Live practice

Count total valence electrons, choose the least electronegative central atom, complete terminal octets, and use multiple bonds or formal charges where needed. Carbonate has three equivalent resonance contributors.

Period 6 fills 6s, 4f, 5d and 6p subshells. Their capacities follow 2(2l+1).

Identify the element from Z and write A as the left superscript and Z as the left subscript.

The balanced equation gives a 1:1:1 mole ratio. In parts (ii) and (iii), oxygen is the limiting reactant.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

A single sinusoid is SHM. Thus (a)=√2 sin(ωt−π/4) is SHM with T=2π/ω, and (c) is SHM with angular frequency 2ω and T=π/ω.

Using sin³u=(3sinu−sin3u)/4, (b) contains two harmonics: it is periodic but non-SHM, T=2π/ω. Expression (d) is also a harmonic sum with common period 2π/ω, hence periodic but non-SHM. The exponential pulse (e) and polynomial (f) never repeat, so both are nonperiodic.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

Use absolute pressures, 16 atm and 12 atm, in PV=nRT. The mass removed is M(n₁−n₂).

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

For an adiabatic ideal-gas process, PV^γ remains constant.

Principle and reasoning. Work from the governing physical relation and apply it to every stated part.

A stiffer material has the larger Young's modulus. Pulling a coil twists its wire and therefore produces shear.

At a turning point the instantaneous kinetic energy is zero, so total energy equals potential energy.

Tension is the only horizontal force and itself supplies the required centripetal force.