Question

For each of the following unbalanced equations, calculate how many moles of the second reactant would be required to react completely with 0.413 moles of the first reactant. a. \(\operatorname{Co}(s)+\mathbf{F}_{2}(g) \rightarrow \operatorname{CoF}_{3}(s)\) b. \(\mathrm{Al}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \rightarrow \mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}(a q)+\mathrm{H}_{2}(g)\) c. \(\mathrm{K}(s)+\mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{KOH}(a q)+\mathrm{H}_{2}(g)\) d. \(\mathrm{Cu}(s)+\mathrm{O}_{2}(g) \rightarrow \mathrm{Cu}_{2} \mathrm{O}(s)\)

Short answer

For the given 0.413 moles of the first reactant: a. 1.239 moles of F2 are needed to react completely with Co. b. 0.6195 moles of H2SO4 are needed to react completely with Al. c. 0.413 moles of H2O are needed to react completely with K. d. 0.2065 moles of O2 are needed to react completely with Cu.

Step-by-step solution

Use the stoichiometry to find moles of F2:

For the given moles of Co: 0.413 moles, the moles of F2 needed are: 0.413 moles of Co × (3 moles of F2 / 1 mole of Co) = 1.239 moles of F2 b. Aluminum (Al) and Sulfuric Acid (H2SO4) reaction 1. Balance the chemical equation: The balanced equation for the reaction is: \(2Al(s) + 3H_2SO_4(aq) \rightarrow Al_2(SO_4)_3(aq) + 3H_2(g)\) 2. Determine the stoichiometry: For every 2 moles of aluminum (Al) reacting, 3 moles of sulfuric acid (H2SO4) are required. 3. Calculate the moles of H2SO4 needed:

Use the stoichiometry to find moles of H2SO4:

For the given moles of Al: 0.413 moles, the moles of H2SO4 needed are: 0.413 moles of Al × (3 moles of H2SO4 / 2 moles of Al) = 0.6195 moles of H2SO4 c. Potassium (K) and Water (H2O) reaction 1. Balance the chemical equation: The balanced equation for the reaction is: \(2K(s) + 2H_2O(l) \rightarrow 2KOH(aq) + H_2(g)\) 2. Determine the stoichiometry: For every 2 moles of potassium (K) reacting, 2 moles of water (H2O) are required. 3. Calculate the moles of H2O needed:

Use the stoichiometry to find moles of H2O:

For the given moles of K: 0.413 moles, the moles of H2O needed are: 0.413 moles of K × (2 moles of H2O / 2 moles of K) = 0.413 moles of H2O d. Copper (Cu) and Oxygen (O2) reaction 1. Balance the chemical equation: The balanced equation for the reaction is: \(2Cu(s) + O_2(g) \rightarrow 2Cu_2O(s)\) 2. Determine the stoichiometry: For every 2 moles of copper (Cu) reacting, 1 mole of oxygen (O2) is required. 3. Calculate the moles of O2 needed:

Use the stoichiometry to find moles of O2:

For the given moles of Cu: 0.413 moles, the moles of O2 needed are: 0.413 moles of Cu × (1 mole of O2 / 2 moles of Cu) = 0.2065 moles of O2

Key concepts

Chemical Reactions

Chemical reactions are processes where substances, known as reactants, are transformed into new substances called products. Each reaction requires breaking down bonds in the reactants and forming new bonds in the products. This process releases or absorbs energy, often as heat.
One of the essential features of chemical reactions is that they follow the Law of Conservation of Mass. This principle states that matter is not created or destroyed in the course of a reaction. As a result, every atom of the reactants must be accounted for in the products. This leads us to another crucial concept: balancing chemical equations. Each chemical reaction can be represented by a chemical equation which shows how reactants are converted into products, ensuring that the quantity of each type of atom is the same on both sides of the equation.

Balancing Equations

Balancing equations allows chemists to adhere to the Law of Conservation of Mass, which ensures the same number of each atom is present on both sides of the chemical equation. A balanced chemical equation provides the correct ratios in which elements or compounds react.
To balance a chemical equation, follow these steps:

• Write down the unbalanced equation. This involves listing all reactants and products with their correct chemical formulas.
• Count the number of atoms for each element in both reactants and products.
• Add coefficients, whole numbers placed in front of the chemical formulas, to balance the number of atoms of each element on both sides.
• Re-check the balanced equation to ensure all elements are accounted for equivalently on both sides.

For example, in the exercise solutions, equations like the reaction of Aluminum and Sulfuric Acid with the formula: \[2Al(s) + 3H_2SO_4(aq) \rightarrow Al_2(SO_4)_3(aq) + 3H_2(g)\]were balanced to ensure proper chemical interaction with each type of atom properly accounted for.

Mole Calculations

Mole calculations are critical in stoichiometry, which is the study of quantitative relationships in chemical reactions. The mole is a fundamental unit in chemistry that allows chemists to count particles, like atoms and molecules, in a consistent way.
When dealing with reactions, chemists often need to calculate how many moles of a reactant are required to react with a given amount of another reactant. This involves using the stoichiometric coefficients from a balanced equation, representing the proportion of reactants and products.For example, if 0.413 moles of Aluminum is available in the reaction with Sulfuric Acid, the balanced equation tells us that 3 moles of H\(_2\)SO\(_4\) are required for every 2 moles of Al. The calculation\[0.413 \text{ moles of Al} \times \left( \frac{3 \text{ moles of H}_2\text{SO}_4}{2 \text{ moles of Al}} \right) = 0.6195 \text{ moles of H}_2\text{SO}_4\]allows us to find the moles of the second reactant needed. This systematic approach ensures accurate and predictable results in chemical reactions.