Question

Suppose you are making turkey sandwiches for your friends. You have lots of friends, so you want to make as many sandwiches as possable. Because you are on a budget, you only have 24 pieces of bread and 15 pieces of turkey. Each sandwich consists of 2 pueces of bread and 1 piece of turkey. (a) How many sandwiches can you make? (b) What is the limiting part? (c) What part is left over? How many are left over?

Short answer

(a) You can make 12 sandwiches. (b) The limiting part is the bread. (c) The turkey is left over, with 3 pieces remaining.

Step-by-step solution

Count the Resources

Take a look at what you have: 24 pieces of bread and 15 pieces of turkey.

Calculate Possible Sandwiches with Given Resources

For bread, you can divide the total bread by the bread pieces needed for one sandwich (24 bread pieces /2 pieces per sandwich = 12 possible sandwiches), and for the turkey, it's 15 turkey pieces / 1 piece per sandwich = 15 possible sandwiches.

Identify the Limiting Part

The limiting part is the resource that allows fewer sandwiches, this case being the bread allowing only 12 sandwiches. Therefore, the maximum number of sandwiches that can be made is 12.

Identify the Leftover

Subtract the number of turkey pieces used for the sandwiches made (12) from the total available turkey pieces (15). This leaves 3 pieces of turkey as leftovers.

Key concepts

Limiting Reagent

In the realm of chemistry education, understanding the concept of a limiting reagent is crucial when performing stoichiometric calculations. Just as in the sandwich-making scenario where the bread limits the number of sandwiches you can make, in a chemical reaction, the limiting reagent is the reactant that is completely used up first. This reagent determines the maximum amount of product that can be formed.

Imagine you're baking cookies and you have just enough flour for 10 cookies but enough chocolate chips for 50. No matter how many chocolate chips you have, you can only bake as many cookies as the flour allows—this is the essence of a limiting reagent. In a chemical equation, identifying the limiting reagent allows you to predict how much product you can expect to be formed, just like predicting the number of sandwiches. It's the starting point for any stoichiometric calculation in a reaction because it dictates the quantities of all other reactants used and products formed.

Theoretical Yield

The theoretical yield is a term used to describe the maximum amount of product that can be generated from a chemical reaction, assuming perfect conditions and that all of the limiting reagent is converted into the desired product. It is essentially a best-case scenario that provides a benchmark for what could be possible under ideal circumstances.

In the sandwich example, the theoretical yield would be the number of full sandwiches that could be made if every slice of bread and piece of turkey were used efficiently without any waste. Think of it as the 'potential output' if everything goes perfectly. In a laboratory or industrial setting, the theoretical yield is a target to strive for, and the efficiency of the reaction can be gauged by comparing the actual yield (the amount actually produced) to the theoretical yield. Knowing how to calculate the theoretical yield is a foundational skill for students and professionals alike, as it allows for the planning and optimization of chemical processes.

Stoichiometric Calculations

Stoichiometric calculations are the mathematical relationships that allow chemists to predict the amounts of reactants and products involved in a chemical reaction based on the law of conservation of mass. This concept ties together the principles of limiting reagents and theoretical yield.

To master stoichiometric calculations, one must first be comfortable with balancing chemical equations, because the coefficients in the balanced equation indicate the ratios by which reactants combine to form products. In the sandwich scenario, stoichiometry is simplified: two pieces of bread pair with one piece of turkey to make a sandwich. In a chemical equation, it's just the same—stoichiometry tells you how many molecules of reactant A will react with reactant B to form product C.

Understanding stoichiometry is fundamental for predicting how reactions will proceed. These calculations involve conversion factors derived from the coefficients in the balanced equation, allowing chemists to quantify how much of each reactant is needed or how much of a product can be formed under given conditions. It is an essential tool in chemistry that ensures reactions are cost-effective, safe, and efficient in terms of both materials and energy.