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How do I rank the following compounds from lowest to highest boiling point: Calcium carbonate, methane, methanol \[\left( {C{H_4}O} \right)\] , dimethyl ether \[\left( {C{H_3}OC{H_3}} \right)\] ?

Answer
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Hint: The boiling point of compounds increases with the strength of intermolecular forces. If the molecule has ionic attraction, it has the highest boiling point. The strength of the intermolecular forces follows the order of non-polar attraction < dipole forces < hydrogen bonding < Ionic forces.

Complete answer:
Given compounds are calcium carbonate which has a molecular formula of \[CaC{O_3}\] it has ionic forces in it, as the calcium and carbonate are ions and made as a molecule.
Another compound is methane which has a molecular formula of \[C{H_4}\] it has weak London dispersion forces and is considered as a nonpolar molecule. It has less boiling point than calcium carbonate.
Another compound is methanol which has a molecular formula of \[C{H_4}O\] it has hydrogen bonding as the hydrogen atom is involved in hydrogen bonding. It has a higher boiling point than methane and a lower boiling point than calcium carbonate.
Another compound is dimethyl ether which has a molecular formula of \[C{H_3}OC{H_3}\]it has dipole-dipole attraction and thus this compound will have high boiling point than methane and low boiling point than methanol and calcium carbonate.
The order of boiling point from lowest boiling point to highest boiling point is
\[C{H_4} < C{H_3}OC{H_3} < C{H_4}O < CaC{O_3}\]

Note:
The boiling point increases with the strength of the intermolecular forces in the molecule. The stringer is the intermolecular forces: more time is required to boil them and high temperature requires for it leads to the high boiling point.