Question

How many grams of rock salt, Naci, do you need to add to a 3.78 kg of ice, to get the temperature to drop to -190?​

Answer 1

1129.9 grams of rock salt, NaCl should be added to a 3.78 kg of ice to get the temperature to drop to -19 °C.

What mass of rock salt is required?

The mass of rock salt required to lower the temperature of ice by 19 °C is determined using the Blagden's Law given below:

• $ΔT = iK_fm$

where;

• ΔT = Change in temperature in °C
• i = van't Hoff factor
• Kf = molal freezing point depression constant
• m = molality of the solute in mol solute/kg solvent.

The van't hoff factor for NaCl, i = 2

Kf for water/ice = 1.86 °C kg/mol

molalityof NaCl = (mass/molar massl) / kg of ice

The mass of NaCl is derived as follows:

• mass of NaCl = molality × mass of ice × molar mass

molar mass of NaCl = 58.5

mass of ice = 3.78 kg

Let molality of NaCl = X

ΔT = 19 °C

Inputting the values above in the equation of Blagden law:

19 = 2 x 1.86 °C kg/mol x X

X = 5.11 mol/kg

Then, the mass of NaCl will be;

mass of NaCl = 5.11 × 3.78 × 58.5

mass of NaCl = 1129.9 g

Therefore, 1129.9 grams of rock salt, NaCl should be added to a 3.78 kg of ice to get the temperature to drop to -19 °C.

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