A geochemist measures the concentration of salt dissolved in Lake Parsons and finds a concentration of 47.·gL−1. The geochemist also measures the concentration of salt in several nearby non-isolated lakes, and finds an average concentration of 5.89·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 2 significant digits.
Question
A geochemist measures the concentration of salt dissolved in Lake Parsons and finds a concentration of 47.·gL−1. The geochemist also measures the concentration of salt in several nearby non-isolated lakes, and finds an average concentration of 5.89·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 2 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 initial and final concentrations of salt. The initial concentration (Ci) in Lake Parsons was 5.89 gL-1 (the same as the average concentration in nearby non-isolated lakes). The final concentration (Cf) in Lake Parsons is 47 gL-1.
Step 2: Use the formula for concentration change due to evaporation. The formula is: Cf = Ci / (1 - E), where E is the fraction of the lake that has evaporated.
Step 3: Rearrange the formula to solve for E. E = 1 - (Ci / Cf)
Step 4: Substitute the given values into the formula. E = 1 - (5.89 gL-1 / 47 gL-1)
Step 5: Calculate the value of E. E = 1 - 0.125 = 0.875
Step 6: Convert the fraction to a percentage. E = 0.875 * 100 = 87.5%
So, approximately 87.5% of Lake Parsons has evaporated since it became isolated.
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