Answer to Question #308922 in General Chemistry for Hatdog

Question

Salt is often used to melt ice and snow on roads in the winter and the temperature right now is - 4.500°C. How much NaCl ( complete dissociation) would be necessary to melt 1000kg of ice by bringing down the freezing temperature to 4.500°C?

Answer 1

M(NaCl) = 58.5 g/mol;

K_f(H₂O) = 1.86 (C * kg/mol)

$\Delta$ T_f = b(molality) * K_f;

b = n(solution)/m(solvent) = m(NaCl)/(M(NaCl) * m(H₂O));

m(NaCl), kg = b *M(NaCl) * m(H₂O)/1000 = $\Delta$ T_f *M(NaCl) * m(H₂O) / (K_f * 1000)= 4.500 * 58.5 * 1000 / (1.86 *1000) = 141.5 kg.

Answer: 141.5 kg.