A chemist requires 1.5 M hydrochloric acid, HCl, for a series of reactions. The only solution available is 6.0 M HCl. What volume of 6.0 M HCl must be diluted to obtain 5.0 L of 1.5 M HCl?

Strategy First, we need to recognize that this is the dilution of the concentrated solution to prepare the desired one. The underlying concept we must use is that the number of moles of HCl will be the same before and after dilution, and this means we can use Equation 3.3. We know the desired final molarity and final volume, as well as the initial molarity. So we can solve for the needed initial volume.

Equation 3.3.

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M₁ X V₁ = M₁ X Vf (3.3)