To determine the percentage composition of nitrogen using Dumas' method, follow these calculations:

Calculate the Pressure of Nitrogen Gas:

$ \text{Pressure of } \mathrm{N}_2 = (715 \text{ mmHg} - 15 \text{ mmHg}) = 700 \text{ mmHg} $

Calculate the Moles of Nitrogen ($\mathrm{n}_{\mathrm{N}_2}$):

$ \mathrm{n}_{\mathrm{N}_2} = \frac{\mathrm{PV}}{\mathrm{RT}} $

Where:

$ P = 700 \text{ mmHg} $

$ V = 60 \times 10^{-3} \text{ L} $

$ R = 0.0821 \text{ L atm/mol K} $

$ T = 300 \text{ K} $

Plug the values into the equation:

$ \mathrm{n}_{\mathrm{N}_2} = \frac{700 \times 60 \times 10^{-3}}{760 \times 0.0821 \times 300} \approx 2.24 \times 10^{-3} \text{ mol} $

Calculate the Mass of Nitrogen Gas:

$ \text{Mass of } \mathrm{N}_2 = 2.24 \times 10^{-3} \text{ mol} \times 28 \text{ g/mol} = 0.06272 \text{ g} $

Determine the Percentage Composition of Nitrogen:

$ \% \mathrm{~N}_2 = \left(\frac{0.06272}{0.5}\right) \times 100 \approx 12.57\% $

Thus, the percentage composition of nitrogen in the compound is approximately 12.57%.