Question

In: Chemistry

If 30g of water at 10C is added to 180g of ice at -110C in an...

If 30g of water at 10C is added to 180g of ice at -110C in an insulated cup, what is the final temperature when equilbrium is reached? How much liquid is in the cup when equilibrium is reached? What is the total entropy change for the reaction?

Note: dH fusion for water = 6.025kJ/mol at 0C, Cp,m for H2O(l) = 75.48 and Cp,m for H2O(s) = 37.68

Solutions

Expert Solution

  • We know that, heat flows from a warmer body to a colder body.
  • So, heat will flow out a warmer body and flow into a colder body, until both of them acquire the same temperature. This is the temperature when equilibrium state is obtained.
  • When the above two mixtures are mixed, 30 g of water will lost the heat of 30 s (10 - t) which is equal to the heat gained by 180 g of ice, i.e, 180 s (t -(-110)= 180 s (t+110). Here, t is the resultant temperature at equilibrium and s is the specific heat capacity.
  • So, 30 s (10 - t) = 180 s (t+110)
  • In the above question, molar heat capacities of ice and water are given.

Molar heat capacity = Specific heat x Molar mass.

  • Molar mass of water or ice = 18 g/mol.

Specific heat of water = 75.48 / 18 = 4.19

Specific heat of ice = 37.68 / 18 = 2.09

= 30 s (10 - t) (water) = 180 s (t+110) (ice)

= 30 x 4.19 ( 10 - t ) = 180 x 2.09 ( t + 110)

= 125.7 ( 10 - t ) = 376.2 ( t + 110 )

= 1257 - 125.7 t = 376.2 t + 41383

= 1257 - 41383 = 376.2 t + 125.7 t

= - 40125 = 501.9 t

= t = - 79.9 C.

  • Amount of liquid after equilibrium:

= 30 g of water would have changed into ice at equilibrium temperature. A part of ice would have changed into water, as temperature of the ice has increased to - 79.9 C.

At - 110 C ------- There is 180 g of ice

At - 79.9 C ------- There is (180 x -79.9) / -110 = 130 g of ice.

  • Liquid in the equilibrium mixture = 180 g - 130 g = 50 g

Total entropy change of the reaction:

Change in entropy = dH fusion / T

( In the above situation ice is melting, hence its a fusion reaction)

= Here T is the absolute temperature at which ice melts = 273 K

= Change in entropy :

=dH fusion = 6.025 kJ/mol = 6025 J/mol.

Change in entropy = 6025 / 273 = 22.1 J/K/mol.


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