Question

2.0 L of a 1.6 M solution is diluted to a total volume of 16.0 L. What is the new molarity

Answer 1

Here we have a dilution problem. Dilution means to add more solvent to a solution without adding more solute.

From a dilution we know that the initial concentration in mols will be equal to the final concentration in mols of the substance.

mols of solute in initial solution (before dilution) = mols of solute in final solution (after dilution)

We know that mols of solute equals molarity times the volume (M.V), so, we can substitute the above equation:

M₁V₁ = M₂V₂

This equation is known as dilution equation.

Knowing that initial molarity of solution is 1.6 M (M₁), initial volume is 2.0 L (V₁) and final volume is 16.0 L (V₂), we can find new molarity of solution.

We substitute for values:

1.6 M x 2.0 L = M₂ x 16.0 L

Rearranging equation: M₂ = M₁V₁ / V₂

M₂ = 1.6 M x 2.0 L / 16.0 L

M₂ = 0.2 M

If we make the relation, to prove we did right calculations, we can see that mols of solute before dilution are equal to mols of solute after dilution.

M₁V₁ = M₂V₂ ------>   1.6 M x 2.0 L = 0.2 M x 16.0 L -------> 3.2 mols of solute before dilution= 3.2 mols of solute after dilution.