Problem 85 - Chemistry: Structure and Properties

Question

Consider the reaction: 4 K(s) + O2(g)-2 K2O(s) The molar mass of K is 39.09 g>mol and that of O2 is 32.00 g>mol. Without doing any calculations, choose the conditions under which potassium is the limiting reactant and explain your reasoning. a. 170 g K, 31 g O2 b. 16 g K, 2.5 g O2 c. 165 kg K, 28 kg O2 d. 1.5 g K, 0.38 g O2

Step-by-Step Solution

Answer

Without detailed calculations, option (b) 16 g K and 2.5 g O2 is where potassium is the limiting reactant because the molar ratio of K to O2 is obviously less than 4:1.

Step 1: Understanding the Stoichiometry

According to the reaction, 4 moles of potassium (K) react with 1 mole of oxygen (O2) to produce 2 moles of potassium oxide (K2O). This means that the stoichiometric ratio is 4 moles of K to 1 mole of O2.

Step 2: Calculating Molar Quantities

Without performing detailed calculations, we need to compare the quantity of each reactant supplied in each option against the stoichiometric requirements. The stoichiometry tells us we need 4 times as many moles of K as O2.

Step 3: Identifying the Limiting Reactant

To determine which reactant is limiting, we should find the option where the molar amount of potassium is less than 4 times that of oxygen. Since 4 moles of K are needed for every 1 mole of O2, if the number of moles of K divided by the number of moles of O2 is less than 4 in any option, then K is the limiting reactant.

Step 4: Applying the Molar Masses

Using the molar masses provided (K=39.09 g/mol and O2=32.00 g/mol), we can estimate the molar ratio in each option to find where K is less than 4 times the molar amount of O2. Option (b) 16 g K and 2.5 g O2 is the most obvious without calculations because if you divide both amounts by their respective molar masses, it will give less than 4 moles of K for every mole of O2.

Key Concepts

Understanding Stoichiometry

Stoichiometry is a branch of chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. It's like a recipe that ensures you have just the right amount of each ingredient to make your desired product.

To master stoichiometry, one must understand the concept of the mole. The mole is a unit of measurement for amount of substance. Stoichiometry relies on the mole ratio provided by the balanced chemical equation to calculate the amounts of reactants needed or products formed. In our exercise, the reaction ratio of potassium to oxygen is 4:1, indicating that four moles of potassium react with one mole of oxygen to form two moles of potassium oxide.

Here is the thing to remember: the coefficients in the balanced equation give us the ratio of moles needed. When the moles of reactants do not come in these exact ratios due to the amounts available, the reactant that runs out first is known as the limiting reactant. It determines the extent of the reaction and therefore, the amount of product formed. Applying the concept of stoichiometry effectively allows us to predict the limiting reactant in a reaction.

The Role of Limiting Reactants in Chemical Reactions

In any chemical reaction, the limiting reactant is the substance that is completely consumed first and therefore limits the reaction from continuing. It's like when you're baking cookies and run out of flour; you can't make more cookies without it, regardless of how much of the other ingredients you have left.

Limiting reactants are central to predicting the outcomes of chemical reactions. Recognize that no matter how much of the other reactants you have, if your limiting reactant is gone, the reaction stops. That is why identifying the limiting reactant is a key step in stoichiometric calculations.

By comparing the mole ratios of the reactants to what is required by the balanced equation, you can deduce which reactant will be exhausted first and thus establish the quantity of product that can be formed. This step informs the practicality and efficiency of industrial chemical processes and is critical in laboratory experiments where precise quantities are paramount.

Molar Mass: The Link Between Mass and Moles in Stoichiometry

Molar mass is the weight of one mole of any chemical species (atoms, molecules, ions, etc.). It serves as the bridge between the mass of a substance and the amount of substance in terms of moles. In basic terms, molar mass tells you how many grams are in one mole of a compound or element.

Molar mass is crucial in stoichiometry because it allows us to convert grams to moles, a necessary step in using the balanced chemical equation for stoichiometric calculations. The molar mass of potassium (K) is given as 39.09 g/mol, and for oxygen (O2) it is 32.00 g/mol. These figures enable us to calculate the number of moles present in a given mass of each reactant.

When solving stoichiometry problems, like identifying a limiting reactant, we use the molar mass to compare the masses of reactants in grams to their stoichiometric ratios in moles. This conversion is significant because reactions happen on a mole basis, not on a gram-by-gram basis. By understanding molar mass and its application in stoichiometry, we can better grasp the quantities involved in a chemical reaction.