Glass is a mixture of several compounds, but a major constituent of most glass is calcium silicate, \(\mathrm{CaSiO}_{3}\). Glass can be etched by treatment with hydrofluoric acid; HF attacks the calcium silicate of the glass, producing gaseous and water-soluble products (which can be removed by washing the glass). For example, the volumetric glassware in chemistry laboratories is often graduated by using this process. Balance the following equation for the reaction of hydrofluoric acid with calcium silicate. $$\mathrm{CaSiO}_{3}(s)+\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$

First, let's identify the elements involved in the reaction. We have Calcium (Ca), Silicon (Si), Oxygen (O), Hydrogen (H), and Fluorine (F). Now, count the number of atoms for each element on both sides of the equation: Reactants: - Ca: 1 - Si: 1 - O: 3 - H: 1 - F: 1 Products: - Ca: 1 - Si: 1 - O: 1 - H: 2 - F: 6

To balance the equation, we will start adjusting the coefficients for the compounds containing the least common elements and work our way through to the most common elements (usually H and O). 1. Balance F: Since there are 6 F atoms in the products and only 1 F atom in the reactants, add a coefficient of 6 to the HF reactant: $$\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l)$$ Now there are 6 H atoms and 6 F atoms in the reactants. 2. Balance O: There are 3 O atoms in the reactants and only 1 O atom in the products. Add a coefficient of 3 to the H2O product to balance the O atoms: $$\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2} \mathrm{O}(l)$$ Now there are 6 H atoms and 3 O atoms in both the reactants and products. 3. Check the balance for Ca and Si: There is no need to adjust the coefficients for Ca and Si, as there is already 1 Ca and 1 Si atom on both sides of the equation. At this point, the equation is balanced. The balanced chemical equation for the reaction of hydrofluoric acid with calcium silicate is: $$\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(aq) \rightarrow \mathrm{CaF}_{2}(aq)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2} \mathrm{O}(l)$$