Answer is: molality is 5.87 m.
ω(HNO₃) = 27.0% = 0.27.
If we use mass of solution 100 grams:
m(solution) = 100 g.
m(HNO₃) = ω(HNO₃) · m(solution).
m(HNO₃) = 0.27 · 100 g.
m(HNO₃) = 27 g.
n(HNO₃) = m(HNO₃) ÷ M(HNO₃).
n(HNO₃) = 27 g ÷ 63 g/mol.
n(HNO₃) = 0.428 mol.
m(H₂O) = 100 g - 27 g.
m(H₂O) = 73 g ÷ 1000 g/kg.
m(H₂O) = 0.073 kg.
b(solution) = n(HNO₃) ÷ m(H₂O).
b(solution) = 0.428 mol ÷ 0.073 kg.
b(solution) = 5.87 mol/kg = 5.87 m.
