Question

Consider a chemical equation with two reactants forming one product. If you know the mass of each reactant, what else do you need to know to determine the mass of the product? Why isn't the mass necessarily the sum of the mass of the reactants? Provide a real example of such a reaction, and support your answer mathematically.

Short answer

To determine the mass of the product in a chemical reaction with two reactants, you need to know the balanced chemical equation, the masses of the reactants, the purity of the reactants, and the conversion or yield of the reaction. The mass of the product isn't necessarily the sum of the masses of the reactants due to stoichiometry, limiting reactants, and side products. For example, in the reaction \(2H_2(g) + O_2(g) \rightarrow 2H_2O(l)\), having 8 grams of hydrogen and 16 grams of oxygen results in 36 grams of water, even though the sum of the masses of reactants is 24 grams. This discrepancy occurs because of stoichiometry and limiting reactants.

Step-by-step solution

Understand the chemical reactions and mass conservation

First, let's understand that during any chemical reaction, the total mass of the reactants is conserved and is equal to the total mass of the products. This is known as the law of conservation of mass. However, not all reactants may necessarily be converted into the products. Some reactants might remain unreacted, or other side products may form, causing the mass of the desired product to be less than the sum of the reactants' masses.

Identify the information needed to determine the mass of the product

To determine the mass of the product, we need the following information: 1. Balanced chemical equation: The balanced chemical equation provides us with the stoichiometric ratios between the reactants and the product. 2. Masses of the reactants: We need to know the masses of the two reactants. 3. Purity of the reactants: Knowing the purity of reactants helps us determine the mass of the product, taking into account any unreacted impurities. 4. Conversion or yield of the reaction: Conversion or percentage yield represents the efficiency of the reaction in converting the reactants into products.

Provide a real example and support mathematically

Let's consider the reaction between hydrogen and oxygen to form water: \(2H_2(g) + O_2(g) \rightarrow 2H_2O(l)\) Suppose we have 8 grams of hydrogen and 16 grams of oxygen. Both reactants have 100% purity. Let's determine the mass of water formed. 1. The balanced equation tells us that for every 2 moles of hydrogen, 1 mole of oxygen is needed to form 2 moles of water. 2. Determine the moles of reactants: Hydrogen: Moles = Mass / Molar mass = \(8g / (1g/mol) = 8 moles\) Oxygen: Moles = Mass / Molar mass = \(16g / (16g/mol) = 1 mole\) 3. Identify the limiting reactant: \(1 mole\) of oxygen reacts with \(2 moles\) of hydrogen to form \(2 moles\) of water. \(8 moles\) of hydrogen would require \(4 moles\) of oxygen, but we only have \(1 mole\) of oxygen. Therefore, oxygen is the limiting reactant. 4. Calculate the mass of the product according to the stoichiometry: The balanced equation and our limiting reactant tell us that we will form \(2\) moles of water for every \(1\) mole of oxygen. Mass of water = Moles * Molar Mass = \(2 moles * 18g/mol = 36g\) So, even though the sum of the masses of reactants is \(8g + 16g = 24g\), due to the stoichiometry and the limiting reactant, the mass of the product (water) is 36 grams.

Key concepts

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It's like a recipe that tells you how much of each ingredient you need to make a certain amount of product. In stoichiometry, the 'ingredients' are the reactants, and the 'recipe' is the balanced chemical equation.

For example, if you were baking cookies, you would need to know the exact measurements of flour, sugar, and butter to ensure the recipe turns out right. Similarly, in chemistry, stoichiometry helps us calculate the exact amounts of reactants required to produce a desired quantity of product. Once you understand these ratios, provided by the balanced chemical equation, you're able to predict how much product can be formed from a certain amount of reactants. This is crucial not only for small-scale laboratory reactions but also for large-scale industrial processes where accuracy can impact cost and safety.

Balanced Chemical Equations

A balanced chemical equation is essentially a statement of equality between the number of atoms of each element in the reactants and products. It is the bedrock of stoichiometry, as it provides the mole ratios needed to relate the different substances in a reaction.

A balanced equation must reflect the Law of Conservation of Mass, which states that matter cannot be created or destroyed in a chemical reaction. For example, if you have a piece of paper that weighs 5 grams and burn it, the ashes, gases, and smoke produced will still weigh 5 grams in total. The same concept applies when you’re balancing equations: if you start with 10 hydrogen atoms, you must end up with 10 hydrogen atoms after the reaction. This balance makes it possible to calculate how much of each reactant is required and how much product will be produced in a reaction.

Limiting Reactant

The limiting reactant is the substance in a chemical reaction that runs out first, thereby limiting the amount of product that can be formed. It's the bottleneck of the reaction, much like how having only three eggs might limit the number of cakes you can bake, even if you have plenty of flour and sugar left.

Identifying the limiting reactant is crucial because it determines the theoretical yield—the maximum amount of product that can be generated from the given amounts of reactants. Once the limiting reactant is used up, the reaction stops, and no more product can be formed, even if the other reactant is still available. Therefore, knowing which reactant will limit the reaction can help in planning and optimizing chemical processes, avoiding waste of excess reactants, and ensuring that reactions are carried out efficiently.

Theoretical Yield

The concept of theoretical yield is akin to the maximum number of cookies you can make given a certain amount of ingredients; it's the maximum amount of product that can be produced in a chemical reaction based on the amount of limiting reactant. Theoretical yield is calculated using stoichiometry and the balanced chemical equation, assuming perfect conditions where the reaction goes to completion without any side reactions and 100% efficiency.

However, in the real world, reactions rarely proceed to 100% completion, and side reactions often occur, meaning the actual yield – the amount of product actually obtained – is normally less than the theoretical yield. The percentage yield is then calculated by dividing the actual yield by the theoretical yield and multiplying by 100. Understanding theoretical yield helps chemists optimize reactions and scale them up from the laboratory to production. It's a vital component in the development of new products and processes in the chemical industry.