Question

For each of the following unbalanced equations, indicate how many moles of the second reactant would be required to react exactly with 0.275 mol of the first reactant. State clearly the mole ratio used for the conversion. a. \(\mathrm{Cl}_{2}(g)+\mathrm{KI}(a q) \rightarrow \mathrm{I}_{2}(s)+\mathrm{KCl}(a q)\) b. \(\operatorname{Co}(s)+P_{4}(s) \rightarrow \operatorname{Co}_{3} P_{2}(s)\) c. \(\mathrm{Zn}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{ZnNO}_{3}(a q)+\mathrm{H}_{2}(g)\) d. \(C_{5} H_{12}(l)+O_{2}(g) \rightarrow C O_{2}(g)+H_{2} O(g)\)

Short answer

a. Using the balanced equation 2KI + Cl₂ → I₂ + 2KCl and the mole ratio of 1:2, 0.550 mol of KI would be required to react with 0.275 mol of Cl₂. b. Using the balanced equation 3Co + 2P₄ → Co₃P₂ and the mole ratio of 3:2, 0.183 mol of P₄ would be required to react with 0.275 mol of Co. c. Using the balanced equation Zn + 2HNO₃ → Zn(NO₃)₂ + H₂ and the mole ratio of 1:2, 0.550 mol of HNO₃ would be required to react with 0.275 mol of Zn. d. Using the balanced equation C₅H₁₂ + 8O₂ → 5CO₂ + 6H₂O and the mole ratio of 1:8, 2.20 mol of O₂ would be required to react with 0.275 mol of C₅H₁₂.

Step-by-step solution

Balance the chemical equation

Given the equation: \(\mathrm{Cl}_{2}(g)+\mathrm{KI}(a q) \rightarrow \mathrm{I}_{2}(s)+\mathrm{KCl}(a q)\), we balance it to get 2KI + Cl2 → I2 + 2KCl Here, the mole ratio between Cl2 and KI is 1:2, meaning one mole of Cl2 requires two moles of KI.

Calculate the moles of KI needed

Using the mole ratio (1:2), we can determine the moles of KI required to react with 0.275 mol of Cl2: Moles of KI = \(0.275 \, \text{mol Cl}_{2}\) × \(\frac{2 \, \text{mol KI}}{1 \, \text{mol Cl}_{2}}\) = 0.550 mol KI Thus, 0.550 mol of KI is required to react with 0.275 mol of Cl2. b. Balancing the chemical equation and finding the mole ratio:

Balance the chemical equation

Given the equation: \(\operatorname{Co}(s)+P_{4}(s) \rightarrow \operatorname{Co}_{3} P_{2}(s)\), we balance it to get 3Co + 2P4 → Co3P2 Here, the mole ratio between Co and P4 is 3:2, meaning three moles of Co require two moles of P4.

Calculate the moles of P4 needed

Using the mole ratio (3:2), we can determine the moles of P4 required to react with 0.275 mol of Co: Moles of P4 = \(0.275 \, \text{mol Co}\) × \(\frac{2 \, \text{mol P}_{4}}{3 \, \text{mol Co}}\) = 0.183 mol P4 Thus, 0.183 mol of P4 is required to react with 0.275 mol of Co. c. Balancing the chemical equation and finding the mole ratio:

Balance the chemical equation

Given the equation: \(\mathrm{Zn}(s)+\mathrm{HNO}_{3}(a q) \rightarrow \mathrm{ZnNO}_{3}(a q)+\mathrm{H}_{2}(g)\), we balance it to get Zn + 2HNO3 → Zn(NO3)2 + H2 Here, the mole ratio between Zn and HNO3 is 1:2, meaning one mole of Zn requires two moles of HNO3.

Calculate the moles of HNO3 needed

Using the mole ratio (1:2), we can determine the moles of HNO3 required to react with 0.275 mol of Zn: Moles of HNO3 = \(0.275 \, \text{mol Zn}\) × \(\frac{2 \, \text{mol HNO}_{3}}{1 \, \text{mol Zn}}\) = 0.550 mol HNO3 Thus, 0.550 mol of HNO3 is required to react with 0.275 mol of Zn. d. Balancing the chemical equation and finding the mole ratio:

Balance the chemical equation

Given the equation: \(C_{5} H_{12}(l)+O_{2}(g) \rightarrow CO_{2}(g)+H_{2} O(g)\), we balance it to get C5H12 + 8O2 → 5CO2 + 6H2O Here, the mole ratio between C5H12 and O2 is 1:8, meaning one mole of C5H12 requires eight moles of O2.

Calculate the moles of O2 needed

Using the mole ratio (1:8), we can determine the moles of O2 required to react with 0.275 mol of C5H12: Moles of O2 = \(0.275 \, \text{mol C}_{5}\text{H}_{12}\) × \(\frac{8 \, \text{mol O}_{2}}{1 \, \text{mol C}_{5}\text{H}_{12}}\) = 2.20 mol O2 Thus, 2.20 mol of O2 is required to react with 0.275 mol of C5H12.

Key concepts

Chemical Equations

A chemical equation is a symbolic representation of a chemical reaction, where the reactants (substances consumed) are shown on the left side and the products (substances produced) are on the right side. The equation also depicts how atoms and molecules rearrange during the reaction. For instance, when we write \(2\text{KI} + \text{Cl}_2 \rightarrow \text{I}_2 + 2\text{KCl}\), we are illustrating the reaction between potassium iodide and chlorine to form iodine and potassium chloride.

It's crucial to interpret the coefficients in front of each substance, as they indicate the relative number of molecules or moles involved in the reaction. These coefficients allow us to determine the proportion of reactants needed and the amount of products formed, making them essential in stoichiometric calculations.

Mole Ratio

The mole ratio is the proportional relationship between the amounts in moles of any two substances involved in a chemical reaction. It's derived from the balanced chemical equation and is key for converting between moles of reactants and moles of products. Using the previous chlorine and potassium iodide example, the balanced reaction \(2\text{KI} + \text{Cl}_2 \rightarrow \text{I}_2 + 2\text{KCl}\) provides a mole ratio of 2:1 between KI and Cl₂. In practical terms, this means that for every mole of chlorine gas, two moles of potassium iodide are required for the reaction to proceed to completion.

Clear understanding of mole ratios is vital, as it enables you to predict the outcome of reactions and to calculate the needed quantities of substances when planning experiments or analyzing results.

Reactants and Products

In the context of a chemical reaction, the reactants are the starting materials that undergo change, while the products are the substances formed as a result of the reaction. If we consider a simple synthesis reaction like \(\text{Zn} + 2\text{HNO}_3 \rightarrow \text{Zn(NO}_3\text{)}_2 + \text{H}_2\), zinc (Zn) and nitric acid (HNO₃) are the reactants, and zinc nitrate (Zn(NO₃)₂) and hydrogen gas (H₂) are the products.

To predict how much product can be produced from given amounts of reactants or to determine what amount of a reactant is needed to make a certain amount of product, it's important to have a quantitative grasp of the reactants and products, which is provided by the coefficients in the balanced chemical equation.

Balancing Chemical Equations

Balancing a chemical equation is a process of ensuring that the number of atoms of each element is equal on both sides of the equation, reflecting the law of conservation of matter. For example, the combustion of pentane \(C_5H_{12}(l) + O_2(g) \rightarrow CO_2(g) + H_2O(g)\) has to be balanced to reflect the actual stoichiometry of the reaction. Upon balancing, it becomes \(C_5H_{12} + 8O_2 \rightarrow 5CO_2 + 6H_2O\).

Without a balanced equation, it would be impossible to correctly use mole ratios for calculations, leading to misunderstanding in the amount of reactants needed or the amount of products formed. When balancing equations, start by balancing elements that appear in only one reactant and one product, and leave hydrogen and oxygen to be balanced last. Correctly balancing chemical equations is foundational to stoichiometry and cannot be overlooked.