Question

The melting point of a fictional substance X is $\mathbf{225}\mathbf{°}\mathbf{C}$ at 10.0 atm. If the density of the solid phase of X is $\mathbf{2}\mathbf{.}\mathbf{67}\mathbf{g}\mathbf{/}{\mathbf{cm}}^3$ and the density of the liquid phase is $\mathbf{2}\mathbf{.}\mathbf{78}\mathbf{g}\mathbf{/}{\mathbf{cm}}^3$ at 10.0 atm, predict whether the normal melting point of X will be less than, equal to, or greater than ${\mathbf{225}}^0\mathbf{C}$ . Explain.

Short answer

The normal melting point of X will be greater than ${225}^0\mathrm{C}.$

Step-by-step solution

Step 1:The phase diagram

The melting point of X is ${225}^0\mathrm{C}\mathrm{at}10.0\mathrm{atm}.$

The density of the solid phase of X is $2.67\mathrm{g}/{\mathrm{cm}}^3.$

The density of the liquid phase is $2.78\mathrm{g}/{\mathrm{cm}}^3$at 10.0 atm.

The normal boiling point from the graph

The slope of the solid-liquid curve in the above graph is negative.

In this graph, as pressure rises, the density of X decreases. From the given data, the liquid phase density is less than the solid phase.

At the normal melting point, the pressure will be 1 atm.

As the pressure is reduced from 10 atm to 1 atm, the temperature of the X will also increase.

The normal melting point will be greater than ${225}^0\mathrm{C}.$