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

Question

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

q=msT

where q is heat in joules, m is mass in grams, sis specific heat in joules per gram-degree Celsius, J/(gC), 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=mH

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

The constants for H2O are shown here:

Specific heat of ice: sice=2.09 J/(gC)

Specific heat of liquid water: swater=4.18 J/(gC)

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 75.0 g of ice at 18.0 Cto water at 25.0 C ?

Part B

How long would it take for 1.50 mol of water at 100.0 C to be converted completely into steam if heat were added at a constant rate of 17.0 J/s ?

Explanation / Answer

Part A

Q = m c T
Q = quantity of heat in joules (J)
m = mass of the substance acting as the environment in
grams (g)
c = specific heat capacity (4.19 for H2O) in J/(g oC)
T = change in temperature = Tfinal - Tinitial in oC

Solution:

1) The ice does three things:

a) heat up from -18 to 0
b) melt at 0
c) heat up from 0 to 25

2) The three calculations are:

qa = (75g) (18 °C) (2.09 J / g °C) = 2821.5 Joules
qb = (75g) (334 J / g ) =25050 Joules
qc = (75) (25.0 °C) (4.18 J / g °C)

Total heat Q = 2821.5 + 25050 + 7837.5 = 35709 Joules

35.71 kilojoules of heat is required to convert 75.0 g of ice at 18.0 Cto water at 25.0 C

Part B

Let us calculate the heat is needed to convert the water into steam at 100 C

1.50 mol of water = 1.5 x 18 = 27 gm

Q = 27 x 2250 = 60750 Joules of heat is needed

let us calculate the time = 60750 / 17 = 3573.5 Seconds

3573.5 Seconds will take for 1.50 mol of water at 100.0 C to be converted completely into steam if heat were added at a constant rate of 17.0 J/s

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