilai kepekatan kompleks enzim / substrat [ES] dan dengan itu tunjukkan bahawa kadar pembentukan produk R diberikan oleh R =kc[E][S]
KM+ [S] di mana kc = k2 adalah kadar pemalar pemangkin dan KM =k−1+k2
k1 adalah pemalar Michaelis.
Perhatikan bahawa jumlah kepekatan enzim diberikan oleh [E] = [E] + [ES] di mana [E] mewakili enzim bebas.
Use the steady state approximation to evaluate the enzyme/substrate complex concentration [ES] and hence show that the rate of product formation R is given by 𝑅 =𝑘𝑐[𝐸][𝑆]
𝐾𝑀+ [𝑆] where kc = k2 is the catalytic rate constant and 𝐾𝑀 = 𝑘−1+𝑘2
𝑘1 is the Michaelis constant. Note that the total enzyme concentration is given by [𝐸] = [𝐸] + [𝐸𝑆] where [E] represents the free enzyme.
(5 markah/marks)
9/11 (b) Apakah bentuk kadar tindak balas apabila kepekatan substrat [S] << KM?
What is the form of the reaction rate when the substrate concentration [S] << KM?
(5 markah/marks) (c) Buat lakaran berlabel bagaimana kadar tindak balas berubah dengan kepekatan substrat dan nyatakan kadar tindak balas maksimum dalam graf.
Make a labeled sketch of the way that the reaction rate varies with substrate concentration and indicate a maximum of the rate of reaction in the graph.
(5 markah/marks) 5. Pada kekuatan ionik 0.100 mol dm-3 dan suhu 25 C, pemalar kadar yang
diperhatikan bagi tindak balas:
At an ionic strength of 0.100 mol dm-3 and a temperature of 25 C, the observed rate constant for the reaction:
adalah 1.1 x 10-2 mol-1 dm3 s-1, manakala bagi tindak balas:
is 1.1 x 10-2 mol-1 dm3 s-1, while that for a reaction:
adalah 3.8 x 10-3 mol-1 dm3 s-1. is 3.8 x 10-3 mol-1 dm3 s-1.
(a) Anggarkan nilai-nilai pemalar kadar pada kekuatan ionik sifar.
Estimate the values of the rate constants for zero ionic strength.
(6 markah/marks) (b) Bandingkan kadar pada kekuatan ionik sifar dan pada I = 0.100 mol dm-3.
Compare the rate at zero ionic strength and at I = 0.100 mol dm-3.
(4 markah/marks)
10/11 BAHAGIAN C (25 MARKAH)
SECTION C (25 MARKS) Jawab SEMUA soalan.
Answer ALL questions.
6. (a) 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.
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.
(5 markah/marks) (b) Terang dengan jelas sebutan fugasiti.
Explain clearly the term fugacity.
(2 markah/marks) (c) Kira pekali fugasiti satu gas yang mempunyai tekanan 100 atm dan suhu
500 K dengan anggapan kebolehmampatannya ialah:
Calculate the fugacity coefficient of a gas at 100 atm and 500 𝐾, assuming its compressibility is:
𝑍 = 1 + 𝐵′
𝑅𝑇𝑝 Diberi 𝐵′= 0.012 L mol−1, 𝑅 = 8.205 × 10−2 𝐿 𝑎𝑡𝑚 𝐾−1𝑚𝑜𝑙−1 Given 𝐵′= 0.012 L mol−1, 𝑅 = 8.205 × 10−2 𝐿 𝑎𝑡𝑚 𝐾−1𝑚𝑜𝑙−1
(5 markah/marks) 7. ∆G° bagi tindakbalas 2NO2(g) → N2O4(g) ialah –5.146 kJ mol-1 pada 298 K. Kira pekali keseimbangan, Kp pada 373 K jika nilai ΔH° ialah –46.860 kJ mol-1 dan anggap nilai ΔH° tersebut tidak berubah dengan perubahan suhu yang terlibat.
∆𝐺° for the following reaction 2𝑁𝑂2(𝑔) → 𝑁2𝑂4(𝑔) is –5.146 kJ mol-1 at 298 K.
Calculate the equilibrium constant, 𝐾𝑝 at 373 K if the value of ΔH° is –46.860 kJ mol-1 and considered ΔH° unchanged for the temperature ranges involved.
(5 markah/marks)
11/11 8. Beberapa tekanan wap cecair raksa diberi seperti berikut:
Some vapour pressures of liquid Hg are given as follow:
T/K 353 373 393 413
P/torr 0.08880 0.2729 0.7457 1.845
(a) Cari ∆𝐻 pengewapan purata bagi julat suhu ini dari plot ln P lawan 1/T.
Find the average ∆𝐻 of vapourization over this temperature range from a plot of ln P versus 1/T.
(6 markah/marks) (b) Tentukan tekanan wap pada 433 K.
Determine the vapour pressure at 433 K.
(2 markah/marks) TAMAT
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