Question

Consider the reaction: $$4 \mathrm{K}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{K}_{2} \mathrm{O}(s)$$ The molar mass of \(\mathrm{K}\) is 39.09 \(\mathrm{g} / \mathrm{mol}\) and that of \(\mathrm{O}_{2}\) is 32.00 \(\mathrm{g} / \mathrm{mol}\) . Without doing any calculations, choose the conditions under which potassium is the limiting reactant and explain your reasoning. \begin{equation} \begin{array}{ll}{\text { a. } 170 \mathrm{gK}, 31 \mathrm{gO}_{2}} & {\text { b. } 16 \mathrm{gK}, 2.5 \mathrm{gO}_{2}} \\ {\text { c. } 165 \mathrm{kg} \mathrm{K}, 28 \mathrm{kg} \mathrm{O}_{2}} & {\text { d. } 1.5 \mathrm{g} \mathrm{K}, 0.38 \mathrm{g} \mathrm{O}_{2}}\end{array} \end{equation}

Short answer

Condition b (16 g K and 2.5 g O2) is where potassium is the limiting reactant because the mass of K is not four times greater than that of O2, which is necessary for the 4:1 molar ratio in the reaction.

Step-by-step solution

Understanding the Stoichiometry

Examine the balanced chemical equation and identify the molar ratio of potassium (K) to oxygen (O2) for the reaction. The equation shows that 4 moles of K react with 1 mole of O2 to produce 2 moles of K2O.

Determine Moles from Given Masses

Use the molar masses to determine how many moles of each reactant you would have in the given conditions. For instance, to convert grams of K to moles of K, divide by the molar mass of K. Perform a similar conversion for O2.

Compare Molar Ratios

For each condition given, compare the available moles of K and O2 to the stoichiometric molar ratio from the equation (4:1). The reactant that provides the lower ratio is the limiting reactant.

Identify Limiting Reactant Conditions

Without calculations, look for a condition where the mass of K is less than four times the mass of O2, since it is required in a 4:1 molar ratio. This condition indicates that K would be the limiting reactant because you need more of it relative to O2 to fully react according to the stoichiometric ratio.

Key concepts

Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It is based on the conservation of mass, where the mass of the reactants equals the mass of the products. To understand stoichiometry, we look at the balanced chemical equation and the ratios of the substances involved.

For example, in the reaction \(4 \text{K}(s) + \text{O}_{2}(g) \rightarrow 2 \text{K}_{2}\text{O}(s)\), the stoichiometric ratio of potassium (K) to oxygen (\(\text{O}_{2}\)) is 4:1, meaning four atoms of potassium react with one molecule of oxygen. Stoichiometry helps us predict how much product will form and which reactant will run out first, known as the limiting reactant.

Improving Understanding of Stoichiometry

To enhance comprehension, contextualize stoichiometry in real-world scenarios, such as cooking recipes, which also use specific ratios of ingredients to create a dish. Draw parallels between measuring cups and moles, emphasizing that just as a recipe fails if ingredient proportions are wrong, reactions depend on precise stoichiometric ratios.

Chemical Reactions

Chemical reactions involve the rearrangement of atoms to form new substances. In education, analogies can be drawn between a chemical reaction and a dance, where participants (atoms or molecules) pair off based on specific rules or patterns (the balanced equation).

During a reaction, the bonds between atoms of the reactants are broken, and new bonds in the products are formed, conserving mass and atoms throughout the process. In our textbook problem, potassium (K) and oxygen (\(\text{O}_{2}\)) combine to form potassium oxide (\(\text{K}_{2}\text{O}\)). Here, we analyze different scenarios to identify which one would result in K being the limited reactant, crucial for predicting the amount of product formed.

Visualizing Reactions

Students may find it helpful to visualize molecules interacting through models or animations to grasp the concepts of breaking and forming bonds. Additionally, practicing with varied scenarios where they must balance equations and identify limiting reactants can solidify their understanding of chemical reactions.

Molar Mass

The molar mass of a substance is the mass of one mole of its particles (atoms, molecules, or ions) and is expressed in units of grams per mole (g/mol). This concept is akin to the idea of a 'dozen', which always equals twelve, regardless of the items being counted. In chemistry, a mole always contains the same number of particles—the Avogadro's number (approximately \(6.022 \times 10^{23}\)).

The molar mass of an element is the mass of one mole of its atoms and is found on the periodic table. For instance, potassium (K) has a molar mass of 39.09 g/mol, while oxygen (\(\text{O}_{2}\)) has a molar mass of 32.00 g/mol. Understanding molar mass is essential for converting between the mass of a substance and the amount in moles, a key step in stoichiometric calculations.

Relating Molar Mass to Everyday Concepts

To make molar mass more approachable, compare it to shopping for fruits, where you might buy apples by the pound. Just as you would use the price per pound to determine the cost of your apples, chemists use the molar mass to calculate how much of a substance is needed for a reaction.