I. Write the chemical reaction involving the synthesis of 4-methylcyclohexene and Calculate their molar mass. Density of 4-methylcyclohexanol Density of phosphoric acid 1.69 g/mL 0.916 g/mL In an empty 5 mL conical vial, 2.7 mL of the 4-methylcyclohexanol and 2.3 mL of phosphoric acid are mixed. (DM/V) (a) How many grams of each reagent is present? (Show your work) Jenny X (b) How many moles of each reagent is present? (Show your work)
(c) Which reagent is the Limiting Reagent? Why? (Show your work) (d) What is the theoretical yield of the “4-methylcyclohexene”? (Show your work) (e) A student reports a 62.5% yield. How much product did the student make? (Show your work)
The Correct Answer and Explanation is :
To tackle this problem, let’s break it down step by step. The chemical reaction for synthesizing 4-methylcyclohexene involves the dehydration of 4-methylcyclohexanol in the presence of phosphoric acid. This is an example of an elimination reaction.
1. Chemical reaction:
The dehydration reaction for 4-methylcyclohexene is as follows: 4-methylcyclohexanol→H3PO44-methylcyclohexene+H2O\text{4-methylcyclohexanol} \xrightarrow{\text{H}_3\text{PO}_4} \text{4-methylcyclohexene} + \text{H}_2\text{O}
2. Molar Mass of 4-methylcyclohexene:
To calculate the molar mass of 4-methylcyclohexene, we sum up the atomic masses of its components:
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol
The molecular formula for 4-methylcyclohexene is C7H12C_7H_{12}. So the molar mass of 4-methylcyclohexene is: 7(12.01 g/mol)+12(1.008 g/mol)=84.07 g/mol+12.096 g/mol=96.166 g/mol7(12.01 \, \text{g/mol}) + 12(1.008 \, \text{g/mol}) = 84.07 \, \text{g/mol} + 12.096 \, \text{g/mol} = 96.166 \, \text{g/mol}
3. Mass Calculation for Reagents:
Given that:
- The density of 4-methylcyclohexanol is 1.69 g/mL
- The density of phosphoric acid is 0.916 g/mL
- The volumes are:
- 4-methylcyclohexanol = 2.7 mL
- Phosphoric acid = 2.3 mL
Now calculate the mass of each reagent using the formula Mass=Density×Volume\text{Mass} = \text{Density} \times \text{Volume}.
For 4-methylcyclohexanol: Mass of 4-methylcyclohexanol=1.69 g/mL×2.7 mL=4.563 g\text{Mass of 4-methylcyclohexanol} = 1.69 \, \text{g/mL} \times 2.7 \, \text{mL} = 4.563 \, \text{g}
For phosphoric acid: Mass of phosphoric acid=0.916 g/mL×2.3 mL=2.107 g\text{Mass of phosphoric acid} = 0.916 \, \text{g/mL} \times 2.3 \, \text{mL} = 2.107 \, \text{g}
4. Moles of Reagents:
To find the number of moles, use the formula Moles=MassMolar Mass\text{Moles} = \frac{\text{Mass}}{\text{Molar Mass}}.
Molar Mass of 4-methylcyclohexanol: The molar mass of 4-methylcyclohexanol is 114.18 g/mol (C7H14O).
Moles of 4-methylcyclohexanol: Moles of 4-methylcyclohexanol=4.563 g114.18 g/mol=0.0399 mol\text{Moles of 4-methylcyclohexanol} = \frac{4.563 \, \text{g}}{114.18 \, \text{g/mol}} = 0.0399 \, \text{mol}
Molar Mass of Phosphoric Acid (H₃PO₄): The molar mass of phosphoric acid is 98.00 g/mol.
Moles of phosphoric acid: Moles of phosphoric acid=2.107 g98.00 g/mol=0.0215 mol\text{Moles of phosphoric acid} = \frac{2.107 \, \text{g}}{98.00 \, \text{g/mol}} = 0.0215 \, \text{mol}
5. Limiting Reagent:
To determine the limiting reagent, we need to look at the stoichiometry of the reaction. The balanced equation shows that 1 mole of 4-methylcyclohexanol reacts with 1 mole of phosphoric acid.
We have:
- 0.0399 mol of 4-methylcyclohexanol
- 0.0215 mol of phosphoric acid
Since phosphoric acid is present in a smaller amount, it is the limiting reagent.
6. Theoretical Yield of 4-Methylcyclohexene:
Since the limiting reagent is phosphoric acid, it will determine the maximum number of moles of 4-methylcyclohexene that can be formed. According to the stoichiometry, 1 mole of phosphoric acid produces 1 mole of 4-methylcyclohexene.
Thus, the theoretical yield in moles of 4-methylcyclohexene is 0.0215 mol.
To find the theoretical yield in grams: Mass of 4-methylcyclohexene=0.0215 mol×96.166 g/mol=2.0676 g\text{Mass of 4-methylcyclohexene} = 0.0215 \, \text{mol} \times 96.166 \, \text{g/mol} = 2.0676 \, \text{g}
7. Actual Yield:
The student reports a 62.5% yield, meaning that the actual yield is 62.5% of the theoretical yield: Actual Yield=62.5%×2.0676 g=1.292 g\text{Actual Yield} = 62.5\% \times 2.0676 \, \text{g} = 1.292 \, \text{g}
Conclusion:
- Moles of 4-methylcyclohexanol: 0.0399 mol
- Moles of phosphoric acid: 0.0215 mol
- Limiting reagent: Phosphoric acid (since it is present in a smaller amount)
- Theoretical yield: 2.0676 g of 4-methylcyclohexene
- Actual yield: 1.292 g of 4-methylcyclohexene (based on a 62.5% yield)