The hydrocarbon (X) with molar mass 80 g mol\(^{-1}\) and 90% carbon has \(\_\_\_\_\) degree of unsaturation.
The hydrocarbon (X) with molar mass 80 g mol\(^{-1}\) and 90% carbon has \(\_\_\_\_\) degree of unsaturation.
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Solution and Explanation
Step 1: Given: \[ \text{Molar mass of } X = 80 \, \text{g mol}^{-1}, \quad \text{Percentage of carbon in } X = 90\%. \] Therefore, mass of carbon in 80 g of \(X\) is \(0.90 \times 80 = 72 \, \text{g}\).
Step 2: The number of moles of carbon in \(72 \, \text{g}\) is: \[ \frac{72 \, \text{g}}{12 \, \text{g mol}^{-1}} = 6 \, \text{mol}. \] Each carbon atom has 4 bonds. Therefore, the total number of bonds contributed by the carbon atoms is \(6 \times 4 = 24 \, \text{bonds}\).
Step 3: The number of hydrogen atoms is determined by subtracting the bonds formed by the carbon atoms from the total bonds formed. The degree of unsaturation (DBE) is given by the formula: \[ \text{Degree of unsaturation} = \frac{2C + 2 - H}{2} \] where \(C\) is the number of carbon atoms and \(H\) is the number of hydrogen atoms in the molecule.
Step 4: Therefore, the degree of unsaturation for this hydrocarbon is \(4\).
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