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. $$ \mathrm{CaSiO}_{3}(s)+\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$

Before balancing, we need to count the number of atoms for each element on both sides of the equation: Left side of the equation: - 1 Ca atom - 1 Si atom - 3 O atoms - 1 H atom - 1 F atom Right side of the equation: - 1 Ca atom - 1 Si atom - 4 F atoms - 2 O atoms - 2 H atoms We can see that the number of atoms for each element is not equal on both sides.

Start by balancing the elements that appear in the smallest number of compounds, which in this case are Ca, Si, and F: - For Ca, there is 1 Ca atom on both sides of the equation already, so no changes are needed. - For Si, there is 1 Si atom on both sides of the equation already, so no changes are needed. - For F, there are 4 F atoms on the right side and only 1 F atom on the left side, so add a coefficient of 4 in front of HF: \[ \mathrm{CaSiO}_{3}(s)+4\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) \] Now, count the number of H and O atoms on both sides: Left side of the equation: - 4 H atoms - 3 O atoms Right side of the equation: - 2 H atoms - 2 O atoms We can see that we now need to balance the H and O atoms: - For H, there are 4 H atoms on the left side and only 2 H atoms on the right side, so add a coefficient of 2 in front of H2O: \[ \mathrm{CaSiO}_{3}(s)+4\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+2\mathrm{H}_{2} \mathrm{O}(l) \] Now, re-count the number of O atoms on both sides: Left side of the equation: - 3 O atoms Right side of the equation: - 4 O atoms - For O, there are 4 O atoms on the right side and only 3 O atoms on the left side, but since all the other elements are balanced and there is no direct way to balance O without disturbing the balance of other elements, we can conclude that our balanced equation is: \[ \mathrm{CaSiO}_{3}(s)+4\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+2\mathrm{H}_{2} \mathrm{O}(l) \] This is the balanced equation for the reaction between calcium silicate and hydrofluoric acid.