1. Conservation of Mass Problem
A brine solution consists of a high concentration of salt in water. It is often used for food processing (like making pickles), cooking, and thawing roads.

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3. Apply Conservation of Mass Equations:
Class Problem: 30kg of water is evaporated from a vat that contains 212kg of a 13% brine solution (13% salt; 87% water). 5kg of salt is then added to the brine. The brine solution that results from this process will contain what percentage of salt?
Apply Conservation of Mass Equations:
30 kg water (Evaporated)
100% water
𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡
Overall:
𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡
Salt:
212 kg Brine Solution
5kg salt
100% salt
212𝑘𝑔+5𝑘𝑔=30𝑘𝑔+𝑋
(.13)212𝑘𝑔+5𝑘𝑔=𝑎𝑋
13% salt
87% water
(1)
(2)
X kg Brine Solution
a% salt
b% water
𝑚 𝑖𝑛 = 𝑚 𝑜𝑢𝑡
Water:
𝑘𝑔=𝑏𝑋+30𝑘𝑔
(3)
Use equation 1 to solve for X and plug into equation 2 to find a:
(1)
(2)
212𝑘𝑔+5𝑘𝑔=30𝑘𝑔+𝑋
(.13)212𝑘𝑔+5𝑘𝑔=𝑎𝑋
(.13)212𝑘𝑔+5𝑘𝑔=𝑎(187𝑘𝑔)
212𝑘𝑔+5𝑘𝑔−30𝑘𝑔=𝑋
𝑋=187𝑘𝑔
(.13)212𝑘𝑔+5𝑘𝑔 187𝑘𝑔 =𝑎
𝑎=.174
17.4% salt in the final brine solution