If 100 mL of a 3 M solution of sodium hydroxide is diluted to a total volume of 600 mL with distilled water, what will the final concentration of sodium hydroxide be?
You can do it one of two ways.
1. Use the dilution formula.
mL x M = mL x M
2. Use reason. You know that it must be more dilute going from 100 mL to 600 mL. So the molarity is
3M x (100/600) = ??
3. A third way, and one some students like is to do it with moles.
How many moles do you have in the original solution? You have M x L = 3 M x 0.1L = 0.3 mole.
You must have 0.3 mole in the diluted solution, of course, but the final volume is 600 mL or 0.6 L.
M = moles/L = 0.3/0.6 = ??
0.5M
To determine the final concentration of sodium hydroxide, we need to use the concept of moles and the equation:
M₁V₁ = M₂V₂
where:
M₁ is the initial concentration of the solution (in moles per liter, or Molarity)
V₁ is the initial volume of the solution (in liters)
M₂ is the final concentration of the solution
V₂ is the final volume of the solution (in liters)
Given information:
- Initial concentration (M₁) = 3 M
- Initial volume (V₁) = 100 mL = 0.1 L
- Final volume (V₂) = 600 mL = 0.6 L (since it is diluted with distilled water)
Now, substitute the given values into the formula:
3 M x 0.1 L = M₂ x 0.6 L
Simplifying the equation:
0.3 mol = 0.6 M₂
To find M₂ (final concentration), rearrange the equation:
M₂ = 0.3 mol / 0.6 L
M₂ = 0.5 M
Therefore, the final concentration of the sodium hydroxide solution is 0.5 M.