Equations The heat energy associated with a change in temperature that does not

Question

Equations

The heat energy associated with a change in temperature that does not involve a change in phase is given by

q=ms?T

where q is heat in joules, m is mass in grams, s is specific heat in joules per gram-degree Celsius, J/(g??C), and ?T is the temperature change in degrees Celsius. The heat energy associated with a change in phase at constant temperature is given by

q=m?H

where q is heat in joules, m is mass in grams, and ?H is the enthalpy in joules per gram.

Physical constants

The constants for H2O are shown here:

Specific heat of ice: sice=2.09 J/(g??C)

Specific heat of liquid water: swater=4.18 J/(g??C)

Enthalpy of fusion (H2O(s)?H2O(l)): ?Hfus=334 J/g

Enthalpy of vaporization (H2O(l)?H2O(g)): ?Hvap=2250 J/g

Part A

How much heat energy, in kilojoules, is required to convert 79.0 g of ice at ?18.0 ?C to water at 25.0 ?C ?

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

The conversion requires :

1) - 18 C to 0 (ice)

2) 0 C to 0 C (ice to liquid)

3) 0 C to 25 C ( liquid)

where

m = 79 g

therefore

step 1)

q = m * s * dT = 79 g x 2.09 J/g-C x ( 0 - (-18)) = 79 g x 2.09 J/g-C x 18 C = 2971.98 J

step 2)

q = m * dHfusion = 79 g x 334 J/g = 26386 J

step 3 )

q = m * s * dT = 79 g x 4.18 J/g-C x ( 25 - 0) =  79 g x 4.18 J/g-C x 25 = 8255.5 J

therefore

total heat required = step 1 + step 2 + step 3

or

Q (total) = 2971.98 J +  26386 J +  8255.5 J = 37613.48 J = 37.6 kJ

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