Arrange the following in increasing order of acid strength with proper explanation: (a) \(\mathrm{HIO}_{2}, \mathrm{HBrO}_{2^{\prime}} \mathrm{HClO}_{2}\) (b) \(\mathrm{HF}, \mathrm{H}_{2} \mathrm{O}, \mathrm{NH}_{3}, \mathrm{CH}_{4}\)

To grasp the nature of oxyacids, we look at compounds that include hydrogen, oxygen, and another element, typically a nonmetal. Their general formula is often represented as H_nXO_m, where 'X' is the nonmetal element. The acid strength in oxyacids is influenced by several factors including the electronegativity of the 'X', the number of oxygen atoms, and the stability of the resulting anion post dissociation.

Electronegativity plays a crucial role; a highly electronegative 'X' can draw more electron density from the O-H bond, making it easier to release a proton (H⁺). The number of oxygens also matters, as each additional oxygen can delocalize the negative charge over a larger area after the proton is released, leading to enhanced acid strength.

When comparing oxyacids of the halogens like HClO₂, HBrO₂, and HIO₂, we see an increase in acidity as we move down the halogen group in the periodic table. This is due to the increasing size and decreasing electronegativity of the central halogen atom, which facilitates easier release of the hydrogen ion.

Binary acids, simple compounds consisting of hydrogen and one other element, display trends in acid strength that largely depend on bond strength and the electronegativity of the non-hydrogen atom. In general, binary acid strength increases with increasing electronegativity of the non-hydrogen atom when looking across a period, and with increasing atomic radius when looking down a group on the periodic table.

In binary acids like HF, the electronegativity difference between hydrogen and fluorine creates a strong polarity, enhancing HF's status as a strong acid. When comparing different binary acids, it's essential to examine period and group trends. HF, found at the top right of the periodic table, is more acidic than water (H₂O), ammonia (NH₃), and methane (CH₄), precisely due to its position, indicating a strong acid due to fluorine's high electronegativity.

Periodicity in acidity refers to the predictable patterns seen across the periodic table, which helps in forecasting the strength of acids. When moving from left to right across a period, acid strength typically increases. This is because elements to the right have a higher electronegativity, exerting greater pull on electron pairs, thereby increasing the acid's tendency to donate protons.

However, as we move down a group on the periodic table, acid strength also increases. This may seem counterintuitive at first glance, but it can be explained by the larger atomic sizes and weaker bonds with hydrogen in lower elements. The weaker the H-X bond, the easier it is for the acid to release its hydrogen ion, thus stronger the acid. This is clearly observed in our exercise example where HF is stronger than water, ammonia, and methane.

The strength of hydrogen bonds directly influences acid strength. A weaker H-X bond makes an acid stronger since it promotes the ease of hydrogen ion (proton) release. Factors affecting this bond strength include the size and electronegativity of the X atom.

In binary acids, as the size of the X atom increases (moving down a group), the bond strength decreases, making the acid stronger. Conversely, when comparing acids across a period where atom size is roughly similar, the bond strength increases with electronegativity. The balance of these forces determines the acid's proclivity to ionize, a critical concept supporting the arrangement of binary acids in our homework exercise.

Understanding these intricacies aids in predicting the behavior of acids in chemical reactions, which is fundamental in chemistry studies and applications.