Problem 142 - General Chemistry: Principles and Modern Applications

Question

In the reaction of \(2.00 \mathrm{mol} \mathrm{CCl}_{4}\) with an excess of \(\mathrm{HF}\), \(1.70 \mathrm{mol} \mathrm{CCl}_{2} \mathrm{F}_{2}\) is obtained. $$ \mathrm{CCl}_{4}+2 \mathrm{HF} \longrightarrow \mathrm{CCl}_{2} \mathrm{F}_{2}+2 \mathrm{HCl} $$ (a) The theoretical yield is \(1.70 \mathrm{mol} \mathrm{CCl}_{2} \mathrm{F}_{2}\) (b) The theoretical yield is \(1.00 \mathrm{mol} \mathrm{CCl}_{2} \mathrm{F}_{2}\) (c) The theoretical yield depends on how large an excess of HF is used. (d) The percent yield is \(85 \%\)

Step-by-Step Solution

Answer

(a) The theoretical yield is 2.00 mol \( \mathrm{CCl}_{2}\mathrm{F}_{2} \) (d) The percent yield is \( 85 \% \)

Step 1: Theoretical Yield Calculation

The theoretical yield is determined from the stochiometric coefficients of reactants and products in the balanced chemical reaction. In this reaction: \( \mathrm{CCl}_4 + 2\mathrm{HF} \rightarrow \mathrm{CCl}_2\mathrm{F}_2 + 2\mathrm{HCl} \) , for every one mole of \( \mathrm{CCl}_4 \) reacted, one mole of \( \mathrm{CCl}_2\mathrm{F}_2 \) is produced. Hence, the theoretical yield of \( \mathrm{CCl}_2\mathrm{F}_2 \) when 2.00 mol of \( \mathrm{CCl}_4 \) are reacted is 2.00 mol.

Step 2: Percent yield Calculation

Percent yield is the ratio of the actual yield to the theoretical yield expressed as a percentage. It is calculated using the formula: \( \text{Percent Yield} = \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \times 100 \) Here, the actual yield is 1.70 mol and the theoretical yield is 2.00 mol. Thus, the percent yield is \( \frac{1.70\, \text{mol}}{2.00\, \text{mol}} \times 100 = 85 \% \)

Key Concepts

Percent Yield

Percent yield is an important concept in chemistry as it tells us how efficient a chemical reaction has been. The percent yield provides insight into how much product was actually obtained from a reaction compared to the maximum expected amount, known as the theoretical yield. To calculate percent yield, we use the formula:

• Percent Yield = \( \left( \frac{\text{Actual Yield}}{\text{Theoretical Yield}} \right) \times 100 \)

In the given problem, the actual yield of \( \text{CCl}_2\text{F}_2 \) is stated to be 1.70 mol, whereas the theoretically possible amount is 2.00 mol. Therefore, calculating the percent yield shows us that the reaction had a yield of 85%.
This means that only 85% of the maximum possible product was produced, implying some inefficiencies or experimental conditions that prevented a full conversion of reactants to products.

Chemical Reaction

Understanding chemical reactions entails knowing how and why reactants convert into products. In chemical equations, reactants are transformed into products when their molecules interact. For instance, the reaction between carbon tetrachloride \((\mathrm{CCl}_4)\) and hydrogen fluoride \((\mathrm{HF})\) is described by the equation:

• \( \mathrm{CCl}_4 + 2 \mathrm{HF} \rightarrow \mathrm{CCl}_2\mathrm{F}_2 + 2\mathrm{HCl} \)

This equation shows that one molecule of \(\mathrm{CCl}_4\) reacts with two molecules of \(\mathrm{HF}\) to produce one molecule of \(\mathrm{CCl}_2\mathrm{F}_2\) and two molecules of \(\mathrm{HCl}\). The coefficients before each compound indicate the proportion of molecules involved in the reaction.
Chemical reactions require specific conditions, such as temperature, pressure, or catalysts, to proceed efficiently. Reactants must be present in adequate amounts, as shown by the reaction's stoichiometry, to maximize the production of products.

Stoichiometry

Stoichiometry plays a key role in understanding chemical reactions, as it relates to the quantitative relationships of reactants and products. It allows chemists to predict how much product can be formed from given amounts of reactants. This is where the concept of theoretical yield comes in.
In the reaction \(\mathrm{CCl}_4 + 2\mathrm{HF} \rightarrow \mathrm{CCl}_2\mathrm{F}_2 + 2\mathrm{HCl}\), the stoichiometric coefficients tell us that one mole of \(\mathrm{CCl}_4\) reacts with two moles of \(\mathrm{HF}\) to produce one mole of \(\mathrm{CCl}_2\mathrm{F}_2\).
To calculate the theoretical yield, you'd use these stoichiometric ratios. With 2.00 moles of \(\mathrm{CCl}_4\) and assuming an excess of \(\mathrm{HF}\), it tells us the maximum amount of \(\mathrm{CCl}_2\mathrm{F}_2\) that can be formed is 2.00 moles.

• This calculation helps predict how much product should form, assuming perfect conditions.
• Any deviation from the theoretical yield hints at reaction inefficiencies or measurement inaccuracies, making stoichiometry crucial for accurate chemical predictions.