Final answer:
The dilution equation, expressed as C₁V₁ = C₂V₂, is used to calculate the new concentration after dilution. It relates the initial and final concentrations and volumes of a solution, allowing one to solve for any unknown variable when the other three are provided.
Step-by-step explanation:
To calculate the new concentration of a solution that has been diluted, you can use the dilution equation, which states that the product of the initial concentration (C₁) and the initial volume (V₁) is equal to the product of the final concentration (C₂) and the final volume (V₂). In mathematical terms, it is expressed as C₁V₁ = C₂V₂. This allows us to calculate any one of the four variables as long as the other three are known.
For example, if you have 100. mL of a 2.0 M solution of HCl and you dilute the solution to a volume of 500. mL, you would use the dilution equation to find the new molarity (M₂) by solving for it: (2.0 M) × (100. mL) = M₂ × (500. mL).
The equation is applicable only when volumes are expressed in the same units and is used to determine either the new concentration (C₂) if the final volume (V₂) is known, or to find the required volume of stock solution (V₁) or diluted solution (V₂) when the desired concentration (C₂) is known.