Problem 19 - Chemistry and Chemical Reactivity

Question

In Example \(4.2,\) you found that a particular mixture of \(\mathrm{CO}\) and \(\mathrm{H}_{2}\) could produce \(407 \mathrm{g}\) \(\mathrm{CH}_{3} \mathrm{OH}\). $$\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{g}) \rightarrow \mathrm{CH}_{3} \mathrm{OH}(\ell)$$ If only \(332 \mathrm{g}\) of \(\mathrm{CH}_{3} \mathrm{OH}\) is actually produced, what is the percent yield of the compound?

Step-by-Step Solution

Answer

The percent yield of \(\text{CH}_3\text{OH}\) is approximately 81.57\%.

Step 1: Understand the Reaction Equation

The balanced chemical equation for the production of methanol (\(\text{CH}_3\text{OH}\)) is: \[ \text{CO}(\text{g}) + 2 \text{H}_2(\text{g}) \rightarrow \text{CH}_3\text{OH}(\ell) \]. This equation shows that one mole of carbon monoxide (CO) reacts with two moles of hydrogen gas (H₂) to produce one mole of methanol.

Step 2: Calculate Theoretical Yield

The theoretical yield is the maximum amount of product that can be produced from a given amount of reactants under perfect conditions. From previous information (Example 4.2), we know that the theoretical yield of \(\text{CH}_3\text{OH}\) is 407 g based on the given mixture of CO and H₂.

Step 3: Determine Actual Yield

The actual yield is the amount of product actually obtained from a chemical reaction. From the problem, the actual yield of \(\text{CH}_3\text{OH}\) is 332 g.

Step 4: Calculate Percent Yield

The percent yield is calculated using the formula: \[ \text{Percent Yield} = \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100 \%. \] Substitute the given values: \[ \text{Percent Yield} = \left( \frac{332}{407} \right) \times 100 \% \approx 81.57\%. \]

Key Concepts

Theoretical Yield

In a chemical reaction, the theoretical yield is the calculated quantity of product that can form based on the complete conversion of the limiting reactant into the desired product. It represents an ideal scenario where every atom of the reacting species is converted without any losses or side reactions. The theoretical yield provides a benchmark for gauging the efficiency of a reaction.

• The theoretical yield is determined by stoichiometric calculations using the balanced equation of the reaction. This involves converting reactant masses to moles, using the mole ratio from the balanced equation to find the moles of product, and then converting back to mass if necessary.
• In practical scenarios, the theoretical yield is seldom achieved due to various practical constraints, such as incomplete reactions, side reactions, or loss of product during handling.

The theoretical yield serves as a crucial point of reference in evaluating a reaction's output and allows chemists to calculate the efficiency with once the actual yield is measured.

Actual Yield

The actual yield refers to the quantity of product that is actually obtained from a chemical reaction. Unlike the theoretical yield, which is based on calculations, the actual yield is measured from the experiment and can vary significantly from the predictions.

• The actual yield is often less than the theoretical yield due to factors such as incomplete reactions, impurities in the reactants, or losses during the product recovery process.
• By comparing the actual yield to the theoretical yield, chemists can compute the percent yield, providing insight into the reaction's efficiency.
• Knowing the actual yield is critical for industrial applications where maximizing efficiency and minimizing loss are essential for economic viability.

The actual yield provides a real-world check against theoretical predictions and is crucial for practical applications in labs and industry.

Chemical Reaction

A chemical reaction is a process where substances, known as reactants, are transformed into new substances, called products. This transformation involves rearranging the atoms in the reactants to form new chemical bonds in the products.

• The balanced chemical equation represents this transformation and shows the ratio in which reactants combine to form products.
• Chemical reactions are directed by the laws of conservation of mass and energy, meaning the quantity of atoms remains unchanged while their arrangement differs in the products.
• Reactions occur under specific conditions which might include temperature, pressure, and the presence of catalysts.

Understanding chemical reactions is fundamental to all chemical processes, whether in laboratory settings, industrial applications, or biological systems. The study of reactions enables scientists to design and optimize processes for the desired output effectively.