Question

Cyclohexanol is dehydrated to cyclohexene on heating with conc. \(\mathrm{H}_{2} \mathrm{SO}_{4}\). If the yield of this reaction is \(75 \%\), how much cyclohexene will be obtained from \(100 \mathrm{~g}\) of cyclohexanol? (a) \(61.5 \mathrm{~g}\) (b) \(82 \mathrm{~g}\) (c) \(109.3 \mathrm{~g}\) (d) \(75 \mathrm{~g}\)

Short answer

61.5 g

Step-by-step solution

Calculate the molar mass of cyclohexanol

To find how much product is formed from a given amount of reactant, first calculate the molar mass of cyclohexanol (C6H11OH). Use periodic table values for C, H, and O, which are approximately 12.01 g/mol, 1.01 g/mol, and 16.00 g/mol, respectively. Molar mass = (6 \(\times\) 12.01) + (11 \(\times\) 1.01) + 16.00 = 100.16 g/mol.

Calculate the moles of cyclohexanol used

Using the molar mass from Step 1, calculate the moles of cyclohexanol in 100 g. Moles of cyclohexanol = 100 g / 100.16 g/mol ≈ 0.9984 mol.

Calculate the theoretical yield of cyclohexene

Assuming a 100% yield, the moles of cyclohexene produced would be the same as the moles of cyclohexanol used because the reaction is a 1:1 mole ratio. Therefore, theoretical yield in grams of cyclohexene = moles of cyclohexanol × molar mass of cyclohexene (C6H10, which has a molar mass of (6 \(\times\) 12.01) + (10 \(\times\) 1.01) ≈ 82.14 g/mol). Thus, theoretical yield = 0.9984 mol × 82.14 g/mol ≈ 82 g.

Calculate the actual yield of cyclohexene

The actual yield is 75% of the theoretical yield. Actual yield = 0.75 × 82 g ≈ 61.5 g.

Key concepts

Theoretical Yield

Understanding the theoretical yield is a fundamental aspect of chemistry, especially when it comes to reaction yield calculation. The theoretical yield is the maximum amount of product that could be formed from a given amount of reactants under perfect conditions, where no products are lost and the reaction goes to completion without any side reactions.

It is important to emphasize that these conditions are ideal and not often met in actual laboratory settings. If we take the dehydration of cyclohexanol to cyclohexene as an example, theoretically, each molecule of cyclohexanol would produce one molecule of cyclohexene. To calculate this, we must know the stoichiometry of the reaction, which, in this case, is a 1:1 ratio. Thus, the theoretical yield can be calculated by converting the mass of cyclohexanol used to moles and then using the molar mass of cyclohexene to convert those moles into grams.

Actual Yield

In contrast to the theoretical yield, the actual yield is the quantity of product actually obtained from the chemical reaction, which is often less due to various practical limitations. Factors such as incomplete reactions, competing side reactions, and loss of product during purification processes can cause the actual yield to be less than the theoretical yield.

It is represented as a percentage of the theoretical yield—known as the percent yield—and is a measure of the reaction's efficiency. For the dehydration of cyclohexanol, if the actual yield is 75%, this means that only 75% of the theoretical amount of cyclohexene was produced. To find the actual amount, simply multiply the theoretical yield by 0.75, which represents the 75% effectiveness in this context.

Molar Mass Calculation

Calculating the molar mass of a compound is a crucial step in yield calculations. The molar mass is the weight of one mole of a substance, and it is usually expressed in grams per mole (g/mol). It is determined by summing the masses of the individual atoms in the molecule, which are found on the periodic table.

To illustrate, for cyclohexanol (C6H11OH), each carbon atom (C) has an average atomic mass of 12.01 g/mol, hydrogen (H) is 1.01 g/mol, and oxygen (O) is 16.00 g/mol. By multiplying each atom's mass by its frequency in the molecule and adding them together, we obtain the molar mass necessary for further calculations in stoichiometry.

Stoichiometry

Stoichiometry is the quantitative relationship between reactants and products in a chemical reaction. It involves using the balanced chemical equation to determine the proportions of reactants that will react and the amount of products that will form. Understanding stoichiometry is key to predicting the results of chemical reactions and is crucial for yield calculation exercises.

In our dehydration example, the stoichiometric ratio is 1:1, which means one mole of cyclohexanol yields one mole of cyclohexene. This ratio provides the necessary conversion factor to calculate the theoretical yield from the given amount of reactant. When students grasp stoichiometry, they can predict the outcomes of reactions and perform precise calculations for any chemical process.