Langmuir adsorption
To illustrate the difference in choices of ensembles.
Canonical ensemble
Find the partition function from the number of ways to distribute
\[
\Omega(N)=\frac{M!}{N!(M-N)!}\\
\implies Q=\frac{M!}{N!(M-N)!}\exp(\beta N\epsilon)
\] With Stirling’s approximation, chemical potentia...
Fundamental idea
Think about thermodynamics
The observable properties of systems containing very large numbers of
particles depend only on specifying a few macroscopic properties -
internal energy, temperature, volume, pressure, density, etc.
Most experiments measure averaged properties - over ma...
Rigorous maths is not essential for the sake of this course, so that
will only be added later if required.
Diffraction
Geometry
Symbol
Meaning
\(\mathbf{r}\)
Position
\(\mathbf{s_0}\)
Unit vector of incident beam
\(\mathbf{s}\)
Unit vector of diffracted beam
\(\mathbf{S=(s-s_0)}/\lam...
It should be obvious but 主题是针对英国。如果没有了解政府进入Stage
II的措施以及理由，在最后附了摘要。（Credit: LZH）
为什么不
在质疑一个人“为什么不”之前，如果你没有站在他的立场上思考一下为什么不，那这个质疑是极不负责任的。
一场瘟疫面前，政府为什么不轻举妄动的理由很多，大家也都能慢慢看到了。最近的例子，美国一封闭欧洲的航班，DJI就暴跌10%。这说明从经济上看，任何的封闭性措施，至少在大多数人（资本）看来，在短期内都会对经济造成更加负面的、极其严重的影响。
同样的，在其他方面，任何措施对国家、社会的影响都不可小觑。多少小企业就此破产、多少投...
Cambridge Part II B7 course.
Representations
The representation matrix of an operation is defined with a
left contraction \[
\hat{R}\phi_i=\sum_j \phi_j D_{ji}(R).
\]
Great Orthogonality Theorem
If \(\Gamma_a\) and \(\Gamma_b\) are two irreducible unitary
representations, then their representatio...
Key equations (need to remember) for Cambridge Part II Theoretical
techniques course.
Huckel
The resonance energy is the difference between total
Huckel energy and the summed energies of isolated bonds in the
structure.
Cyclic polyenes
Energy - this is equivalent to drawing a Frost circle! \[\beg...
A brief note on the use of enolates in syntheses.
Enolate alkylation
Condition overview
By electrophile
Electrophile type
Conditions
Note
Activated R-X
Best with enamines1. \(\ce{R2NH},\
\rm{cat\ }\ce{H+}\)2. \(\ce{R-X}\)3. \(\ce{H+}\)
Tertiary R-X
Lewis acid to form cation\(\ce{Ti...
Updated to electronic spectroscopies.
Interaction of
molecules with radiation
n
i
n
j
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Three types of interactions
Absorption
Stimulated emission
Spontaneous emission
Depending on situations, the rate of one process may
dominate.
...
Essential Thermodynamics - summary of Cambridge IA chemistry TD
course.
Laws
First Law:
\[
dU =\delta q+ \delta w \label{td1}\tag{1}
\]
Second Law: entropy of the Universe increases in a
spontaneous process.
Entropy is classically defined as
\[
dS=\frac{\delta q_{rev}}{T}. \tag{2}\label{entro...
让对滑雪完全无感的我，回到全法最大滑雪度假村Val Thoren的唯一动力。
The motivation for a ski-phobia like me to return to Val Thoren.
参与牛剑Varsity
trip前往法国享受的一次滑雪之旅已经过去半年多了，而这家餐厅的记忆也自然而然随时间开始淡去。
“不行，不能忘，必须记录下来！”它给我带来的体验就是有这么优越。
于是，在这不尴不尬的时间点，胡编了一个“之最”的名号来赞美它。不想说得太绝对，毕竟我也没去过足够多的优秀餐厅。“学年最佳”，就一点也不假，完全可以甩心中的第二名13条街。
在短短的一周时间中，我们...
