In Dumas' method for estimation of nitrogen, 1mathrm~g$1\mathrm{~g}$ of an organic compound gave 150mathrm~mL$150\mathrm{~mL}$ of nitrogen collected at 300mathrm~K$300\mathrm{~K}$ temperature and 900mathrm~mmHg$900\mathrm{~mmHg}$ pressure. The percentage composition of nitrogen in the compound is _______ %$%$ (nearest integer). (Aqueous tension at 300mathrm~K = 15mathrm~mmHg$300\mathrm{~K} = 15\mathrm{~mmHg}$)

### Related Formula P_textdry N_2 = P_texttotal - P_textaqueous tension$$P_{\text{dry } N_2} = P_{\text{total}} - P_{\text{aqueous tension}}$$ PV = nRT implies n = fracPVRT$$PV = nRT \implies n = \frac{PV}{RT}$$ \% N = fractextMass of NitrogentextMass of Organic Compound times 100$$\% N = \frac{\text{Mass of Nitrogen}}{\text{Mass of Organic Compound}} \times 100$$ ### Core Logic First, calculate the actual pressure exerted by the dry nitrogen gas: P_N_2 = 900 - 15 = 885mathrm~mmHg = frac885760mathrm~atm$$P_{N_2} = 900 - 15 = 885\mathrm{~mmHg} = \frac{885}{760}\mathrm{~atm}$$ Convert volume data to liters: V = 150mathrm~mL = 0.15mathrm~L$V = 150\mathrm{~mL} = 0.15\mathrm{~L}$. Using the ideal gas law to determine the moles of N_2$N_2$ collected: n = fracleft(frac885760right) times 0.150.0821 times 300 = frac1.1645 times 0.1524.63 approx 0.0071mathrm~moles$$n = \frac{\left(\frac{885}{760}\right) \times 0.15}{0.0821 \times 300} = \frac{1.1645 \times 0.15}{24.63} \approx 0.0071\mathrm{~moles}$$ Calculate the total mass of the liberated nitrogen gas: textMass = n times M_textmolar = 0.0071 times 28 = 0.1988mathrm~g$$\text{Mass} = n \times M_{\text{molar}} = 0.0071 \times 28 = 0.1988\mathrm{~g}$$ Determine the percentage composition relative to the initial 1mathrm~g$1\mathrm{~g}$ sample size: \% N = frac0.19881 times 100 = 19.88\% approx 20\%$$\% N = \frac{0.1988}{1} \times 100 = 19.88\% \approx 20\%$$ ### Pattern Recognition Always remember to subtract the aqueous tension value first. Failing to correct for water vapor pressure is the most common pitfall in Dumas' method calculations. ### Evaluation Rubric / Model Answer null ### Chapter Mix Class 11 Chemistry: Organic Chemistry - Some Basic Principles and Techniques