Answer :
The weight percentage of nitrogen in the protein is approximately 15.09%.
The steps are:
1. Find the amount of protein in the solution:
Volume of the solution (V) = 256 µL = 0.256 mL
Concentration of protein = 37.9 mg/mL
Convert the volume into mL because the concentration is given in mg/mL.
Amount of protein = 37.9 mg/mL * 0.256 mL
Amount of protein = 9.7024 mg
2. Calculate the moles of HCl originally present:
Volume of HCl = 5 mL = 0.005 L
Molarity of HCl = 0.0336 M
Moles of HCl = Molarity × Volume
Moles of HCl = 0.0336 M × 0.005 L
Moles of HCl = 1.68 × 10⁻⁴ mol
3. Calculate the moles of NaOH used in the back titration:
Volume of NaOH solution = 6.34 mL = 0.00634 L
Molarity of NaOH = 0.010 M
Moles of NaOH = Molarity × Volume
Moles of NaOH = 0.010 M × 0.00634 L
Moles of NaOH = 6.34 × 10⁻⁵ mol
4. Determine the moles of HCl that reacted with ammonia:
The reacted HCl will be the initial moles of HCl minus the moles of NaOH used in the back titration.
Moles of HCl that reacted = 1.68 × 10⁻⁴ mol - 6.34 × 10⁻⁵ mol
Moles of HCl that reacted = 1.046 × 10⁻⁴ mol
5. Calculate the moles of NH₃ liberated:
The moles of NH₃ will be equal to the moles of HCl that reacted since they react in a 1:1 ratio.
Moles of NH₃ = 1.046 × 10⁻⁴ mol
6. Find the grams of nitrogen in the liberated ammonia:
Molar mass of nitrogen (N) = 14 g/mol
Mass of nitrogen = Moles of NH₃ × Molar mass of nitrogen
Mass of nitrogen = 1.046 × 10⁻⁴ mol × 14 g/mol
Mass of nitrogen = 1.4644 × 10⁻³ g = 1.4644 mg
7. Calculate the weight percentage of nitrogen in the protein:
Percentage of nitrogen = (Mass of nitrogen / Mass of protein) × 100%
Percentage of nitrogen = (1.4644 mg / 9.7024 mg) × 100%
Percentage of nitrogen = 15.09%
