# Crystallization Created Problem

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Physics
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Crystallization Created Problem
PROBLEM:
Sal Soda (Na
2
CO
3
· 10H
2
O) is made by crystallization from an aqueous solution at 30°C that contains 20 %
sodium carbonate cooled to a certain temperature. 70% of the Na
2
CO
3
in the feed is crystallized as Na
2
CO
3
·
10H
2
O and leaves the Swenson-Walker crystallizer with the mother liquor. The wet crystals enter a drier where
the all of the mother liquor is dried and added to the total crystals produced.
The crystallizer has an area of 2.5 m
2
per 1 m length and the overall heat transfer coefficient is 500 W/m
2
K.
The cooling water enters the crystallizer at 5°C and leaves at 15°C. The heat capacity of the feed is 3.55 kJ/kg
K.
If 1000 L/hr of feed with a specific gravity of 1.085 enters the crystallizer, determine the:
a. Amount of crystals leaving the crystallizer and the total crystals produced
b. Temperature of the magma leaving the crystallizer
c. Amount of cooling water needed (Cp of water is 4.187 kJ/kg K)
d. Units of SWC needed
ANALYSIS:
To solve the problem, we need to know that:





We also need to know that specific gravity is the ratio of the density of the substance to the density of water at
4°C.
For this problem, 

 
, therefore,


 
 



In this problem, the temperature of the magma is asked. To determine the temperature of the magma, the
solubility of the mother liquor must be determined first. Then, we can interpolate for the temperature using
Table 2-122 in PHB.

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DIAGRAM:
REQUIRED:
a. Amount of crystals leaving the crystallizer and the total crystals produced (kg/hr)
b. Temperature of the magma leaving the crystallizer (°C)
c. Amount of cooling water needed (Cp of water is 4.187 kJ/kg K) in kg/hr
d. Units of SWC needed
SOLUTION:
Basis: 1000 L of feed





 




OMB around the crystallizer: OMB around the system
F = L+C F = V + C
1085 = L + C equation (1) 1085 = V + C






 



  








F
1000 L of feed
20% Na
2
CO
3
t
f
= 30°C
SG = 1.085

Na
2
CO
3
· 10H
2
O
70% Na
2
CO
3
crystallized
t
l
= ?
V
C
MW Na
2
CO
3
= 105.98
MW Na
2
CO
3
· 10H
2
O = 285.98
t
2
= 15°C
w

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Crystallization Created Problem PROBLEM: Sal Soda (Na2CO3 · 10H2O) is made by crystallization from an aqueous solution at 30°C that contains 20 % sodium carbonate cooled to a certain temperature. 70% of the Na 2CO3 in the feed is crystallized as Na 2CO3 · 10H2O and leaves the Swenson-Walker crystallizer with the mother liquor. The wet crystals enter a drier where the all of the mother liquor is dried and added to the total crystals produced. The crystallizer has an area of 2.5 m2 per 1 m length and the overall heat transfer coefficient is 500 W/m2 K. The cooling water enters the crystallizer at 5°C and leaves at 15°C. The heat capacity of the feed is 3.55 kJ/kg K. If 1000 L/hr of feed with a specific gravity of 1.085 enters the crystallizer, determine the: a. Amount of crystals leaving the crystallizer and the total crystals produced b. Temperature of the magma leaving the crystallizer c. Amount of cooling water needed (Cp of water is 4.187 kJ/kg K) d. Units of SWC needed ANALYSIS: To solve the problem, we need to know that: %Na2CO3 crystallized = 𝐶𝑥𝑐 𝑥 100 % 𝐹𝑥𝐹 We also need to know that specific gravity is the ratio of the density of the substance to the density of water at 4°C. For this problem, 𝑆𝐺 = 𝜌𝑓𝑒𝑒𝑑 𝜌𝐻2 𝑂 𝑎𝑡 4℃ , therefore, 𝜌𝑓𝑒𝑒𝑑 = 𝑆𝐺(𝜌𝐻2𝑂 𝑎𝑡 4℃ ) = 1.085 (1 𝑘𝑔 𝐿 ) = 1.085 𝑘𝑔 𝐿 In this problem, the temperature of the magma is ask ...
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