Final answer:
To prepare 0.152 L of a 0.50 M CuSO₄ solution from a 2.5 M stock solution, you need 30.4 ml of the stock solution. This was calculated using the dilution equation C₁V₁ = C₂V₂.
Step-by-step explanation:
Calculating the Volume of a Stock Solution Needed for Dilution
To determine how many milliliters (ml) of a 2.5 M CuSO₄ stock solution are needed to prepare 0.152 l of a 0.50 M diluted solution, we use the dilution equation C₁V₁ = C₂V₂, where C₁ and V₁ are the concentration and volume of the stock solution, and C₂ and V₂ are the concentration and volume of the diluted solution, respectively.
First, we substitute the known values into the dilution equation: (2.5 M) x (V₁) = (0.50 M) x (0.152 L). To isolate V₁, we divide both sides by the stock concentration: V₁ = (0.50 M x 0.152 L) / 2.5 M. After calculation, V₁ equals to 0.0304 L, which is 30.4 ml. This means you need 30.4 ml of the 2.5 M CuSO₄ stock solution to make the desired diluted solution.
It's important to note that this method can be adapted to various problems involving dilutions such as finding the volume needed to dilute a different salt or acid solution, which is a fundamental concept in stoichiometry and solution preparation.