課程名稱︰普通化學一
課程性質︰化學系必修
課程教師︰鄭原忠
開課學院：理學院
開課系所︰化學系
考試日期（年月日）︰2016.11.9
考試時限（分鐘）：120
試題 :
1.(5%) What kind of separation method uses the differing abilities of substances
to adhere to the surfaces of solids to separate mixtures? Very briefly explain
how this method works.
2.(4%) Consider a gold bar that measures at 5.0 cm x 1.20 cm x 4.25 cm. Answer
the following questions regarding significant figures:
(a) How do you report the volume of the gold bar?
(b) If the mass of the bar is 492.15 g, how many significant figures should be
reported when its density is determined using the calculated volume?
3.(5%) The elements of group 5A show an interesting change in properties moving
down the group. Give the chemical symbol of each element in the group and label
it as non-metal, metalloid, or metal ( up to n=6).
4.(8%) Write the chemical formulas for the following compounds:
(a) potassium cyanide (b) calcium hypochlorite (c) lithium hydride
(d) sodium peroxide (e) zinc nitrate (f) cyclopropane
(g) hydrogen tellurate ion (h) n-hexane
5.(5%) A 60.00 g sample of a dry-cleaning fluid was analyzed and found to
contain 10.80 g carbon, 1.36 g hydrogen, and 47.84 g chlorine. Answer the
following questions:
(a) Determine the empirical formula of the compound using the following atomic
masses: C: 12.0, H: 1.0, Cl: 25.5.
(b) Suggest a molecular formula for this compound that is stable in air.
6.(10%) A chemical plant uses electrical energy to decompose aqueous solutions
of NaCl to give Cl2, H2 and NaOH.
(a) Give the balanced equation.
(b) If the plant produces 1.5x10^6 kg of Cl2 daily, estimate the quantities of H2 and NaOH produced (in kg). (atomic masses: Na: 23, O: 16)
7.The figure on the right (*註一) shows the effect of pressure on the behavior of several real gases.
(a) (2%) Consider the curve for N2. What is the number of N2 molecules in the system when the experiment is carried out?
(b) (6%) These curves are described by the van der Waals equation,
n^2
(P+a ——— ) (V-nb) = nRT. Give the units of a and b, respectively. What does a
V^2
and b each represent?
(c) (3%) Explain the curves for real gases by describing the physics at P —>0, small P, and large P.
(d) (4%) Do you think the "unknown"curve is for He, Ne, or CO2? Give your answer and explain your choice.
8.The time-independent Schrödinger equation (TISE) for a particle in one
- h^2 d^2Ψ
dimention is ———— ——— + V(x)Ψ = EΨ. Consider a particle in a 1-D
8π^2m dx^2
box of length L between x=0 and x=L.
(a) (3%) Clearly and concisely define the parameters, operators, and functions appear in the TISE.
(b) (3%) What is the time-independent Schrödinger equation of the particle-in-a-box system? Clearly identify the boundary conditions for the stationary states.
nπx
(c) (5%) The stationary wave functions are Ψ (x) = N sin —— .
n a
Explain what is n and its range. Insert the expression into the TISE to derive an expression for energy levels in terms of n and L.
(d) (4%) Sketch the wave function and probability density for a particle in the box at the n=6 energy level.
(e) (3%) Give the probability of locating the particle between x=L/3 and x=2L/3 in a box of length L, if the particle is in its second excited state?
9. Consider the TISE for the 1-D harmonic oscillator model
-h^2 d^2Ψ 1
———— ——— + —— kx^2Ψ = EΨ.
8π^2m dx^2 2
(a) (5%) Show that a Gaussian wave function, Ψ(x)=Ne^(-αx^2), where α is a positive parameter, is a stationary solution. Determine α and explain why this is the ground state.
(b) (4%) Give the zero-point energy of the system. Give the vibrational frequency in terms of the force constant and the mass.
(c) (6%) Sketch the wave functions of the three lowest-energy levels of the harmonic oscillator. Give their energies in terms of the frequency you found in (b).
10. Consider four hydrogen orbitals (shown are the contour plot, the radial function, and the radial distribution function) (*註二).
(a) (12%) Give the principle quantum number and angular momentum quantum number for each of the orbitals. Use the s, p, d, f symbols in your answers.
(b) (3%) Sort the orbitals from low energy to high energy.
Answer true or false (2 points each):
(a) Sodium nitrate is a strong electrolyte in aqueous solution.
(b) Zinc is above lead in the activity series.
(c) Molecules with a longer π-conjugated system tend to absorb photons with higher frequency.
(d) The zero point energy is higher for a He atom in a box than for an electron in the same box.
(e) An example of vibrational isotope effect: v(H-Cl )/ v(D-Cl) is roughly the square root of 2.
(f) The wave function of a system must always satisfy the time-independent Schrödinger equation.
(g) An orbital is an electronic state of a many-electron atom.
(h) Mixing Mg(NO3)2 with NaOH leads to a metathesis reaction.
(i) All gases behave more like an ideal gas as the temperature increases.
(j) The electron configuration of Te is [Ar]5s^(2)4d^(10)5p^(4)
*註一
http://i.imgur.com/i5zFDDE.png (大概長這樣，不過CO2那邊是標示“Unknown gas")
*註二 http://i.imgur.com/jbswuOQ.jpg