Live practice

A metal displaces another metal from its oxide only if it is more reactive. The order is \(\ce{Mg > Zn > Cu}\).

• Magnesium displaces zinc from \(\ce{ZnO}\): \(\ce{Mg + ZnO -> MgO + Zn}\).
• Magnesium displaces copper from \(\ce{CuO}\): \(\ce{Mg + CuO -> MgO + Cu}\).
• Zinc displaces copper from \(\ce{CuO}\): \(\ce{Zn + CuO -> ZnO + Cu}\).

No metal listed can displace magnesium from \(\ce{MgO}\), and copper cannot displace zinc or magnesium.

Water undergoes slight self-ionisation, so both \(\ce{H+}\) (as \(\ce{H3O+}\)) and \(\ce{OH-}\) are present in every aqueous solution. A solution is basic when its hydroxide-ion concentration is greater than its hydronium-ion concentration. Thus the presence of a small amount of \(\ce{H+}\) does not prevent basic behaviour.

Principle. Ignoring external loss, heat lost by metal equals heat gained by water plus calorimeter.

If heat escapes, the metal supplied more energy than the water and calorimeter received. Ignoring that missing energy makes the calculated specific heat too small.

Principle. Bulk modulus obeys ΔV/V=−ΔP/B; the minus sign represents contraction.

Principle. Treat molecule plus wall as the isolated collision system. Equal incoming and outgoing speeds give equal molecular kinetic energies.

Principle. Straight x-t segments have constant velocity and zero acceleration. An instantaneous velocity change produces impulse m delta-v.

Add the van speed to obtain bullet speed relative to ground, then subtract the car speed.

Principle. Use the spherical volume and multiply by the number of atoms in one mole.

Define the sample space and count each favourable outcome once.

The final value lies in [0,1]; complement pairs also sum to one, providing an independent check.

Form the required totals explicitly and divide by the full number of observations.

The variance is nonnegative and the reported standard deviation is its positive square root.