Problem 6 - Chemistry An Atoms First Approach

Question

You know that chemical \(A\) reacts with chemical \(B\). You react \(10.0 \mathrm{g} A\) with \(10.0 \mathrm{g} B .\) What information do you need to determine the amount of product that will be produced? Explain.

Step-by-Step Solution

Answer

To determine the amount of product that will be produced, you will need the balanced chemical equation for the reaction, the molar masses of the reactants (chemical A and B) and product(s). Then, convert the given mass of each reactant into moles, determine the limiting reactant, calculate the moles of product formed using stoichiometry, and finally convert the moles of product into grams using the molar mass of the product(s).

Step 1: Identify Necessary Information

You will need the balanced chemical equation representing the reaction, as well as the molar masses of the reactants (chemical A and chemical B) and the product(s).

Step 2: Find Moles of Reactants

Convert the given mass of each reactant (A and B) into moles using their respective molar masses. To do this, divide the mass of each reactant by its molar mass. For example, for chemical A: \(moles A = \frac{10.0\mathrm{g}}{molar\ mass\ of\ A}\).

Step 3: Determine the Limiting Reactant

Using the balanced chemical equation, compare the ratio of moles of reactants A and B to their stoichiometric ratio in the equation. The reactant which has a lower value, when dividing the moles by their respective stoichiometric coefficients, is the limiting reactant.

Step 4: Calculate Moles of Product

Use the stoichiometry of the balanced chemical equation to determine the moles of the product formed by the limiting reactant. For example, if reactant A is the limiting reactant and x moles of product are formed for every y moles of A: \(moles\ of\ product = \frac{x}{y} \times moles\ of\ limiting\ reactant\).

Step 5: Find the Mass of Product Produced

Convert the moles of product formed to grams using the molar mass of the product(s). Multiply the moles of the product by its molar mass: \(mass\ of\ product = moles\ of\ product \times molar\ mass\ of\ product\). In conclusion, to determine the amount of product that will be produced, you will need the balanced chemical equation, the molar masses of the reactants and product, and then perform stoichiometric calculations to find the limiting reactant and the mass of product formed.

Key Concepts

Limiting Reactant

Understanding the concept of the limiting reactant is like knowing which ingredient will run out first when you're baking a cake. In chemical reactions, the limiting reactant is the substance that is completely used up first, thus determining the maximum amount of product that can be formed. It's the bottleneck of the reaction.

To identify the limiting reactant, start by calculating the number of moles of each reactant. Then, using the balanced chemical equation, compare the mole ratio of the reactants with the coefficients in the equation. The reactant that runs out first, or the one that you have less of than required according to the reaction's proportions, is the limiting reactant. This is critical to calculate because it lets you predict the amounts of products formed in a reaction.

Balanced Chemical Equation

Chemistry is all about balance. A balanced chemical equation represents exactly what happens in a chemical reaction at the most fundamental level. It tells us how many molecules of reactants combine and how many molecules of products are formed. It's crucial because it ensures the law of conservation of mass is respected, meaning matter is neither created nor destroyed.

The coefficients in a balanced equation indicate the ratios in which substances react and are formed. These ratios are the foundation of stoichiometric calculations. Without a balanced chemical equation, we cannot correctly determine the stoichiometry of the reaction, hence we can't accurately predict the amount of products or identify the limiting reactant.

Molar Mass

Every baker knows you can't start without knowing how much a cup of flour weighs. In chemistry, molar mass serves a similar purpose—it tells us the mass of one mole of a substance. It's a bridge between the mass of a material and the number of particles contained in that mass.

Since the number of particles in a reaction is fundamental but tricky to count individually, we use moles to measure them. To convert grams to moles, divide by the molar mass; to convert back, multiply moles by the molar mass. This way, molar mass allows chemists to 'count' atoms or molecules in a bulk substance, which is essential for stoichiometric calculations and determining how much of a reactant is needed, or how much of a product is produced.

Product Yield

Imagine following a recipe and trying to predict how many cookies you'll end up with—that's exactly what product yield is in chemistry. It's the actual amount of product obtained from a chemical reaction.

The theoretical yield is the maximum amount of product expected as calculated from the stoichiometry of the balanced chemical equation, assuming all the limiting reactant is used up. The actual yield is what you really get after running the reaction, often less due to inefficiencies. By comparing the actual yield to the theoretical yield, chemists can evaluate the efficiency of reaction processes. This concept is central for practical applications, such as manufacturing pharmaceuticals or designing a chemical synthesis.