What mass of the water freezes when metal at -200 degrees C is dropped into 10mL water at 10 degrees C?

A piece of Tungsten is dropped into a cup calorimeter filled with 10mL of water at 10C.
The Tungsten is 60g and is at -200C. The water starts to freeze as the temperature cools to 0C.
What mass of the water freezes as the freezing continues?
Cp Tungsten = 0.132 J/gC, density = 20.5g/cm3
Enthalpy of fusion for water = 6.01 kJ/mol.
Enthalpy vaporization of tungsten = 806.7kJ/mol

Thank you!

1 Answer
Apr 24, 2018

#3.49g#

Explanation:

The tungsten density and vaporization values are useless for this problem, but you do need to look up the heat capacity of water. The first calculation is the heat transfer to reduce the 10mL of water from #10^oC# to #0^oC#. ALL of the water must be at #0^oC# before any of it will freeze. The second calculation is the amount of heat transfer available to change the phase of water, and how many grams of water that will affect.

Heat (loss) available from cold metal:
#Q = C_p xx g xx Delta(t) = 0.132 xx 60 xx (200) = 1584J#

Heat removal from water: #10mL = 10g#
Cool from #10^oC# to #0^oC#:
#Q = C_p xx g xx Delta(t) = 4.186 xx 10 xx 10 = 418.6J#

Remaining heat sink: #1584 - 418.6 = 1165.4J#
Freezing (heat of fusion of water):
#6010J/"mol" xx 10g/18"g/mol" = 3339J#

#1165.4/3339 xx 10g = 3.49g#