Question

For cach of the following reactions, give the balanced cquation 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. ${\mathrm{PCl}}_3(l)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+\mathrm{HCl}(g)$ b. ${\mathrm{XeF}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)\to \mathrm{Xe}(g)+\mathrm{HF}(g)+{\mathrm{O}}_2(g)$ c. $\mathrm{S}(s)+{\mathrm{HNO}}_3(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_4(aq)+{\mathrm{H}}_2\mathrm{O}(l)+{\mathrm{NO}}_2(g)$ d. ${\mathrm{NaHSO}}_3(s)\to {\mathrm{Na}}_2{\mathrm{SO}}_3(s)+{\mathrm{SO}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)$

Short answer

The balanced chemical equations and their interpretations are as follows: a. $${\mathrm{PCl}}_3(l)+3{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+3\mathrm{HCl}(g)$$ One molecule of PCl₃ reacts with three molecules of H₂O, producing one molecule of H₃PO₃ and three molecules of HCl. In terms of moles, for every one mole of PCl₃, three moles of H₂O are required and one mole of H₃PO₃ and three moles of HCl are produced. b. $${\mathrm{XeF}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(l)\to \mathrm{Xe}(g)+2\mathrm{HF}(g)+{\mathrm{O}}_2(g)$$ One molecule of XeF₂ reacts with two molecules of H₂O, producing one molecule of Xe, two molecules of HF, and one molecule of O₂. In terms of moles, for every one mole of XeF₂, two moles of H₂O are required and one mole of Xe, two moles of HF, and one mole of O₂ are produced. c. $$S(s)+6HN{O}_3(aq)\to H_{2}S{O}_4(aq)+2H_{2}O(l)+6N{O}_2(g)$$ One molecule of S reacts with six molecules of HNO₃, producing one molecule of H₂SO₄, two molecules of H₂O, and six molecules of NO₂. In terms of moles, for every one mole of S, six moles of HNO₃ are required and one mole of H₂SO₄, two moles of H₂O, and six moles of NO₂ are produced. d. $$2{\mathrm{NaHSO}}_3(s)\to {\mathrm{Na}}_2{\mathrm{SO}}_3(s)+{\mathrm{SO}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)$$ Two molecules of NaHSO₃ react to produce one molecule of Na₂SO₃, one molecule of SO₂, and one molecule of H₂O. In terms of moles, for every two moles of NaHSO₃, one mole of Na₂SO₃, one mole of SO₂, and one mole of H₂O are produced.

Step-by-step solution

a. Balancing the Equation

For the reaction $${\mathrm{PCl}}_3(l)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+\mathrm{HCl}(g)$$ we have to balance the number of atoms of each element on both sides of the equation. The balanced equation is: $${\mathrm{PCl}}_3(l)+3{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+3\mathrm{HCl}(g)$$

a. Interpretation of the Equation

The balanced equation indicates that one molecule of PCl₃ reacts with three molecules of H₂O, producing one molecule of H₃PO₃ and three molecules of HCl. In terms of moles, for every one mole of PCl₃, three moles of H₂O are required and one mole of H₃PO₃ and three moles of HCl are produced.

b. Balancing the Equation

For the reaction $${\mathrm{XeF}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)\to \mathrm{Xe}(g)+\mathrm{HF}(g)+{\mathrm{O}}_2(g)$$ the balanced equation is: $${\mathrm{XeF}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(l)\to \mathrm{Xe}(g)+2\mathrm{HF}(g)+{\mathrm{O}}_2(g)$$

b. Interpretation of the Equation

The balanced equation indicates that one molecule of XeF₂ reacts with two molecules of H₂O, producing one molecule of Xe, two molecules of HF, and one molecule of O₂. In terms of moles, for every one mole of XeF₂, two moles of H₂O are required and one mole of Xe, two moles of HF, and one mole of O₂ are produced.

c. Balancing the Equation

For the reaction $$\mathrm{S}(s)+{\mathrm{HNO}}_3(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_4(aq)+{\mathrm{H}}_2\mathrm{O}(l)+{\mathrm{NO}}_2(g)$$ the balanced equation is: $$S(s)+6HN{O}_3(aq)\to H_{2}S{O}_4(aq)+2H_{2}O(l)+6N{O}_2(g)$$

c. Interpretation of the Equation

The balanced equation indicates that one molecule of S reacts with six molecules of HNO₃, producing one molecule of H₂SO₄, two molecules of H₂O, and six molecules of NO₂. In terms of moles, for every one mole of S, six moles of HNO₃ are required and one mole of H₂SO₄, two moles of H₂O, and six moles of NO₂ are produced.

d. Balancing the Equation

For the reaction $${\mathrm{NaHSO}}_3(s)\to {\mathrm{Na}}_2{\mathrm{SO}}_3(s)+{\mathrm{SO}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)$$ the balanced equation is: $$2{\mathrm{NaHSO}}_3(s)\to {\mathrm{Na}}_2{\mathrm{SO}}_3(s)+{\mathrm{SO}}_2(g)+{\mathrm{H}}_2\mathrm{O}(l)$$

d. Interpretation of the Equation

The balanced equation indicates that two molecules of NaHSO₃ react to produce one molecule of Na₂SO₃, one molecule of SO₂, and one molecule of H₂O. In terms of moles, for every two moles of NaHSO₃, one mole of Na₂SO₃, one mole of SO₂, and one mole of H₂O are produced.

Key concepts

Balancing Equations

Balancing chemical equations is an essential skill in understanding chemical reactions. It involves making sure that the number of atoms for each element is the same on both the reactant and product sides of the equation. This maintains the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.

For example, consider the reaction of phosphorus trichloride (${\mathrm{PCl}}_3$) with water (${\mathrm{H}}_2\mathrm{O}$) to form phosphorous acid (${\mathrm{H}}_3{\mathrm{PO}}_3$) and hydrochloric acid ($\mathrm{HCl}$). The initial unbalanced equation is:$${\mathrm{PCl}}_3(l)+{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+\mathrm{HCl}(g)$$To balance it, we ensure each element's atom count matches on both sides: ${\mathrm{PCl}}_3(l)+3{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+3\mathrm{HCl}(g)$.

• Check each element: Phosphorus (P) is balanced with 1 on each side.
• Chlorine (Cl) now has 3 atoms on each side.
• Hydrogen (H), with 6 (from 3 water molecules) on each side, and oxygen (O) has the requisite 3 atoms per side.

This systematic approach to adjusting coefficients is how we balance equations.

Molecular Interpretation

Molecular interpretation involves understanding what the balanced equation signifies at the molecular level. Each term indicates the type and number of molecules or atoms involved in the reaction

Using the ${\mathrm{PCl}}_3(l)+3{\mathrm{H}}_2\mathrm{O}(l)\to {\mathrm{H}}_3{\mathrm{PO}}_3(aq)+3\mathrm{HCl}(g)$ reaction as an example:

• One molecule of phosphorus trichloride undergoes a reaction with three molecules of water.
• This reaction produces one molecule of phosphorous acid and three molecules of hydrochloric acid.

This interpretation helps visualize the molecular process, focusing on the quantity and type of molecules participating in and resulting from the reaction.

In essence, it breaks down the chemical equation into understandable parts, shedding light on the reaction's inner workings.

Stoichiometry

Stoichiometry is the quantitative heart of chemistry that relates to the calculation of reactants and products in chemical reactions. It helps in predicting how much of a substance reacts or is formed. Stoichiometry ensures that chemical equations reflect the conservation of mass.

Continuing with our example, consider the stoichiometric interpretation of ${\mathrm{XeF}}_2(g)+2{\mathrm{H}}_2\mathrm{O}(l)\to \mathrm{Xe}(g)+2\mathrm{HF}(g)+{\mathrm{O}}_2(g)$.

• For one mole of Xenon difluoride (${\mathrm{XeF}}_2$), we need two moles of water to produce:
• One mole of xenon gas
• Two moles of hydrogen fluoride
• One mole of oxygen gas

Understanding the mole concept here is vital as it allows scaling reactions up or down. For instance, if you start with 2 moles of ${\mathrm{XeF}}_2$, you should ensure to have 4 moles of water to get twice the products. Thus, stoichiometry provides a bridge between the results of an atomic scale reaction and practical laboratory measurements.

Reaction Equations

Reaction equations give us a concise way to describe chemical reactions using symbols and formulas for the involved substances.

These equations tell us what substances start the reaction (reactants) and what new substances are formed at the end (products). For example, the equation $\mathrm{S}(s)+6{\mathrm{HNO}}_3(aq)\to {\mathrm{H}}_2{\mathrm{SO}}_4(aq)+2{\mathrm{H}}_2\mathrm{O}(l)+6{\mathrm{NO}}_2(g)$ indicates:

• Solid sulfur ($\mathrm{S}$) reacts with nitric acid (${\mathrm{HNO}}_3$).
• As a result, sulfuric acid (${\mathrm{H}}_2{\mathrm{SO}}_4$), water, and nitrogen dioxide gas (${\mathrm{NO}}_2$) are produced.

This concise representation captures complex reactions in a clear format. In balancing and reading these equations, note the states of substances (solid $s$, liquid $l$, aqueous $aq$, and gas $g$), as they affect how substances can interact. Reaction equations summarize big ideas in chemistry simply and effectively.