Final answer:
To find the final concentration of a diluted solution, use the formula M1V1 = M2V2. For a 2.04-M solution of CH3OH diluted from 25.0 mL to 500.0 mL, the final concentration is 0.051 M, or 5.1% v/v.
Step-by-step explanation:
When diluting a solution, the concentration of the solution changes according to the volume of solvent added. To calculate the new concentration after dilution, you can use the formula M1V1 = M2V2, where M1 is the initial molarity, V1 is the initial volume, M2 is the final molarity, and V2 is the final volume of the solution.
For your question, if we have a solution that is initially 2.04 M (M1) with a volume of 25.0 mL (V1), and this solution is diluted to 500.0 mL (V2), we want to find the concentration M2. We can rearrange the formula to solve for M2:
M2 = (M1V1) / V2
Plugging in the numbers:
M2 = (2.04 mol/L * 25.0 mL) / 500.0 mL
Now, we convert milliliters to liters for proper unit consistency, so:
M2 = (2.04 mol/L * 0.025 L) / 0.500 L
M2 = 0.051 mol/L or 0.051 M
The final concentration of the solution after dilution is 0.051 M, which can also be expressed as 5.1% v/v if we refer to percentage concentration by volume.