Question

The hydrocarbon (X) with molar mass 80 g mol\(^{-1}\) and 90%carbon has ________________ degree of unsaturation.

Hint:

To find the degree of unsaturation, calculate the number of possible bonds based on the number of carbon and hydrogen atoms, and use the formula to find the unsaturation.

Answer 1

Step 1: Determine the Formula of the Hydrocarbon

We are given that the molar mass of the hydrocarbon (X) is 80 g/mol and it contains 90% carbon by mass. To find the degree of unsaturation, we first need to determine the empirical formula of the compound.

The mass of carbon in 80 g of the compound is 90% of 80, which is:

Mass of carbon = \( 0.90 \times 80 = 72 \, \text{g} \)

The mass of hydrogen is the remainder, which is:

Mass of hydrogen = \( 80 - 72 = 8 \, \text{g} \)

Step 2: Calculate Moles of Carbon and Hydrogen

Now, calculate the moles of carbon and hydrogen using their respective atomic masses (C = 12 g/mol and H = 1 g/mol):

Moles of carbon = \( \frac{72 \, \text{g}}{12 \, \text{g/mol}} = 6 \, \text{mol} \)

Moles of hydrogen = \( \frac{8 \, \text{g}}{1 \, \text{g/mol}} = 8 \, \text{mol} \)

Step 3: Determine the Empirical Formula

The mole ratio of carbon to hydrogen is 6:8, which simplifies to 3:4. Therefore, the empirical formula of the compound is C₃H₄.

Step 4: Calculate the Molecular Formula

The molar mass of the empirical formula C₃H₄ is:

Molar mass of C₃H₄ = \( 3 \times 12 + 4 \times 1 = 36 + 4 = 40 \, \text{g/mol} \)

The given molar mass of the compound is 80 g/mol. To find the molecular formula, divide the molar mass of the compound by the molar mass of the empirical formula:

Ratio = \( \frac{80}{40} = 2 \)

This means the molecular formula is twice the empirical formula, or C₆H₈.

Step 5: Calculate the Degree of Unsaturation

The degree of unsaturation (DU) can be calculated using the formula:

\[ \text{DU} = \frac{2C + 2 - H}{2} \]

For C₆H₈, we have:

DU = \( \frac{2(6) + 2 - 8}{2} = \frac{12 + 2 - 8}{2} = \frac{6}{2} = 3 \)

Conclusion

The hydrocarbon (X) with a molar mass of 80 g/mol and 90% carbon has a degree of unsaturation of 3.