Question

For each of the following reactions, give the balanced equation for the reaction and state the meaning of the equation in terms of the numbers of individual molecules and in terms of moles of molecules. a. \(\mathrm{PCl}_{3}(l)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(a q)+\mathrm{HCl}(g)\) b. \(\mathrm{XeF}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Xe}(g)+\mathrm{HF}(g)+\mathrm{O}_{2}(g)\) c. \(S(s)+H N O_{3}(a q) \rightarrow H_{2} S O_{4}(a q)+H_{2} O(l)+N O_{2}(g)\) d. \(\mathrm{NaHSO}_{3}(s) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{3}(s)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\)

Short answer

The balanced equations are: a. \(\mathrm{PCl}_{3}(l)+3\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(a q)+3\mathrm{HCl}(g)\) b. \(\mathrm{XeF}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Xe}(g)+2\mathrm{HF}(g)+\mathrm{O}_{2}(g)\) c. \(S(s)+6\mathrm{HNO}_{3}(a q) \rightarrow\mathrm{H}_{2}\mathrm{SO}_{4}(a q)+4\mathrm{H}_{2} \mathrm{O}(l)+2\mathrm{NO}_{2}(g)\) d. \(2\mathrm{NaHSO}_{3}(s) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{3}(s)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\) Interpretation: a. 1 mole of \(\mathrm{PCl}_{3}\) reacts with 3 moles of \(\mathrm{H}_{2} \mathrm{O}\) to produce 1 mole of \(\mathrm{H}_{3} \mathrm{PO}_{3}\) and 3 moles of \(\mathrm{HCl}\). b. 1 mole of \(\mathrm{XeF}_{2}\) reacts with 2 moles of \(\mathrm{H}_{2} \mathrm{O}\) to produce 1 mole of \(\mathrm{Xe}\), 2 moles of \(\mathrm{HF}\), and 1 mole of \(\mathrm{O}_{2}\). c. 1 mole of \(S\) reacts with 6 moles of \(\mathrm{HNO}_{3}\) to produce 1 mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), 4 moles of \(\mathrm{H}_{2}\mathrm{O}\), and 2 moles of \(\mathrm{NO}_{2}\). d. 2 moles of \(\mathrm{NaHSO}_{3}\) react to produce 1 mole of \(\mathrm{Na}_{2}\mathrm{SO}_{3}\), 1 mole of \(\mathrm{SO}_{2}\), and 1 mole of \(\mathrm{H}_{2}\mathrm{O}\).

Step-by-step solution

Balancing the equations

For each of the reactions, we will balance the chemical equations by making sure that the number of atoms of each element is the same on both sides of the equation. a. \(\mathrm{PCl}_{3}(l)+3\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(a q)+3\mathrm{HCl}(g)\) b. \(\mathrm{XeF}_{2}(g)+2\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{Xe}(g)+2\mathrm{HF}(g)+\mathrm{O}_{2}(g)\) c. \(S(s)+6\mathrm{HNO}_{3}(a q) \rightarrow\mathrm{H}_{2}\mathrm{SO}_{4}(a q)+4\mathrm{H}_{2} \mathrm{O}(l)+2\mathrm{NO}_{2}(g)\) d. \(2\mathrm{NaHSO}_{3}(s) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{3}(s)+\mathrm{SO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)\)

Interpret the balanced equations in terms of individual molecules

For each of the balanced reactions, we will now describe the reactions in terms of the numbers of individual molecules involved. a. 1 molecule of phosphorus trichloride reacts with 3 molecules of water to produce 1 molecule of phosphorous acid and 3 molecules of hydrogen chloride. b. 1 molecule of xenon hexafluoride reacts with 2 molecules of water to produce 1 molecule of xenon, 2 molecules of hydrofluoric acid, and 1 molecule of oxygen. c. 1 molecule of sulfur reacts with 6 molecules of nitric acid to produce 1 molecule of sulfuric acid, 4 molecules of water, and 2 molecules of nitrogen dioxide. d. 2 molecules of sodium bisulfite react to produce 1 molecule of sodium sulfite, 1 molecule of sulfur dioxide, and 1 molecule of water.

Interpret the balanced equations in terms of moles of molecules

For each of the balanced reactions, we will now describe the reactions in terms of moles of molecules involved. a. 1 mole of \(\mathrm{PCl}_{3}\) reacts with 3 moles of \(\mathrm{H}_{2} \mathrm{O}\) to produce 1 mole of \(\mathrm{H}_{3} \mathrm{PO}_{3}\) and 3 moles of \(\mathrm{HCl}\). b. 1 mole of \(\mathrm{XeF}_{2}\) reacts with 2 moles of \(\mathrm{H}_{2} \mathrm{O}\) to produce 1 mole of \(\mathrm{Xe}\), 2 moles of \(\mathrm{HF}\), and 1 mole of \(\mathrm{O}_{2}\). c. 1 mole of \(S\) reacts with 6 moles of \(\mathrm{HNO}_{3}\) to produce 1 mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\), 4 moles of \(\mathrm{H}_{2}\mathrm{O}\), and 2 moles of \(\mathrm{NO}_{2}\). d. 2 moles of \(\mathrm{NaHSO}_{3}\) react to produce 1 mole of \(\mathrm{Na}_{2}\mathrm{SO}_{3}\), 1 mole of \(\mathrm{SO}_{2}\), and 1 mole of \(\mathrm{H}_{2}\mathrm{O}\).

Key concepts

Chemical Reaction Stoichiometry

Stoichiometry is the cornerstone of chemical reactions, providing a quantitative relationship between reactants and products. It is the mathematical art of balancing chemical equations to ensure that the number of atoms for each element is conserved throughout the reaction.

Consider the example of phosphorus trichloride reacting with water to form phosphorous acid and hydrogen chloride. The equation \(\mathrm{PCl}_{3}(l) + 3\mathrm{H}_{2}O(l) \rightarrow \mathrm{H}_{3}\mathrm{PO}_{3}(aq) + 3\mathrm{HCl}(g)\)illustrates the stoichiometry of the reaction, indicating that one mole of phosphorus trichloride and three moles of water react to form one mole of phosphorous acid and three moles of hydrogen chloride. Learning to balance equations such as this is crucial for predicting the amounts of products and reactants.

When considering stoichiometry, it's essential to keep in mind the law of conservation of mass. This law states that mass is neither created nor destroyed in a chemical reaction. Stoichiometry ensures this law is respected, often requiring a step-by-step approach to identify how many moles of each substance are involved and what their molar ratios are.

Molecular Interpretation of Chemical Equations

The molecular interpretation of chemical equations allows us to visualize the discrete particles involved in chemical reactions. For instance, envisioning individual molecules reacting according to the balanced equation can enhance understanding:

For the reaction between xenon difluoride and water, the balanced equation is \(\mathrm{XeF}_{2}(g) + 2\mathrm{H}_{2}O(l) \rightarrow \mathrm{Xe}(g) + 2\mathrm{HF}(g) + \mathrm{O}_{2}(g)\).At the molecular level, it represents one molecule of xenon difluoride reacting with two water molecules to yield one molecule of xenon, two molecules of hydrofluoric acid, and one molecule of oxygen. This interpretation helps clarify the role of each chemical species during the reaction and is particularly useful when discussing reaction mechanisms or the physical movement of atoms and electrons during the transformation.

Molecular interpretations are not only valuable for learning purposes but also provide insights into the potential energy changes, molecular interactions, and dynamics within a chemical reaction.

Moles of Molecules in Reactions

The mole concept is vital in chemistry as it relates the countable number of molecules to a quantity that can be measured in the laboratory. A mole represents Avogadro's number, \(6.022 \times 10^{23}\) entities, be it atoms, molecules, ions or other particles.

In reactions, we frequently discuss the reactants and products in terms of moles. For example, the reaction of sulfur with nitric acid \(S(s) + 6\mathrm{HNO}_{3}(aq) \rightarrow \mathrm{H}_{2}\mathrm{SO}_{4}(aq) + 4\mathrm{H}_{2}O(l) + 2\mathrm{NO}_{2}(g)\)implies that one mole of sulfur and six moles of nitric acid result in one mole of sulfuric acid, four moles of water, and two moles of nitrogen dioxide.

Discussing reactions in terms of moles allows chemists to conveniently measure and predict the amounts of substances produced or consumed in a reaction. It simplifies the conversion between the microscopic scale of individual molecules and the macroscopic scale, where we can physically measure the masses of reactants and products to carry out practical work in laboratories.