You have 120.0 mL of a 0.245 M solution of NaCl in an open beaker. After several days, you
test the solution and find that it now has a concentration of 0.348 M. How much water must
have evaporated from the beaker given the new concentration?
See your post below.
To calculate how much water must have evaporated from the beaker, we can use the formula for molarity:
Molarity = moles of solute / volume of solution
Given that the initial concentration of the solution was 0.245 M and the final concentration is 0.348 M, we can calculate the amount of solute that remains unchanged in the solution.
Initial moles of NaCl = initial concentration × initial volume
Final moles of NaCl = final concentration × final volume
Let's solve for the initial and final moles of NaCl.
Initial moles of NaCl = 0.245 M × 120.0 mL = 29.4 mmol (millimoles)
Final moles of NaCl = 0.348 M × Vf (unknown)
To determine how much water has evaporated, we need to find the difference in moles of NaCl between the initial and final states. Since NaCl does not evaporate, this difference in moles corresponds to the amount of water evaporated.
Difference in moles = initial moles - final moles
Difference in moles = 29.4 mmol - (0.348 M × Vf)
Since the volume is measured in mL, the final volume should be converted from moles to mL.
Final volume (Vf) = final moles / final concentration
Now, let's substitute the values into the equation:
Difference in moles = 29.4 mmol - (0.348 M × (final moles / final concentration))
Simplifying the equation further:
Difference in moles = 29.4 mmol - (0.348 M × (final moles / 0.348 M))
We can cancel out the concentration terms:
Difference in moles = 29.4 mmol - final moles
Now, let's solve for the final moles:
29.4 mmol - final moles = 29.4 mmol - 0.348 M × (final moles / 0.348 M)
Simplifying:
29.4 mmol - final moles = 29.4 mmol - final moles
Since the right-hand side of the equation cancels out, the equation becomes:
0 = 0
This indicates that the value of final moles can be any value. Therefore, there is no unique solution for the amount of water evaporated based on the given information.