When a compound is dissolved in water, the freezing point of the solution decreases to below that of pure water. The decrease in temperature can be found by using the following equation:
T = Kf * m * i, where T is the change in the freezing point that is noticed, Kf is known as the cryoscopic constant which is a constant for water irrespective of the solute and is equal to 1.853 K*kg/mol, m is the molality of the solute and i is called the van't Hoff factor which for NaCl is 2.
The freezing point has to be decreased by 10 degree Celsius as the normal freezing point of pure water is 0 degree Celsius. We need to determine the weight of salt that has to be added to 3 kg of water.
10 = 1.853 * m * 2
=> m = 10/ (2* 1.853)
=> m = 2.698
The required molality is 2.698 or we need to add 2.698 moles of NaCl to every kilogram of water. 3 kg of water requires the addition of 3*2.698 = 8.094 moles. The mass of one mole of NaCl is 58.443 g. The mass of 8.094 moles is 58.443*8.094 = 473.09 g
We need to add 473.09 g of NaCl to 3 kg of water to reduce the freezing point to -10 degree Celsius.