Here are the solutions to the questions: a) i) The Group VII elements (Halogens) in order of increasing atomic number with their physical states at room temperature are: Fluorine ($\text{F}_2$): Gas* Chlorine ($\text{Cl}_2$): Gas* Bromine ($\text{Br}_2$): Liquid* Iodine ($\text{I}_2$): Solid* Astatine ($\text{At}_2$): Solid* ii) The variation in the physical states of the Halogens is due to the increasing strength of London dispersion forces (van der Waals forces) as the atomic number increases down the group. As the number of electrons in the halogen molecules ($\text{X}_2$) increases, the electron cloud becomes larger and more polarizable, leading to stronger temporary dipoles and thus stronger intermolecular forces. More energy is required to overcome these stronger forces, resulting in higher melting and boiling points, causing a transition from gases to liquid to solid at room temperature. b) i) Hydrogen bromide ($\text{HBr}$) and hydrogen iodide ($\text{HI}$) cannot be prepared conveniently by reacting their corresponding potassium salts with concentrated sulphuric acid because concentrated sulphuric acid ($\text{H}_2\text{SO}_4$) is a strong oxidizing agent. Bromide ions ($\text{Br}^-$) and especially iodide ions ($\text{I}^-$) are reducing agents, with their reducing power increasing down the group. When $\text{KBr}$ or $\text{KI}$ react with concentrated $\text{H}_2\text{SO}_4$, the $\text{HBr}$ and $\text{HI}$ formed are subsequently oxidized by the sulphuric acid to elemental bromine ($\text{Br}_2$) and iodine ($\text{I}_2$) respectively, contaminating the desired product. ii) A balanced chemical equation showing how hydrogen bromide can be prepared in the laboratory using a non-oxidizing acid like phosphoric acid: $$\boxed{\text{NaBr}(s) + \text{H}_3\text{PO}_4(conc) \to \text{NaH}_2\text{PO}_4(aq) + \text{HBr}(g)}$$ c) i) Fluorinating toothpaste: The importance of fluorinating toothpaste is to prevent tooth decay (dental caries). Fluoride ions ($\text{F}^-$) react with the hydroxyapatite in tooth enamel to form fluoroapatite, which is more resistant to acid attack by bacteria in the mouth, thereby strengthening the enamel and reducing cavities. ii) Iodinating kitchen salt: The importance of iodinating kitchen salt is to prevent iodine deficiency disorders. Iodine is an essential trace element required by the thyroid gland to produce hormones that regulate metabolism, growth, and development. A lack of iodine can lead to conditions such as goitre (enlargement of the thyroid gland) and cretinism (severe developmental issues in children).