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 hydrogen fluoride: HF attacks the calcium silicate of the glass, producing gaseous and water-soluble products (which can be removed by washing the glass). Balance the following equation fo the reaction of hydrogen fluoride with calcium silicate. $$ \mathrm{CaSiO}_{3}(s)+\mathrm{HF}(g) \rightarrow \mathrm{CaF}_{2}(a q)+\mathrm{SiF}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(l) $$

Short answer

To balance the given equation for the reaction of hydrogen fluoride with calcium silicate, multiply the H₂O by 3 and the HF by 6. This results in the balanced equation: \(\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(g) \rightarrow \mathrm{CaF}_{2}(aq)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2}\mathrm{O}(l)\)

Step-by-step solution

Identify the unbalanced elements

First, we need to identify the elements in the given equation that are not balanced. The elements involved in this reaction are Calcium (Ca), Silicon (Si), Oxygen (O), Hydrogen (H), and Fluorine (F).

Write the initial atom counts for each element

Next, let's count the number of atoms for each element on both sides of the unbalanced equation: Reactants: Ca: 1, Si: 1, O: 3, H: 1, F: 1 Products: Ca: 1, Si: 1, O: 1, H: 2, F: 6 As we can see, both Oxygen (O) and Fluorine (F) atoms are not balanced in the given equation.

Balance the Oxygen atoms

To balance the Oxygen atoms, we need to have the same number of them on both sides. Since there are 3 Oxygen atoms on the left side, and 1 Oxygen atom on the right side (in the water molecule), we can multiply the H₂O by 3, so we get 3 Oxygen atoms on the right side as well: $$\mathrm{CaSiO}_{3}(s)+\mathrm{HF}(g) \rightarrow \mathrm{CaF}_{2}(aq)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2}\mathrm{O}(l)$$ Now, the Oxygen atoms are balanced, but we have introduced more Hydrogen atoms on the right side by multiplying H₂O by 3. So, let's update the atom counts: Reactants: Ca: 1, Si: 1, O: 3, H: 1, F: 1 Products: Ca: 1, Si: 1, O: 3, H: 6, F: 6

Balance the Hydrogen and Fluorine atoms

Now we need to balance the Hydrogen and Fluorine atoms. Since there are 6 Hydrogen atoms and 6 Fluorine atoms on the product side, we can multiply the HF by 6 on the reactants side: $$\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(g) \rightarrow \mathrm{CaF}_{2}(aq)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2}\mathrm{O}(l)$$ By doing this, we update the atom counts one last time: Reactants: Ca: 1, Si: 1, O: 3, H: 6, F: 6 Products: Ca: 1, Si: 1, O: 3, H: 6, F: 6

Verify the balanced equation

Finally, we need to make sure that the balanced equation has the same number of atoms for each element on both sides. Since the atom counts match for all the elements involved, our equation is now balanced: $$\mathrm{CaSiO}_{3}(s)+6\mathrm{HF}(g) \rightarrow \mathrm{CaF}_{2}(aq)+\mathrm{SiF}_{4}(g)+3\mathrm{H}_{2}\mathrm{O}(l)$$

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the law of conservation of mass, which states that matter is neither created nor destroyed in a chemical reaction. Therefore, the number of atoms of each element must be the same before and after a reaction occurs.

To apply stoichiometry in solving problems, one must be able to read and write chemical equations accurately and then use mole ratios to convert between mass, moles, and number of particles. This allows chemists and chemistry students to predict the amounts of substances consumed and produced in a reaction, and is an essential skill in chemical analysis and industrial processes.

Stoichiometry in the Context of Balancing Equations

During the balancing of a chemical equation, such as the reaction of hydrogen fluoride with calcium silicate, stoichiometry helps us understand the exact proportions of reactants needed to produce the desired products. In this process, it is crucial to adjust the coefficients of the various reactants and products until the same number of atoms of each element appears on both sides of the equation, thus ensuring that the mass is conserved.

Chemical Equations

Chemical equations provide a symbolic representation of a chemical reaction, where the reactants are written on the left side and the products on the right side, usually separated by an arrow indicating the direction of the reaction. Each substance is represented by its chemical formula, and the coefficients next to each substance indicate the number of moles of that substance involved in the reaction.

Writing a balanced chemical equation requires careful analysis of the atom counts for each element involved in the reactants and products. The process of balancing involves determining the coefficients that provide the same number of atoms of each element on both sides of the equation. This is crucial for making quantitative predictions about the outcome of a reaction.

Improving Understanding of Chemical Equations

To enhance comprehension of chemical equations, it is helpful to practice identifying and counting the atoms of each element before and after the reaction has been shown. Additionally, using visual aids such as diagrams or molecular models can aid in the understanding of how atoms are rearranged during a reaction.

Acid-Base Reactions

Acid-base reactions, also known as neutralization reactions, are a type of chemical reaction where an acid reacts with a base to produce water and a salt. Acids are substances that can donate a hydrogen ion (H+), while bases can accept a hydrogen ion. The reaction generally follows the pattern: acid + base → salt + water.

In the context of the reaction between hydrogen fluoride (HF) and calcium silicate (CaSiO3), the HF acts as the acid, and the calcium silicate behaves more like a base, even though it is not a classic Arrhenius or Brønsted-Lowry base. The result of this reaction is the formation of water (H2O) and calcium fluoride (CaF2), which is the salt in this context, along with silicon tetrafluoride (SiF4).

Characteristics of Acid-Base Reactions

Acid-base reactions are crucial for many biological systems and industrial processes. Understanding the stoichiometry of such reactions is important, as it allows us to calculate the concentrations of acids and bases and determine their reactivity. During the balancing of an acid-base reaction, attention must be paid to both the conservation of mass and charge, ensuring that the numbers of H+ and OH- ions are equal to maintain neutrality.