A mixture of ice and water, initially at 0◦C, poured into 50.0 g aluminum cup, initially at 30.0 ◦C. When the combined system reaches equilibrium at constant pressure, with no heat flow from the
A mixture of ice and water, initially at 0◦C, poured into 50.0 g aluminum cup, initially at 30.0 ◦C. When the combined system reaches equilibrium at constant pressure, with no heat flow from the
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Question
A mixture of ice and water, initially at 0◦C, poured into 50.0 g aluminum cup, initially at 30.0 ◦C.
When the combined system reaches equilibrium at constant pressure, with no heat flow from the
surroundings, it is found that the final temperature is 0◦C. Find the total entropy change associated
with this process. [Note that while some ice will melt, the temperature of the water/ice mixture is
constant here.]
![Useful info
NA = 6.022x103 mol
g =9.807 m/s?
P[H>O] =1.00 g/mL
1 bar = 10° Pa
1 atm =1.013bar
R = 8.314 J/K-mol
= 8.206x10? L-atm/K-mol
= 8.206x10° m-atm/K-mol
= 62.36 L-Tor/K-mol
1J = 10 L-bar = 9.870×10³ L-atm= 0.2390 cal
1m = 10° cm = 10° mm = 10° um = 10° nm = 101º A
= 760 Torr
1 mbar = 10 bar
RT = 2.478 kJ/mol for T = 298 K. (= 24.46 L-atm/mol)
1 L-atm = 101.3J
1 m = 10° L = 10° cm
1 kg = 1000 g
1 Watt (W) = 1 J/s
Physical Properties of Selected Substances
Cp.m
J/(mol-K) J/(mol-K) kJ/mol
24.3
AH melting temp AHap boiling temp
kJ/mol
mol. wt.
fas
g/mol
kJ/mol
K
K
Al(s)
CH,OH(I)
CH;OH(g)
H,(g)
H;O(1)
H,O(g)
H,O(s)
1,(s)
L(g)
I(g)
N2(g)
Na(s)
NaN,(s)
0:(g)
Properties of pure phases are for standard conditions of 298 K and 1 atm.
Phase transition enthalpies are valid at the indicated phase transition temperature, at 1 atm.
27.0
28.3
32.04
-238.66
81.6
3.16
175.2
35.29
337.2
32.04
-200.66
43.9
2.0
131.7
28.8
18.0
-285.8
69.9
75.3
6.0
273
40.6
373
18.0
-241.8
188.8
33.6
18.0
38.0
37.0
253.8
116.14
54.44
15.5
386.8
41.8
458.4
253.8
+62.44
260.69
36.90
126.9
+106.84
180.79
20.79
28.0
191.61
29.1
23.0
51.2
28.2
2.6
371
97.4
1156
65.0
+21.76
70.5
76.6
32.0
205.1
29.4
Integrals
Maxwell relations
n# -1
n+1
av
as
In z
as
P
rp-
1
- In(az – b)
as
av
T
T
Properties of Some Materials
Density (293 K)
g/cm
KT
10-4 K-1
10-" bar
C, graphite
C, diamond
Cu, solid
Water, liquid
2.26
3
Euler chain rule
3.5
0.030
0.187
az
8.9
0.501
0.735
= -1
az
0.997
2.1
49.6](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40ec8258-164a-4e20-98f8-11ad6654b8f1%2F137b006e-3482-438e-8d8a-9e88e7e12087%2F005njfi_processed.png&w=3840&q=75)
Transcribed Image Text:Useful info
NA = 6.022x103 mol
g =9.807 m/s?
P[H>O] =1.00 g/mL
1 bar = 10° Pa
1 atm =1.013bar
R = 8.314 J/K-mol
= 8.206x10? L-atm/K-mol
= 8.206x10° m-atm/K-mol
= 62.36 L-Tor/K-mol
1J = 10 L-bar = 9.870×10³ L-atm= 0.2390 cal
1m = 10° cm = 10° mm = 10° um = 10° nm = 101º A
= 760 Torr
1 mbar = 10 bar
RT = 2.478 kJ/mol for T = 298 K. (= 24.46 L-atm/mol)
1 L-atm = 101.3J
1 m = 10° L = 10° cm
1 kg = 1000 g
1 Watt (W) = 1 J/s
Physical Properties of Selected Substances
Cp.m
J/(mol-K) J/(mol-K) kJ/mol
24.3
AH melting temp AHap boiling temp
kJ/mol
mol. wt.
fas
g/mol
kJ/mol
K
K
Al(s)
CH,OH(I)
CH;OH(g)
H,(g)
H;O(1)
H,O(g)
H,O(s)
1,(s)
L(g)
I(g)
N2(g)
Na(s)
NaN,(s)
0:(g)
Properties of pure phases are for standard conditions of 298 K and 1 atm.
Phase transition enthalpies are valid at the indicated phase transition temperature, at 1 atm.
27.0
28.3
32.04
-238.66
81.6
3.16
175.2
35.29
337.2
32.04
-200.66
43.9
2.0
131.7
28.8
18.0
-285.8
69.9
75.3
6.0
273
40.6
373
18.0
-241.8
188.8
33.6
18.0
38.0
37.0
253.8
116.14
54.44
15.5
386.8
41.8
458.4
253.8
+62.44
260.69
36.90
126.9
+106.84
180.79
20.79
28.0
191.61
29.1
23.0
51.2
28.2
2.6
371
97.4
1156
65.0
+21.76
70.5
76.6
32.0
205.1
29.4
Integrals
Maxwell relations
n# -1
n+1
av
as
In z
as
P
rp-
1
- In(az – b)
as
av
T
T
Properties of Some Materials
Density (293 K)
g/cm
KT
10-4 K-1
10-" bar
C, graphite
C, diamond
Cu, solid
Water, liquid
2.26
3
Euler chain rule
3.5
0.030
0.187
az
8.9
0.501
0.735
= -1
az
0.997
2.1
49.6
Expert Solution
Step 1
Given:
T1=0oC=0+273
T1=271K
T2=30oC=30+273
T2=303K
m=50.0g
Atomic mass of aluminium is 27 g/mol
So number of moles are
=1.85 mol
Molar heat capacity at constant pressure is
Cp=24.2 J/mol.K
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