Question

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

Short answer

The balanced equation for the reaction between calcium silicate and hydrofluoric acid is: \[ \mathrm{CaSiO}_{3}(s)+4\mathrm{HF}(a q) \longrightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+2\mathrm{H}_{2} \mathrm{O}(l) \]

Step-by-step solution

Count the number of atoms of each element on both sides of the equation

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.

Balance the equation by adjusting coefficients

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.

Key concepts

Calcium Silicate

Calcium silicate, often abbreviated as CaSiO₃, is a compound commonly found in various industrial applications. It plays a vital role in the manufacturing of glass, where it serves as a major constituent. In the context of the chemical reaction at hand, calcium silicate reacts with hydrofluoric acid. This reaction is crucial, particularly in glass etching processes. During the etching process, the calcium silicate compound dissolves and facilitates the creation of precise markings on glassware. If you're working with chemical reactions involving calcium silicate, it's important to remember its reactivity and behavior when interacting with acids like hydrofluoric acid. Knowing the formula .CaSiO₃ is equally important. It gives you insights into the atomic composition of the compound, which is essential for balancing chemical equations correctly.

Hydrofluoric Acid

Hydrofluoric acid, known by its chemical formula HF, is a notoriously reactive and dangerous acid, commonly used in industrial applications, including glass etching. When hydrofluoric acid comes into contact with calcium silicate, it facilitates a chemical reaction that helps in shaping and designing glass components. Given its high reactivity, HF should always be handled with care. In chemical reactions, it acts as a source of fluoride ions, which interact with other components such as calcium silicate. Understanding hydrofluoric acid's role in reactions is essential for working safely and efficiently. During the balancing of a chemical equation, adding more of its molecules might be necessary, as seen in our equation with calcium silicate, where 4 molecules of HF are required to fully balance the reaction.

Stoichiometry

Stoichiometry is a fundamental aspect of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It provides a set of principles essential for balancing chemical equations. In the chemical reaction between calcium silicate and hydrofluoric acid, stoichiometry allows us to balance the number of atoms on both sides of the equation accurately. The process begins by focusing on the number of atoms of each element present in the reactants and products.
By following stoichiometric principles, one can establish the proper coefficient for each reactant and product. For this reaction, identifying each part, such as Ca, Si, and F, and working on them sequentially ensures that the reaction equation remains balanced while adhering to the conservation of mass. This systematic approach is what makes stoichiometry a vital tool in chemical reaction analysis.

Molecular Formula Balancing

Balancing a chemical equation means ensuring that the number of atoms of each element is the same on both sides of the equation. This step is critical to reflect the conservation of mass in a chemical reaction. The process begins by identifying the molecular formulas of all participating compounds and counting the atoms involved.
Start with the smallest group of elements or those appearing in fewer compounds within the equation, such as calcium and silicon, in the case of the calcium silicate reaction. Then proceed to tackle elements like hydrogen and oxygen, which may appear multiple times or in different compounds.
Using coefficients to balance the equation, especially for compounds appearing only once on either side, helps maintain equilibrium across all involved elements. For instance, placing a "4" in front of HF is necessary because four fluorine atoms are needed to match with those appearing in the products. It's a crucial technique that combines keen observation with methodical adjustments.