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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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: .87 212𝑘𝑔=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