If the yield of chloroform obtainable from acetone and bleaching powder is \(75 \%\), what mass of acetone is required for producing \(30 \mathrm{~g}\) of chloroform? (a) \(40 \mathrm{~g}\) (b) \(9.4 \mathrm{~g}\) (c) \(10.92 \mathrm{~g}\) (d) \(14.56 \mathrm{~g}\)

Understanding the theoretical yield is an essential part of stoichiometry, a fundamental concept in chemistry that deals with the quantitative aspects of chemical reactions. Essentially, the theoretical yield is the maximum amount of product that can be generated from a given amount of reactants in a chemical reaction, assuming that the reaction goes to completion without any losses.

When calculating the theoretical yield, we start by looking at the balanced chemical equation to understand the molar ratio between the reactants and the products. If the balanced equation is not provided, as can be the case in certain textbook exercises, assumptions might have to be made based on the information available. In the provided exercise, an assumption is made that the mass of acetone, if converted with 100% efficiency, would equal the mass of chloroform produced.

This equality simplifies the calculation, as we can directly use the mass of the desired product to establish what the theoretical yield would be if the conversion was fully efficient. From there, we can use this theoretical yield as a reference point to determine how much of the reactant is needed in a real-world scenario where the yield is less than 100%, demonstrating the practical application of theoretical yield calculations in laboratory and industrial settings.

Percentage yield is a measure of the efficiency of a chemical reaction and is calculated by comparing the actual yield (the amount of product actually obtained) to the theoretical yield (the amount that would be obtained if the reaction were 100% efficient). The percentage yield formula is a simple, yet powerful tool for chemists to evaluate how well a reaction has proceeded.

The formula is given as follows:
\[\text{Percentage Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%\]
To apply this formula, chemists first determine the actual yield, usually by weighing the product, and then calculate the theoretical yield as we did in the step-by-step solution. The exercise provided a unique opportunity to flip this formula. Instead of starting with the actual yield and the percentage to find the theoretical yield, it rearranged the formula to determine the mass of acetone needed when the percentage yield was given, demonstrating the versatility of the percentage yield formula in various stoichiometry problems.

Chemical reaction stoichiometry is the cornerstone of the science that quantifies these relationships in chemical reactions. It involves the use of a balanced chemical equation to determine the proportions of reactants and products involved in a chemical reaction.

Understanding stoichiometry is crucial for predicting how much of each reactant is needed and what quantity of product will be formed under certain conditions. In practical terms, it helps chemists design reactions, to be efficient and cost-effective by minimizing waste and optimizing the use of resources.

In the exercise, the chemical reaction wasn't fully described, so stoichiometry was inferred from the given data. Typically, one would identify the molar ratios from the balanced chemical equation and apply it to the mass of reactants and products. But the prompt provided a simplified scenario where 1 gram of acetone yields 1 gram of chloroform at 100% efficiency. This assumption allowed the calculation to progress without the actual stoichiometric details, demonstrating the necessity of a clear understanding of stoichiometry for all levels of chemistry.