A geochemist measures the concentration of salt dissolved in Lake Parsons and finds a concentration of 56.77·gL−1. The geochemist also measures the concentration of salt in several nearby non-isolated lakes, and finds an average concentration of 4.60·gL−1.Assuming the salt concentration in Lake Parsons before it became isolated was equal to the average salt concentration in nearby non-isolated lakes, calculate the percentage of Lake Parsons which has evaporated since it became isolated.Round each of your answers to 3 significant digits.
Question
A geochemist measures the concentration of salt dissolved in Lake Parsons and finds a concentration of 56.77·gL−1. The geochemist also measures the concentration of salt in several nearby non-isolated lakes, and finds an average concentration of 4.60·gL−1.Assuming the salt concentration in Lake Parsons before it became isolated was equal to the average salt concentration in nearby non-isolated lakes, calculate the percentage of Lake Parsons which has evaporated since it became isolated.Round each of your answers to 3 significant digits.
Solution
To calculate the percentage of Lake Parsons which has evaporated since it became isolated, we need to compare the current salt concentration to the original salt concentration.
Step 1: Identify the original and current salt concentrations. The original salt concentration (before evaporation) is given as the average salt concentration in nearby non-isolated lakes, which is 4.60 gL-1. The current salt concentration (after evaporation) in Lake Parsons is given as 56.77 gL-1.
Step 2: Calculate the ratio of the current concentration to the original concentration. This is done by dividing the current concentration by the original concentration:
56.77 gL-1 / 4.60 gL-1 = 12.34
This means that the salt concentration is now 12.34 times higher than it was originally.
Step 3: Calculate the percentage of the lake that has evaporated. Since the salt concentration is now 12.34 times higher, this means that 1/12.34, or approximately 0.081 or 8.1% of the original water volume remains.
Therefore, since 100% - 8.1% = 91.9%, we can conclude that approximately 91.9% of Lake Parsons has evaporated since it became isolated.
So, the answer is 91.9%.
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