Question

Hexamethylenediamine \(\left(\mathrm{C}_{6} \mathrm{H}_{6} \mathrm{N}_{2}\right)\) is one of the starting materials for the production of nylon. It can be prepared from adipic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}\right)\) by the following overall equation: $$ \mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}(l)+2 \mathrm{NH}_{3}(g)+4 \mathrm{H}_{2}(g) \rightarrow \mathrm{C}_{6} \mathrm{H}_{16} \mathrm{N}_{2}(l)+4 \mathrm{H}_{2} \mathrm{O}(l) $$ What is the percent yield for the reaction if 765 g of hexamethylenediamine is made from \(1.00 \times 10^{3} \mathrm{g}\) of adipic acid?

Short answer

The percent yield for the reaction is 109.41%, which is not possible as it cannot be greater than 100%. There might be errors in the measurements or calculations.

Step-by-step solution

Calculate the number of moles of adipic acid

To find the number of moles of adipic acid, we'll use its molar mass and the given mass: $$ \text{Moles of adipic acid} = \frac{\text{Mass of adipic acid}}{\text{Molar mass of adipic acid}} $$ The molar mass of adipic acid (C6H10O4) is: $$ (6 \times 12.01 + 10 \times 1.01 + 4 \times 16.00)g/mol = 166.14 \,g/mol $$ So, the number of moles of adipic acid is: $$ \text{Moles of adipic acid} = \frac{1.00 \times 10^3 g}{166.14 \,g/mol} = 6.018 \,mol $$

Determine the molar ratio of hexamethylenediamine to adipic acid

From the balanced chemical equation, we can see that 1 mole of adipic acid is needed to produce 1 mole of hexamethylenediamine: $$ \mathrm{C}_{6} \mathrm{H}_{10} \mathrm{O}_{4}(l) \rightarrow \mathrm{C}_{6} \mathrm{H}_{16} \mathrm{N}_{2}(l) $$ So, the molar ratio of hexamethylenediamine to adipic acid is 1:1.

Calculate the theoretical yield of hexamethylenediamine

Since we have a 1:1 molar ratio, we can use the number of moles of adipic acid to find the theoretical yield of hexamethylenediamine: $$ \text{Moles of hexamethylenediamine} = 6.018 \,mol $$ Now, we will convert moles of hexamethylenediamine to mass using its molar mass: $$ \text{Theoretical yield} = \text{Moles of hexamethylenediamine} \times \text{Molar mass of hexamethylenediamine} $$ The molar mass of hexamethylenediamine (C6H16N2) is: $$ (6 \times 12.01 + 16 \times 1.01 + 2 \times 14.01)g/mol = 116.21 \,g/mol $$ So, the theoretical yield of hexamethylenediamine is: $$ \text{Theoretical yield} = 6.018 \,mol \times 116.21 \,g/mol = 699.26 \,g $$

Calculate the percent yield

Finally, we will calculate the percent yield using the actual and theoretical yields: $$ \text{Percent yield} = \frac{\text{Actual yield}}{\text{Theoretical yield}} \times 100\% $$ We are given the actual yield as 765 g. Therefore, the percent yield is: $$ \text{Percent yield} = \frac{765 \,g}{699.26 \,g} \times 100\% = 109.41\% $$ However, it's not possible to obtain a yield greater than 100%. This may be due to some error in the measurements or calculations.

Key concepts

Hexamethylenediamine

It's fascinating to learn about hexamethylenediamine, which has the chemical formula \( C_6H_{16}N_2 \). It is a crucial compound in manufacturing nylon, a synthetic polymer widely used in textiles and plastics. This compound is known for having two amine (-NH₂) groups attached to a six-carbon alkane chain, which gives it reactive properties. These properties make it ideal for polymerization reactions to form polyamide chains in nylon.
- Hexamethylenediamine is not only important because of its role in nylon production but also because of its influence on the properties of the resulting nylon. For instance, it helps impart strength and elasticity to the nylon fibers.
- In the reaction that produces hexamethylenediamine, it is synthesized by reacting adipic acid with hydrogen and ammonia. Its production involves transforming the acid groups of adipic acid into amine groups. This transformation makes it an integral product in industrial chemistry.

Adipic Acid

Adipic acid, represented by the chemical formula \( C_6H_{10}O_4 \), is an organic compound that plays a significant role as a precursor in the production of various industrial materials including hexamethylenediamine. This compound is part of a group of carboxylic acids known for their acidic properties and involvement in forming other chemical products through reaction processes.
- It commonly appears as a crystalline, white powder and is used to produce nylon, which is a polymer. During its chemical reaction with ammonia and hydrogen, adipic acid undergoes a conversion process to produce hexamethylenediamine, a critical component of nylon.
- Adipic acid is somewhat unique due to its ability to easily react with other chemicals. Its reactivity is attributed to its two carboxylic (-COOH) groups, which are essential for the transformations leading to other valuable compounds in industrial applications.
- It is also valued outside of the nylon industry. For example, it serves as an additive in food and pharmaceuticals due to its acidity and chemical stability.

Theoretical Yield

Theoretical yield is a fundamental concept in chemistry that helps us understand the efficiency of a chemical reaction. It is the maximum amount of product that can be formed from a given amount of reactants, assuming perfect conditions with no losses or side reactions.
- To calculate the theoretical yield, the first step is to identify the balanced equation for the reaction, which provides the stoichiometry needed. This includes understanding the molar ratios between the reactants and products.
- In our example, the balanced chemical equation shows a 1:1 molar ratio between adipic acid and hexamethylenediamine, causing the same number of moles of each to form under ideal conditions. From here, applying the molar mass of hexamethylenediamine allows us to convert moles into grams, which gives us the theoretical yield.
- The significance of the theoretical yield lies in its role in determining the percent yield. It's a comparison of the actual yield obtained from an experiment to the theoretical amount, which is a key indicator of a reaction's efficiency. Understanding this concept can prevent misleading results, such as obtaining over 100% yield, which often points to errors in measurement or calculation.