CHEM 214 - Midterm 2012
CHEMISTRY 214 QUESTIONS 1. Write spectroscopic term symbols for the ground states: a) F(Z = 9) K2s22p5 b) Ni (Z = 28) KL3s23p63d84s2 (7) a) F(Z = 9) L m (1 1) (0 0) (1) 1 P
1 1 1 1 1 1 S ms 2 2 2 2 2 2 2
Term (ground state) = P3 2
L + S = 1+1/2 = 3/2
> half filled
b) Ni (Z = 28)
L m (2 2) (1 1) (0 0) (1) (2) 3 F 1 1 1 1 1 1 1 1 S ms 1 S 2 2 2 2 2 2 2 2 2S1
Term (ground state) =
Ll S 3F4
L S 3 1 4
half filled
2. An emission line (486.1 nm) in the Balmer series for the H-atom is associated with the n = 4 n = 2 transition. (a) Would the electron velocity increase or decrease as a result of the transition? Justify (qualitatively). Ans: There would be an increase in electron velocity and EK associated with the decrease in EP and ET as the electron is attracted more strongly toward the proton in the n = 2 state. Virial Theorem (b) Calculate the change in electron velocity. (10)
ETotal
RH R R H2 H2 , 2 2 n4 n2 n4 n2
2.18 x10 18 J me v 22 , 4 2 v2
E K ETotal
RH RH 2.18 x10 18 J 2.18 x10 18 J n22 n42 4 16
2.18 x10 18 J me v 24 16 2
1.09 x10 18 J 2.725 x10 19 J 6 1 1 . 094 x 10 ms v 5.47 x105 ms 1 2 31 31 9.1094 x10 kg 9.1094 x10 kg
v v 2 v1 5.47 x105 ms 1
1
CHEMISTRY 214 3. Write the relation between ET and EK for each of the following systems: Comment if needed. a) a particle in a 3D cubic box b) a Bohr atom c) a harmonic oscillator d) planetary e.g. Earth/Sun systems (8) Ans:
a) b) c) d)
EK = ET, since EP = 0 EK =ET, Virial Theorem for a 1/r potential average EK = average EP, EK varies from 0 to ET EK =ET, Virial Theorem for a 1/r potential
4. The DSC data for a globular protein displays a denaturation peak of 160 kJ mol-1 at 75oC. With decreasing temperature the fraction in the denatured state decreases to 2.7% at 32.9oC, and then increases again. Calculate the fraction in the denatured state predicted at 0oC. Ans: . . .
The fraction in the denatured state is a minimium, and therefore K is a minimum at 32.90C or 305.9K. From the van’t Hoff relation dlnK/dT = Ho/RT2 and therefore: Ho = 0 at 305.9oC. 0 = 160 kJ mol-1 +Cp(32.90oC-75oC) Cp = 160 kJ mol-1/(32.9 oC -75oC) = 3.8 kJ mol-1
(10) o 1 H 273 3.8 kJmol 1 K 1 (0 75) 125 kJ mol 1 K 160 kJmol o 1 1 1 S 273 K (160 kJmol / 348 K ) 3.8n( 273K / 348 K ) 0.4626 kJmol K
…….
o 1 G273 273K (0.4626) 1.29 kJ mol 1 K 125 kJ mol
K 273K e 1.29x10 Jmol 3
1
/ 8.314Jmol 1 x 273K
0.566
f den 0.566 /(1 0.566) 0.36 or 36% denatured
.
At Tc f den 0.5, therefore approaching, but not quite at Tc The problem could have been solved by calculating K at 32.9oC, and thenGo . at 32.9oC. Write Go in terms of Ho and TSo relative to the values at Tm, and thus find CP. Then use CP to calculate Go and K at 273K. (much longer )
2
CHEMISTRY 214 5. A photoactive metal is irradiated with light of a particular frequency, and 5 -1 photoelectrons with a velocity of 6.11 x 10 ms are produced. The longest wavelength (nm) that results in the production of photoelectrons with this metal is 705 nm. Calculate the wavelength (nm) of the initial radiation?
6. To determine the spectroscopic term symbols 2s+1LJ for the possible electron states for Gallium (Z=31), form a table of ML\MS values that includes all of the microstates. Determine by elimination the allowed electronic states and identify the ground state.
(10)
3
CHEMISTRY 214 7. Account for the following: . (10)
a) The spin angular momentum vector for a single unpaired electron forms either: i) an angle wrt the z-axis of 54.7o and a magnitude along the z-axis of 1 2 , or . 125.3o and 1 2 . b) The spin angular momentum vector for 3 coupled unpaired electrons also has a . component with a projection of 1 2 along the z-axis, but it forms an angle of . 75o wrt to that axis. Hint*: focus on the length of the spin angular momentum vector in the 2 cases. *concession to J.M.
4
McGILL UNIVERSITY FACULTY OF SCIENCE CHEMISTRY 214 MIDTERM EXAM 2 HOURS Examiner: Dr. W.C. Galley
March 5, 2012 6:00-8:00 PM
________________________________________ SURNAME (Print) INITIALS
_______________________ STUDENT NUMBER
CONSTANTS + CONVERSIONS R (gas constant)………..8.314 J mol-1K-1, 8.314x107 erg mol-1K-1, 0.083l4 atm mol-1K-1 k (Boltzmann constant…1.381 x 10-23 JK-, 0.695 cm-1K-1 h (Planck’s constant)…..6.626 x 10-34 Js RH (Rydberg constant)...109,677 cm-1, 2.18x10-18 J e (electronic charge)…...1.6027 x 10-19 C No (Avogadro’s #)……..6.022 x 1023 mol-1 Me (electron rest mass)...9.1094 x 10-31 kg Mp (proton rest mass)….1.673 x 10-27 kg c(speed of light)……….2.997 x 108 ms-1, 2.997 x 1010 cm s-1 Å(angstrom)…………...1.0 x 10-10m, 1.0 x 10-8 cm -1 o………………………8.758 x 10-12 C2N m-2 (permittivity of empty space) -1 4o = 1.11 x 10-10 C2N m-2 INSTRUCTIONS QUESTION VALUE MARK
1. There are 7 questions on the exam. 2. Answer all questions on the exam paper. 3. The total value is 60 marks with the marks for each question in the margin. 5. All work must be carried out on the exam. 6. No extraneous material, e.g. formula sheet, allowed. 7. Calculators with alphanumeric memory are not permitted. 8. RETURN THE EXAM PAPER & ID NUMBER ON IT.
5
1 2 3 4 5 6 7 TOTAL
7 10 8 10 5 10 10 60
6
1 1 1 1 1 1 S ms 2 2 2 2 2 2 2
Term (ground state) = P3 2
L + S = 1+1/2 = 3/2
> half filled
b) Ni (Z = 28)
L m (2 2) (1 1) (0 0) (1) (2) 3 F 1 1 1 1 1 1 1 1 S ms 1 S 2 2 2 2 2 2 2 2 2S1
Term (ground state) =
Ll S 3F4
L S 3 1 4
half filled
2. An emission line (486.1 nm) in the Balmer series for the H-atom is associated with the n = 4 n = 2 transition. (a) Would the electron velocity increase or decrease as a result of the transition? Justify (qualitatively). Ans: There would be an increase in electron velocity and EK associated with the decrease in EP and ET as the electron is attracted more strongly toward the proton in the n = 2 state. Virial Theorem (b) Calculate the change in electron velocity. (10)
ETotal
RH R R H2 H2 , 2 2 n4 n2 n4 n2
2.18 x10 18 J me v 22 , 4 2 v2
E K ETotal
RH RH 2.18 x10 18 J 2.18 x10 18 J n22 n42 4 16
2.18 x10 18 J me v 24 16 2
1.09 x10 18 J 2.725 x10 19 J 6 1 1 . 094 x 10 ms v 5.47 x105 ms 1 2 31 31 9.1094 x10 kg 9.1094 x10 kg
v v 2 v1 5.47 x105 ms 1
1
CHEMISTRY 214 3. Write the relation between ET and EK for each of the following systems: Comment if needed. a) a particle in a 3D cubic box b) a Bohr atom c) a harmonic oscillator d) planetary e.g. Earth/Sun systems (8) Ans:
a) b) c) d)
EK = ET, since EP = 0 EK =ET, Virial Theorem for a 1/r potential average EK = average EP, EK varies from 0 to ET EK =ET, Virial Theorem for a 1/r potential
4. The DSC data for a globular protein displays a denaturation peak of 160 kJ mol-1 at 75oC. With decreasing temperature the fraction in the denatured state decreases to 2.7% at 32.9oC, and then increases again. Calculate the fraction in the denatured state predicted at 0oC. Ans: . . .
The fraction in the denatured state is a minimium, and therefore K is a minimum at 32.90C or 305.9K. From the van’t Hoff relation dlnK/dT = Ho/RT2 and therefore: Ho = 0 at 305.9oC. 0 = 160 kJ mol-1 +Cp(32.90oC-75oC) Cp = 160 kJ mol-1/(32.9 oC -75oC) = 3.8 kJ mol-1
(10) o 1 H 273 3.8 kJmol 1 K 1 (0 75) 125 kJ mol 1 K 160 kJmol o 1 1 1 S 273 K (160 kJmol / 348 K ) 3.8n( 273K / 348 K ) 0.4626 kJmol K
…….
o 1 G273 273K (0.4626) 1.29 kJ mol 1 K 125 kJ mol
K 273K e 1.29x10 Jmol 3
1
/ 8.314Jmol 1 x 273K
0.566
f den 0.566 /(1 0.566) 0.36 or 36% denatured
.
At Tc f den 0.5, therefore approaching, but not quite at Tc The problem could have been solved by calculating K at 32.9oC, and thenGo . at 32.9oC. Write Go in terms of Ho and TSo relative to the values at Tm, and thus find CP. Then use CP to calculate Go and K at 273K. (much longer )
2
CHEMISTRY 214 5. A photoactive metal is irradiated with light of a particular frequency, and 5 -1 photoelectrons with a velocity of 6.11 x 10 ms are produced. The longest wavelength (nm) that results in the production of photoelectrons with this metal is 705 nm. Calculate the wavelength (nm) of the initial radiation?
6. To determine the spectroscopic term symbols 2s+1LJ for the possible electron states for Gallium (Z=31), form a table of ML\MS values that includes all of the microstates. Determine by elimination the allowed electronic states and identify the ground state.
(10)
3
CHEMISTRY 214 7. Account for the following: . (10)
a) The spin angular momentum vector for a single unpaired electron forms either: i) an angle wrt the z-axis of 54.7o and a magnitude along the z-axis of 1 2 , or . 125.3o and 1 2 . b) The spin angular momentum vector for 3 coupled unpaired electrons also has a . component with a projection of 1 2 along the z-axis, but it forms an angle of . 75o wrt to that axis. Hint*: focus on the length of the spin angular momentum vector in the 2 cases. *concession to J.M.
4
McGILL UNIVERSITY FACULTY OF SCIENCE CHEMISTRY 214 MIDTERM EXAM 2 HOURS Examiner: Dr. W.C. Galley
March 5, 2012 6:00-8:00 PM
________________________________________ SURNAME (Print) INITIALS
_______________________ STUDENT NUMBER
CONSTANTS + CONVERSIONS R (gas constant)………..8.314 J mol-1K-1, 8.314x107 erg mol-1K-1, 0.083l4 atm mol-1K-1 k (Boltzmann constant…1.381 x 10-23 JK-, 0.695 cm-1K-1 h (Planck’s constant)…..6.626 x 10-34 Js RH (Rydberg constant)...109,677 cm-1, 2.18x10-18 J e (electronic charge)…...1.6027 x 10-19 C No (Avogadro’s #)……..6.022 x 1023 mol-1 Me (electron rest mass)...9.1094 x 10-31 kg Mp (proton rest mass)….1.673 x 10-27 kg c(speed of light)……….2.997 x 108 ms-1, 2.997 x 1010 cm s-1 Å(angstrom)…………...1.0 x 10-10m, 1.0 x 10-8 cm -1 o………………………8.758 x 10-12 C2N m-2 (permittivity of empty space) -1 4o = 1.11 x 10-10 C2N m-2 INSTRUCTIONS QUESTION VALUE MARK
1. There are 7 questions on the exam. 2. Answer all questions on the exam paper. 3. The total value is 60 marks with the marks for each question in the margin. 5. All work must be carried out on the exam. 6. No extraneous material, e.g. formula sheet, allowed. 7. Calculators with alphanumeric memory are not permitted. 8. RETURN THE EXAM PAPER & ID NUMBER ON IT.
5
1 2 3 4 5 6 7 TOTAL
7 10 8 10 5 10 10 60
6
