Answer
The structure of isomer having formula $C_{2}H_{6}O$ that boils at $-23^{\circ}$C is : $CH_{3}-O-CH_{3}$ i.e. methoxy methane.
And the structure of isomer that boils at $78.5^{\circ}C$ is : $ CH_{3}CH_{2}OH$ i.e. ethanol.
Work Step by Step
Two structural isomers are possible having molecular formula $C_{2}H_{6}O$ which are $CH_{3}-O-CH_{3}$ and $ CH_{3}CH_{2}OH$. Between this, ethanol has boiling point greater than that of di methyl ether because of intermolecular H bonding occurs between the molecules of ethanol. H bonding occurs because here H is bonded with more electronegative atom O. So, it will participate in intermolecular H bonding as seen below. So, the molecules of $ CH_{3}CH_{2}OH$ are bonded together in liquid state and as a result it will need more energy to break the bond i.e. boiling point increases.
On the other hand, in dimethyl ether H is bonded with C atom which are less electronegative than O atom. So, they cannot participate in intermolecular H bonding. so, the boiling point is low.
