Live practice

\[\begin{aligned}n(A)^2 &= 9\Rightarrow n(A)\\&= 3\end{aligned}\]. The displayed pairs show that \(-1,0,1\in A\); hence these are exactly its elements.

\(A\times A=\{(-1,-1),(-1,0),(-1,1),(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1)\}\).

All six p orbitals overlap continuously and the six pi electrons are delocalised over the ring, satisfying Hückel’s 4n+2 rule for n=1.

A C–H sigma bond on the alpha carbon overlaps with the neighbouring empty/partly filled p or pi system. Its electrons delocalise into that system.

Fluorine has oxidation number −1 in AgF₂, so silver must be +2. Ag(II) readily gains an electron to form much more stable Ag(I).

Here Δn=2−3=−1, hence Kp=Kc(RT)⁻¹ and Kc=KpRT.

Cool liquid water to 0°C, freeze it, then cool the ice to −10°C. Add all three enthalpy changes.

The potential energy of two bonded atoms is minimum at an equilibrium internuclear distance. Experimentally it is inferred by diffraction or spectroscopy.

Across a period, nuclear charge rises while electrons enter the same shell, so effective nuclear attraction increases and radius falls. Down a group, a new principal shell is added and shielding increases, so radius rises.

At threshold, photon energy equals the ionisation energy per atom. Multiply by the Avogadro constant.

Read the atom ratios from the molecular formula and use the Avogadro constant for the molecule count.