The density of water is 1g/cm\(^3\) while that of ice is 0.9g/cm\(^3\). Calculate the change in volume when 90g of ice is completely melted.

Answer Details

Melting changes the arrangement of the molecules but not how many there are, so the mass is conserved while the volume changes because the density changes. The route through the problem is therefore: use \(V = \dfrac{m}{\rho}\) for the ice, use it again for the water formed, then subtract.

The change in volume is \[\Delta V = 100 - 90 = 10\,\text{cm}^3,\] and it is a decrease, because water is denser than ice. This is the well-known anomaly of water: the open hydrogen-bonded lattice of ice collapses on melting, so a given mass of ice shrinks when it turns to liquid. It is also why ice floats and why a full bottle of water bursts when it freezes.

Two traps are worth naming. Answering \(90\,\text{cm}^3\) means the volume of the water was quoted instead of the change in volume. Answering \(9\,\text{cm}^3\) comes from taking \(10\%\) of \(90\), which wrongly assumes the water volume is the starting figure; the \(10\%\) difference in density applies to the ice volume of \(100\,\text{cm}^3\). In any density question, work out each volume separately from \(m/\rho\) and only then subtract, and state clearly whether the change is an increase or a decrease.