Question

For each of the following reactions, give the balanced cquation for the reaction and state the meaning of the equation in terms of numbers of individual molecules and in terms of moles of molccules. a. \(\mathrm{UO}_{2}(s)+\mathrm{HF}(a q) \rightarrow \mathrm{UF}_{4}(a q)+\mathrm{H}_{2} \mathrm{O}(l)\) b. \(\mathrm{NaC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+\mathrm{HC}_{2} \mathrm{H}_{3} \mathrm{O}_{2}(a q)\) c. \(\mathrm{Mg}(s)+\mathrm{HCl}(a q) \rightarrow \mathrm{MgCl}_{2}(a q)+\mathrm{H}_{2}(g)\) d. \(\mathrm{B}_{2} \mathrm{O}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{B}(\mathrm{OH})_{3}(a q)\)

Short answer

a. The balanced equation is: \( \mathrm{UO}_{2}(s) + 4\mathrm{HF}(aq) \rightarrow \mathrm{UF}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l) \). It means that one molecule of \(\mathrm{UO}_{2}\) reacts with four molecules of \(\mathrm{HF}\) to produce one molecule of \(\mathrm{UF}_{4}\) and two molecules of \(\mathrm{H}_{2}\mathrm{O}\). In terms of moles, one mole of \(\mathrm{UO}_{2}\) reacts with four moles of \(\mathrm{HF}\) to produce one mole of \(\mathrm{UF}_{4}\) and two moles of \(\mathrm{H}_{2}\mathrm{O}\). b. The balanced equation is: \( 2\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}(aq) + \mathrm{H}_{2}\mathrm{SO}_{4}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}(aq) \). It means that two molecules of \(\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\) react with one molecule of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) to produce one molecule of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) and two molecules of \(\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\). In terms of moles, two moles of \(\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\) react with one mole of \(\mathrm{H}_{2}\mathrm{SO}_{4}\) to produce one mole of \(\mathrm{Na}_{2}\mathrm{SO}_{4}\) and two moles of \(\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}\). c. The balanced equation is: \( \mathrm{Mg}(s) + 2\mathrm{HCl}(aq) \rightarrow \mathrm{MgCl}_{2}(aq) + \mathrm{H}_{2}(g) \). It means that one molecule of \(\mathrm{Mg}\) reacts with two molecules of \(\mathrm{HCl}\) to produce one molecule of \(\mathrm{MgCl}_{2}\) and one molecule of \(\mathrm{H}_{2}\). In terms of moles, one mole of \(\mathrm{Mg}\) reacts with two moles of \(\mathrm{HCl}\) to produce one mole of \(\mathrm{MgCl}_{2}\) and one mole of \(\mathrm{H}_{2}\). d. The balanced equation is: \( \mathrm{B}_{2}\mathrm{O}_{3}(s) + 3\mathrm{H}_{2}\mathrm{O}(l) \rightarrow 2\mathrm{B}(\mathrm{OH})_{3}(aq) \). It means that one molecule of \(\mathrm{B}_{2}\mathrm{O}_{3}\) reacts with three molecules of \(\mathrm{H}_{2}\mathrm{O}\) to produce two molecules of \(\mathrm{B}(\mathrm{OH})_{3}\). In terms of moles, one mole of \(\mathrm{B}_{2}\mathrm{O}_{3}\) reacts with three moles of \(\mathrm{H}_{2}\mathrm{O}\) to produce two moles of \(\mathrm{B}(\mathrm{OH})_{3}\).

Step-by-step solution

1. Balance the equation

To balance the chemical equation for the reaction between \(\mathrm{UO}_{2}(s)\) and \(\mathrm{HF}(aq)\), we need to adjust the coefficients as follows: \[ \mathrm{UO}_{2}(s) + 4\mathrm{HF}(aq) \rightarrow \mathrm{UF}_{4}(aq) + 2\mathrm{H}_{2}\mathrm{O}(l) \]

2. Meaning in terms of individual molecules

The balanced equation means that one molecule of solid uranium dioxide reacts with four molecules of aqueous hydrogen fluoride to produce one molecule of aqueous uranium tetrafluoride and two molecules of liquid water.

3. Meaning in terms of moles of molecules

The balanced equation means that one mole of solid uranium dioxide reacts with four moles of aqueous hydrogen fluoride to produce one mole of aqueous uranium tetrafluoride and two moles of liquid water. b.

1. Balance the equation

To balance the chemical equation for the reaction between \(\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}(aq)\) and \(\mathrm{H}_{2}\mathrm{SO}_{4}(aq)\), we need to adjust the coefficients as follows: \[ 2\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}(aq) + \mathrm{H}_{2}\mathrm{SO}_{4}(aq) \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4}(aq) + 2\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2}(aq) \]

2. Meaning in terms of individual molecules

The balanced equation means that two molecules of aqueous sodium acetate react with one molecule of aqueous sulfuric acid to produce one molecule of aqueous sodium sulfate and two molecules of aqueous acetic acid.

3. Meaning in terms of moles of molecules

The balanced equation means that two moles of aqueous sodium acetate react with one mole of aqueous sulfuric acid to produce one mole of aqueous sodium sulfate and two moles of aqueous acetic acid. c.

1. Balance the equation

To balance the chemical equation for the reaction between \(\mathrm{Mg}(s)\) and \(\mathrm{HCl}(aq)\), we need to adjust the coefficients as follows: \[ \mathrm{Mg}(s) + 2\mathrm{HCl}(aq) \rightarrow \mathrm{MgCl}_{2}(aq) + \mathrm{H}_{2}(g) \]

2. Meaning in terms of individual molecules

The balanced equation means that one molecule of solid magnesium reacts with two molecules of aqueous hydrogen chloride to produce one molecule of aqueous magnesium chloride and one molecule of gaseous hydrogen.

3. Meaning in terms of moles of molecules

The balanced equation means that one mole of solid magnesium reacts with two moles of aqueous hydrogen chloride to produce one mole of aqueous magnesium chloride and one mole of gaseous hydrogen. d.

1. Balance the equation

To balance the chemical equation for the reaction between \(\mathrm{B}_{2}\mathrm{O}_{3}(s)\) and \(\mathrm{H}_{2}\mathrm{O}(l)\), we need to adjust the coefficients as follows: \[ \mathrm{B}_{2}\mathrm{O}_{3}(s) + 3\mathrm{H}_{2}\mathrm{O}(l) \rightarrow 2\mathrm{B}(\mathrm{OH})_{3}(aq) \]

2. Meaning in terms of individual molecules

The balanced equation means that one molecule of solid boron oxide reacts with three molecules of liquid water to produce two molecules of aqueous boron hydroxide.

3. Meaning in terms of moles of molecules

The balanced equation means that one mole of solid boron oxide reacts with three moles of liquid water to produce two moles of aqueous boron hydroxide.

Key concepts

Balancing Chemical Equations

When it comes to chemical reactions, one of the fundamental tasks is balancing the chemical equation. This involves ensuring that the number of atoms of each element on the reactant side is equal to the number on the product side. This is crucial because it complies with the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. To balance a chemical equation:

• First, write down the unbalanced equation.
• Count the number of atoms for each element on both sides.
• Adjust the coefficients in front of the chemical formulas to balance the atoms for each element.

Remember: Never change the subscripts within a chemical formula, as doing so changes the compound itself. For example, when balancing \( \mathrm{UO}_{2} + \mathrm{HF} \rightarrow \mathrm{UF}_{4} + \mathrm{H}_{2}\mathrm{O} \), we adjust to obtain: \[ \mathrm{UO}_{2} + 4\mathrm{HF} \rightarrow \mathrm{UF}_{4} + 2\mathrm{H}_{2}\mathrm{O} \]This means one uranium atom and four hydrogen fluoride molecules react to give one uranium tetrafluoride molecule and two water molecules.

Moles and Molecules

Understanding moles and molecules is vital in chemistry, especially when interpreting chemical equations. A mole is a basic unit in chemistry that is used to describe an amount of substance. It is equivalent to Avogadro's number, which is \(6.022 \times 10^{23}\) particles per mole.
The idea behind moles allows chemists to count atoms, molecules, and ions in a given mass of a substance in a practical and manageable way. For instance, in the reaction:\[ \mathrm{Mg}(s) + 2\mathrm{HCl}(aq) \rightarrow \mathrm{MgCl}_{2}(aq) + \mathrm{H}_{2}(g) \],
The balanced equation can be interpreted in terms of moles as follows:

• One mole of magnesium (\( \mathrm{Mg} \)) reacts with two moles of hydrochloric acid (\( \mathrm{HCl} \)).
• This reaction produces one mole of magnesium chloride (\( \mathrm{MgCl}_{2} \)) and one mole of hydrogen gas (\( \mathrm{H}_{2} \)).

The concept of moles connects the macroscopic world to the molecular level, allowing chemists to make predictions about amounts of substances consumed and produced in reactions.

Stoichiometry

Stoichiometry is the area of chemistry that involves calculating the quantities of reactants and products in chemical reactions. It uses balanced chemical equations and the mole concept to relate different substances in a reaction.
In stoichiometry, you often perform calculations to determine:

• How much product can be produced from given reactants.
• How much of a reactant is needed to produce a desired amount of product.
• Limiting reactants that may stop a reaction from proceeding.

These calculations begin by identifying the ratios of reactants and products as described in a balanced equation. For instance, in the reaction:\[ 2\mathrm{NaC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} + \mathrm{H}_{2}\mathrm{SO}_{4} \rightarrow \mathrm{Na}_{2}\mathrm{SO}_{4} + 2\mathrm{HC}_{2}\mathrm{H}_{3}\mathrm{O}_{2} \],
The stoichiometric coefficients tell us that two moles of sodium acetate react with one mole of sulfuric acid to produce one mole of sodium sulfate and two moles of acetic acid. This molar relationship allows for precise calculations between reactants and products, ensuring that chemists can predict outcomes accurately in both lab and industrial scenarios.