To determine the percent composition of boron in diborane ([tex]\( \text{B}_2 \text{H}_6 \)[/tex]), we can follow a step-by-step method. Here's a detailed breakdown of the solution:
1. Identify the Molar Masses:
- The atomic mass of boron (B) is 10.81 g/mol.
- The atomic mass of hydrogen (H) is 1.008 g/mol.
2. Calculate the Molar Mass of Diborane ([tex]\( \text{B}_2 \text{H}_6 \)[/tex]):
- Diborane consists of 2 boron atoms and 6 hydrogen atoms.
- The molar mass of diborane can be calculated as:
[tex]\[
\text{Molar mass of } \text{B}_2\text{H}_6 = (2 \times \text{molar mass of B}) + (6 \times \text{molar mass of H})
\][/tex]
[tex]\[
\text{Molar mass of B}_2 \text{H}_6 = (2 \times 10.81 \text{ g/mol}) + (6 \times 1.008 \text{ g/mol})
\][/tex]
[tex]\[
\text{Molar mass of B}_2 \text{H}_6 = 21.62 \text{ g/mol} + 6.048 \text{ g/mol}
\][/tex]
[tex]\[
\text{Molar mass of B}_2\text{H}_6 = 27.668 \text{ g/mol}
\][/tex]
3. Calculate the Mass Contribution of Boron in Diborane:
- The total mass of boron in diborane is given by:
[tex]\[
\text{Total mass of B} = 2 \times 10.81 \text{ g/mol} = 21.62 \text{ g/mol}
\][/tex]
4. Determine the Percent Composition of Boron:
- The percent composition of boron is calculated using the formula:
[tex]\[
\text{Percent composition of B} = \left( \frac{\text{Total mass of B}}{\text{Molar mass of } \text{B}_2 \text{H}_6} \right) \times 100
\][/tex]
[tex]\[
\text{Percent composition of B} = \left( \frac{21.62 \text{ g/mol}}{27.668 \text{ g/mol}} \right) \times 100
\][/tex]
[tex]\[
\text{Percent composition of B} \approx 78.14\%
\][/tex]
From these calculations, the percent composition of boron in diborane is approximately 78%. Therefore, the correct answer is:
E. [tex]\( 78\% \)[/tex]
