Ask Question
11 June, 03:23

150 lb of NaCl are initially dissolved in 500 gal of a NaCl solution in a container. Water is continuously added to the container at a rate of 5 gal/min and the container content, which is kept uniform by mixing, is also withdrawn out of the container at 5 gal/min. Determine how much NaCl will be in the tank at the end of 1.5 hours.

+4
Answers (1)
  1. 11 June, 03:39
    0
    After 90 minutes there will be 60.5 lb NaCl in the tank

    Explanation:

    Initially, you have 150 lb/500 gal = 0.300 lb/gal NaCl

    After 1 minute, the volume will be the same but you will have less NaCl in the solution.

    After the first minute, the mass of NaCl you will lose will be:

    0.3 lb/gal · 5 gal = 1.5 lb

    Then, the concentration of the solution will be:

    (150 lb - 1.5 lb) / 500 gal = 0.297 lb/gal

    After the second minute:

    mass of NaCl lost = 0.297 lb/gal · 5 gal = 1.485 lb

    concentration of the solution = (148.5 lb - 1.485 lb) / 500 gal = 0.29403 lb/gal

    After the third minute:

    mass of NaCl lost = 0.294 lb/gal · 5 gal = 1.47015 lb

    concentration of the solution = 147.015 lb - 1.47015 lb / 500 gal = 0.2910897 lb/gal

    Notice that the solution is being diluted by 1% every minute. Then, the concentration of the solution after every minute will be 99% of the previous solution. For example, after the first minute, the concentration of the solution will be 99% of the original solution (99% of 0.3 lb/gal = 0.297 lb/gal). Mathematically, we can express it as follows:

    0.3 lb/gal · 0.99 = 0.297 lb/gal

    After the second minute:

    0.297 lb/gal · 0.99 = 0.29403 lb/gal

    Since 0.297 lb/gal = 0.3 lb/gal · 0.99

    we can write for the second minute:

    0.3 lb/gal · 0.99 · 0.99 = 0.29403 lb/gal

    And for the third minute:

    0.3 lb/gal · 0.99 · 0.99 · 0.99 = 0.2910897 lb/gal

    And for the nth minute:

    0.3 lb/gal · 0.99ⁿ = concentration of the solution after n minutes

    Now, we can find the concentration of the solution after 90 min:

    0.300 lb/gal · 0.99^90 = 0.121 lb/gal

    The mass of NaCl after 90 minutes will be:

    0.121 lb/gal · 500 gal = 60.5 lb
Know the Answer?
Not Sure About the Answer?
Find an answer to your question ✅ “150 lb of NaCl are initially dissolved in 500 gal of a NaCl solution in a container. Water is continuously added to the container at a rate ...” in 📘 Chemistry if you're in doubt about the correctness of the answers or there's no answer, then try to use the smart search and find answers to the similar questions.
Search for Other Answers