You have a solution of 0.250 M NaCl. If you boil away 2/3 of the volume of water, what is the concentration of this solution?
It makes it easier if we assume a starting volume and I'll show it makes no difference what volume you choose initially. Let's take a volume of 180 mL initially. If we boil away 2/3 of that we are left with 1/3 of 180 mL or 60 mL so the new concentration is 0.250 M x 180/60 = 0.250 x 3 = 0.750 M.
Suppose we chose a volume of 240 mL and boil away 2/3 we are left with 80 mL so the final concentration will be 0.250 x 240/80 = 0.250 x 3 = 0.750 M
To find the concentration of the solution after boiling away 2/3 of the volume of water, you need to consider that the amount of solute (NaCl) remains constant while the volume of the solution changes.
Here's how to calculate it:
1. Start with the initial concentration of the solution: 0.250 M NaCl.
2. Let's assume the initial volume of the solution is V liters.
3. If you boil away 2/3 of the volume, you're left with 1/3 of the initial volume. So, the final volume is (1/3)V liters.
4. Since the amount of solute remains constant, you can set up the following equation using the dilution formula:
Initial concentration x Initial volume = Final concentration x Final volume
0.250 M x V liters = Final concentration x (1/3)V liters
5. Simplify the equation by canceling out the V liters from both sides:
0.250 M = Final concentration x (1/3)
6. Solve for the final concentration by multiplying both sides of the equation by 3:
Final concentration = 0.250 M x 3
Final concentration = 0.750 M
Therefore, the concentration of the solution after boiling away 2/3 of the volume of water is 0.750 M NaCl.
To find the concentration of the solution after boiling away a fraction of the water, you can use the equation:
C1V1 = C2V2
Where:
C1 = initial concentration
V1 = initial volume
C2 = final concentration
V2 = final volume
In this case, the initial concentration (C1) is 0.250 M NaCl, and the final volume (V2) is 1/3 of the initial volume since 2/3 was boiled away. Therefore, V2 = (1/3)V1.
Substituting the values into the equation:
C1V1 = C2V2
0.250 M * V1 = C2 * (1/3)V1
Now, we need to solve for C2:
C2 = (0.250 M * V1) / ((1/3)V1)
Simplifying:
C2 = 0.250 M * 3/1
C2 = 0.750 M
Therefore, the concentration of the solution after boiling away 2/3 of the volume of water is 0.750 M NaCl.