Which of the following compounds contain(s) no covalent bond(s)?
KCl, PH$$_3$$, O$$_2$$, B$$_2$$H$$_6$$, H$$_2$$SO$$_4$$

First, we recall the basic definition of bond types. A covalent bond is formed when two atoms share electron pairs, generally occurring between non-metals of comparable electronegativity. An ionic bond is produced when one atom donates electrons completely to another, leading to cations and anions held together by electrostatic attraction; such bonds are typical when a metal combines with a non-metal having a large electronegativity difference.

Now we inspect every given compound one by one and decide whether at least one covalent bond is present.

We begin with potassium chloride, $$\text{KCl}$$. Potassium is a metal belonging to Group 1 and readily loses one electron to form the cation $$\text{K}^+$$. Chlorine, a non-metal of Group 17, gains that electron to form the anion $$\text{Cl}^-$$. The attraction between $$\text{K}^+$$ and $$\text{Cl}^-$$ is purely electrostatic. No pair of electrons is shared; therefore the bond in $$\text{KCl}$$ is strictly ionic. Hence $$\text{KCl}$$ contains no covalent bond.

Next we look at phosphine, $$\text{PH}_3$$. Phosphorus (P) and hydrogen (H) are both non-metals. Phosphorus contributes one electron and hydrogen contributes one electron in each P-H linkage, creating three shared pairs in total. These P-H linkages are covalent. So $$\text{PH}_3$$ definitely possesses covalent bonds.

For dioxygen, $$\text{O}_2$$, each oxygen atom shares two electrons to make a double bond, written as $$\text{O}= \text{O}$$. This is the classical example of a covalent bond, specifically a covalent double bond. Hence $$\text{O}_2$$ contains covalent bonds.

Consider diborane, $$\text{B}_2\text{H}_6$$. The structure involves four conventional two-centre two-electron B-H covalent bonds and two special three-centre two-electron B-H-B bridge bonds, which are also classified as covalent (though multicentre). Thus $$\text{B}_2\text{H}_6$$ is a fully covalently bonded molecule.

Finally, sulfuric acid, $$\text{H}_2\text{SO}_4$$, has the following connectivity: each hydrogen is bonded to oxygen in an $$\text{O-H}$$ single bond, each outer oxygen is bonded to sulfur through $$\text{S=O}$$ double bonds or $$\text{S-O}$$ single bonds depending on the resonance structure. All these $$\text{O-H}, \text{S-O},$$ and $$\text{S=O}$$ linkages are covalent. So $$\text{H}_2\text{SO}_4$$ certainly contains covalent bonds.

Summarising our findings:

$$\begin{aligned} \text{KCl} & : \text{no covalent bond} \\ \text{PH}_3 & : \text{contains covalent bonds} \\ \text{O}_2 & : \text{contains covalent bonds} \\ \text{B}_2\text{H}_6 & : \text{contains covalent bonds} \\ \text{H}_2\text{SO}_4 & : \text{contains covalent bonds} \end{aligned}$$

Hence, the only compound in the list that contains no covalent bond is $$\text{KCl}$$.

Therefore, the correct option is D, comprising only $$\text{KCl}$$.

Hence, the correct answer is Option D.