Question

For each of the following reactions, give the balanced equation for the reaction and state the meaning of the equation in terms of numbers of individual molecules and in terms of moles of molecules. 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. \(\operatorname{Mg}(s)+\operatorname{HCl}(a q) \rightarrow \operatorname{MgCl}_{2}(a q)+\mathrm{H}_{2}(g)\) 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. UO2(s) + 4HF(aq) → UF4(aq) + 2H2O(l) 1 molecule UO2 reacts with 4 molecules HF to produce 1 molecule UF4 and 2 molecules H2O. 1 mole UO2 reacts with 4 moles HF to produce 1 mole UF4 and 2 moles H2O. b. NaC2H3O2(aq) + H2SO4(aq) → Na2SO4(aq) + HC2H3O2(aq) 1 molecule NaC2H3O2 reacts with 1 molecule H2SO4 to produce 1 molecule Na2SO4 and 1 molecule HC2H3O2. 1 mole NaC2H3O2 reacts with 1 mole H2SO4 to produce 1 mole Na2SO4 and 1 mole HC2H3O2. c. Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g) 1 atom Mg reacts with 2 molecules HCl to produce 1 molecule MgCl2 and 1 molecule H2. 1 mole Mg reacts with 2 moles HCl to produce 1 mole MgCl2 and 1 mole H2. d. B2O3(s) + 3H2O(l) → 2B(OH)3(aq) 1 molecule B2O3 reacts with 3 molecules H2O to produce 2 molecules B(OH)3. 1 mole B2O3 reacts with 3 moles H2O to produce 2 moles B(OH)3.

Step-by-step solution

a. Balancing the equation

To balance the given chemical equation, adjust the coefficients of the species so that the number of atoms of each type is equal on both sides of the equation: UO2(s) + 4HF(aq) → UF4(aq) + 2H2O(l)

a. Meaning of the balanced equation

The balanced equation means that: 1) One molecule of uranium dioxide (UO2) reacts with 4 molecules of hydrofluoric acid (HF) to produce one molecule of uranium tetrafluoride (UF4) and 2 molecules of water (H2O). 2) One mole of uranium dioxide (UO2) reacts with 4 moles of hydrofluoric acid (HF) to produce one mole of uranium tetrafluoride (UF4) and 2 moles of water (H2O).

b. Balancing the equation

To balance the given chemical equation, adjust the coefficients of the species so that the number of atoms of each type is equal on both sides of the equation: NaC2H3O2(aq) + H2SO4(aq) → Na2SO4(aq) + HC2H3O2(aq)

b. Meaning of the balanced equation

The balanced equation means that: 1) One molecule of sodium acetate (NaC2H3O2) reacts with one molecule of sulfuric acid (H2SO4) to produce one molecule of sodium sulfate (Na2SO4) and one molecule of acetic acid (HC2H3O2). 2) One mole of sodium acetate (NaC2H3O2) reacts with one mole of sulfuric acid (H2SO4) to produce one mole of sodium sulfate (Na2SO4) and one mole of acetic acid (HC2H3O2).

c. Balancing the equation

To balance the given chemical equation, adjust the coefficients of the species so that the number of atoms of each type is equal on both sides of the equation: Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)

c. Meaning of the balanced equation

The balanced equation means that: 1) One atom of magnesium (Mg) reacts with 2 molecules of hydrochloric acid (HCl) to produce one molecule of magnesium chloride (MgCl2) and one molecule of hydrogen gas (H2). 2) One mole of magnesium (Mg) reacts with 2 moles of hydrochloric acid (HCl) to produce one mole of magnesium chloride (MgCl2) and one mole of hydrogen gas (H2).

d. Balancing the equation

To balance the given chemical equation, adjust the coefficients of the species so that the number of atoms of each type is equal on both sides of the equation: B2O3(s) + 3H2O(l) → 2B(OH)3(aq)

d. Meaning of the balanced equation

The balanced equation means that: 1) One molecule of boric oxide (B2O3) reacts with 3 molecules of water (H2O) to produce two molecules of boric acid (B(OH)3). 2) One mole of boric oxide (B2O3) reacts with 3 moles of water (H2O) to produce two moles of boric acid (B(OH)3).

Key concepts

Balancing Chemical Equations

Balancing chemical equations is a fundamental skill in chemistry. It involves making sure that the number of each type of atom is the same on both sides of the equation. This is important because it respects the law of conservation of mass, which states that mass cannot be created or destroyed in a chemical reaction.
To achieve balance, we adjust the coefficients (the numbers in front of the molecules or atoms) in the equation, not the subscripts within molecules. For instance, in the reaction \[ \text{UO}_2(s) + 4 \text{HF(aq)} \rightarrow \text{UF}_4(aq) + 2 \text{H}_2\text{O}(l) \], we balanced the equation by recognizing that four hydrogen atoms from 4 molecules of hydrofluoric acid (HF) combine with uranium dioxide (UO2) to form uranium tetrafluoride (UF4) and water (H2O). Each reaction equation may need different coefficients to balance the atoms.
Key tips for balancing equations include:

• Start by balancing elements that appear in only one reactant and one product.
• Balance polyatomic ions as a unit if they appear unchanged on both sides of the equation.
• Leave hydrogen and oxygen for last, as they are often in multiple compounds.

Moles and Molecules

Moles and molecules are two ways to describe the quantities in chemical reactions. Molecules refer to the smallest units of a compound that retain its chemical properties. In contrast, moles are a unit used to count large quantities of molecules.
One mole is equal to Avogadro's number, which is approximately \(6.022 \times 10^{23}\) of whatever you are counting - usually atoms or molecules. Therefore, when you read a balanced equation like \( \text{Mg}(s) + 2 \text{HCl}(aq) \rightarrow \text{MgCl}_2(aq) + \text{H}_2(g) \), it can be interpreted in two ways:

• One atom of magnesium and two molecules of hydrochloric acid react.
• Or, one mole of magnesium reacts with two moles of hydrochloric acid.

This equivalence allows chemists to connect laboratory scales with quantities involved in chemical reactions. Understanding both aspects helps bridge the gap between the microscopic world (molecules) and the macroscopic world (moles) we work with.

Reaction Stoichiometry

Reaction stoichiometry involves using a balanced chemical equation to calculate the relationships between reactants and products in a chemical reaction. This concept allows us to predict how much product will be formed from a given amount of reactant or how much reactant is needed to produce a desired amount of product.
Let's look at the equation:\[ \text{B}_2\text{O}_3(s) + 3 \text{H}_2\text{O}(l) \rightarrow 2 \text{B(OH)}_3(aq) \]
The coefficients in the balanced equation (1 for B2O3, 3 for H2O, and 2 for B(OH)3) tell us the stoichiometric ratios. They indicate that one molecule or mole of B2O3 reacts with three molecules or moles of H2O to produce two molecules or moles of B(OH)3. So, if you start with 1 mole of B2O3, you need exactly 3 moles of H2O to form 2 moles of B(OH)3.

• This allows for precise calculations in lab settings.
• It helps to determine limiting reactants that limit the product formation.
The balanced coefficients act as a conversion factor for scaling up chemical reactions to match experimental or industrial needs.

Molar Relationships

Molar relationships use the concept of the mole to connect the amount of a substance to its mass and volume. These relationships are central to quantitative chemistry, allowing you to convert between units like grams, moles, and molecules.
Every chemical substance has a molar mass, which is the mass of one mole of that substance, usually in grams per mole. For example, one mole of water (H2O) has a molar mass of approximately 18 g/mol. This means 18 grams of water contains \(6.022 \times 10^{23}\) water molecules.
Using the balanced equation \( \text{NaC}_2\text{H}_3\text{O}_2(aq) + \text{H}_2\text{SO}_4(aq) \rightarrow \text{Na}_2\text{SO}_4(aq) + \text{HC}_2\text{H}_3\text{O}_2(aq) \), if we have 60 grams of NaC2H3O2, we can calculate moles as follows:

• Calculate the molar mass of NaC2H3O2.
• Use mole ratios from the balanced equation to find moles of other substances.
• Convert moles back to grams or volume as needed.

This approach provides a quantitative framework for predicting and analyzing chemical changes. By mastering molar relationships, you gain the ability to handle chemically relevant numbers with precision and confidence.