Question

When ethane \(\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) reacts with chlorine \(\left(\mathrm{Cl}_{2}\right)\), the main product is \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\); but other products containing \(\mathrm{Cl}\). such as \(\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{Cl}_{2}\), are also obtained in small quantities. The formation of these other products reduces the yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\). (a) Calculate the theoretical yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) when \(125 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}\) reacts with \(255 \mathrm{~g}\) of \(\mathrm{Cl}_{2}\), assuming that \(\mathrm{C}_{2} \mathrm{H}_{6}\) and \(\mathrm{Cl}_{2}\) react only to form \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) and \(\mathrm{HCl}\). (b) Calculate the percent yield of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\) if the reaction produces \(206 \mathrm{~g}\) of \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{Cl}\)

Short answer

The theoretical yield of \(C_2H_5Cl\) is 232.11 g, and the percent yield is 88.76%.

Step-by-step solution

Balanced Chemical Equation

The chemical equation for the reaction of ethane with chlorine is: \[C_{2}H_{6} + Cl_{2} \rightarrow C_{2}H_{5}Cl + HCl\] Step 2: Convert grams to moles

Moles Calculation

First, find the molar mass of the reactants and product: - \(C_2H_6\): 2(12.01 g/mol) + 6(1.01 g/mol) = 30.07 g/mol - \(Cl_2\): 2(35.45 g/mol) = 70.90 g/mol - \(C_2H_5Cl\): 2(12.01 g/mol) + 5(1.01 g/mol) + 35.45 g/mol = 64.52 g/mol Now, convert the given mass to moles: - Moles of \(C_2H_6\): 125 g / 30.07 g/mol = 4.158 mol - Moles of \(Cl_2\): 255 g / 70.90 g/mol = 3.599 mol Step 3: Find the limiting reactant

Limiting Reactant

The stoichiometry of the balanced equation shows a 1:1 ratio between \(C_2H_6\) and \(Cl_2\). So, we'll divide the moles of both reactants by their coefficients to find the limiting reactant: - \(C_2H_6\): 4.158 mol / 1 = 4.158 - \(Cl_2\): 3.599 mol / 1 = 3.599 Since 3.599 < 4.158, \(Cl_2\) is the limiting reactant. Step 4: Calculate the theoretical yield

Theoretical Yield

Use the limiting reactant (\(Cl_2\)) to find the theoretical yield of \(C_2H_5Cl\): Moles of \(C_2H_5Cl\) = 3.599 mol (1:1 ratio with \(Cl_2\)) Mass of \(C_2H_5Cl\) = 3.599 mol × 64.52 g/mol = 232.11g The theoretical yield of \(C_2H_5Cl\) is 232.11 g. Now, let's solve part (b). Step 5: Calculate the percent yield

Percent Yield

The given actual mass of \(C_2H_5Cl\) is 206 g. The percent yield can be calculated using the following formula: Percent Yield = (Actual Yield / Theoretical Yield) × 100 Percent Yield = (206 g / 232.11 g) × 100 = 88.76% The percent yield of \(C_2H_5Cl\) is 88.76%.

Key concepts

Stoichiometry

Stoichiometry is an essential concept in chemistry, where it describes the quantitative relationships between the reactants and products in a chemical reaction. It is often likened to a recipe in cooking, where ingredients must be mixed in specific proportions to yield the desired product. In the case of a chemical reaction, the 'ingredients' are the reactants, and the 'recipe' is the balanced chemical equation.

To perform stoichiometric calculations, we first need to balance the chemical equation. This means ensuring that the number of atoms of each element is equal on both sides of the equation. Once the equation is balanced, one can use the coefficients to determine the molar ratios in which reactants and products interact. In more practical terms, these ratios allow chemists to calculate how much product can be produced from a given amount of reactants – a task fundamental to material and cost efficiency in industrial chemistry.

For instance, in the exercise example provided, the balanced equation indicates a 1:1 molar ratio between ethane (\(C_2H_6\)) and chlorine (\(Cl_2\)), leading to the principal product chloroethane (\(C_2H_5Cl\)) and a secondary product hydrogen chloride (\(HCl\)).

Limiting Reactant

The limiting reactant (or limiting reagent) is the substance in a chemical reaction that is totally consumed when the chemical reaction is complete. Once this reactant is used up, the reaction stops, and no further products can be formed, thus limiting the amount of product that can be obtained. Identifying the limiting reactant is crucial for calculating the theoretical yield of a reaction, which is the maximum amount of product that can be formed from the given reactants.

In the practice problem, though we start with a certain mass of both ethane and chlorine, the stoichiometry of the reaction and the initial amounts present determine that chlorine is the limiting reactant. After converting their respective masses to moles, it becomes evident that there are fewer moles of chlorine available than ethane, which means it will be depleted first. Therefore, in order to calculate the theoretical yield of chloroethane (\(C_2H_5Cl\)), we only consider the moles of chlorine, as the reaction can produce no more chloroethane than what the amount of chlorine allows.

Understanding and identifying the limiting reactant is vital for calculating yields in chemical experiments and industrial processes to optimize the use of chemical reagents.

Percent Yield

Percent yield is a key indicator of efficiency in a chemical reaction. It is the ratio of the actual yield (the amount of product actually produced when the chemical reaction is carried out in an experiment or an industrial setting) to the theoretical yield (the amount of product that should result if all reactants were converted to products without any waste). The percent yield is expressed as a percentage.

The equation to find the percent yield is as follows:
\[\text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\%\]
Percent yield can be affected by various factors such as reaction conditions, purity of reactants, measurement errors, and unforeseen reactions. For example, in laboratory settings, a reaction may not proceed to complete conversion, or side reactions might occur, leading to the formation of by-products that can reduce the actual yield.

In the given problem, the actual yield obtained from the experiment was 206 g of chloroethane, whereas the theoretical yield was calculated to be 232.11 g. Using these values, the percent yield was calculated to be 88.76%. This figure indicates that a majority of the limiting reactant was converted to the desired product, but not all. It's a crucial metric in practical chemistry, serving not just in assessing the success of a reaction but also in optimizing processes for better outcomes and cost savings.