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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.

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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%.

This problem has been solved

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