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Solutions

Question
CBSEENCH12010252

(a) Differentiate between molarity and molality for a solution. How does a change in temperature influence their values? 

(b) Calculate the freezing point of an aqueous solution containing 10.50 g of MgBr2in 200 g of water. (Molar mass of MgBr2 = 184 g) (Kf for water = 1.86 K kg mol-1

Solution

Molarity is defined as the number of moles of solute dissolved per liter of solution. 

 

  straight M equals space fraction numerator Number space of space moles space of space solute over denominator Volume space of space solution space in space litres left parenthesis dm cubed right parenthesis end fraction

 Molality of a solution is defined as the number of moles of solute dissolved in 1000 grams of solvent. 

  straight m space equals space fraction numerator Number space of space moles space of space solute over denominator Volume space of space solution space in space liters space Kg end fraction

While molarity decreases with an increase in temperature, molality is independent of temperature. This happens because molality involves mass, which does not change with a change in temperature, while molarity involves volume, which is temperature dependent.

 

b) Given 

 w2 = 10.50 g 

w1 = 200 g 

Molar mass of MgBr2 (M2) = 184 g 

 Using the formula, 
increment straight T subscript straight f space equals fraction numerator 1000 straight x space straight k subscript straight f space straight x space straight w subscript 2 over denominator straight w subscript 1 space straight x space straight M subscript 2 end fraction

equals space fraction numerator 1000 space straight x space 1.86 space straight x space 10.50 over denominator 200 space straight x space 184 end fraction

equals space fraction numerator 19.53 over denominator 200 straight x space 184 end fraction space equals space 0.53

Now comma space
straight T subscript straight f space equals space straight T subscript 0 space minus increment straight T subscript straight f space
space equals 273 minus 0.53 space equals space 272.47 space straight K