Question

What is the molarity of sodium ions in a solution prepared by diluting 250. mL of 0.550 M Na2SO4 to 1.25 L? (A) 0.110 M (C) 0.220 M (B) 0.138 M (D) 0.275 M

Answer 1

(C) 0.220 M

Step-by-step explanation:

Given parameters:

volume of the dillutant = 250mL = 0.25L

Molarity of Na₂SO₄ before being diluted = 0.55M

Volume of Na₂SO₄ after dilution = 1.25L

Unknown:

Molarity of Na⁺ ions in the diluted solution

Solution

We can simply adopt the mole concept in solving this dilution problem. During dilution, we intend to reduce the concentration of a particular solution by increasing its volume. Therefore, we have to find the new concentration of the diluted Na₂SO₄. From here, we can be able to find the molarity of the sodium ions in the diluted solution:

Using dilution equation:
`(C_(1) )/(V_(1) )` =
`(C_(2) )/(V_(2) )`

we can solve for the molarity of the diluted solution

C₁ = concentration of the original solution

V₁ = volume of the original solution

V₂ = final volume of the diluted solution

C₂ = final volume

We are solving of C₂:

Making C₂ the subject of the formula gives:

C₂ =
`(C_(1)V_(1) )/(V_(2) )`

Therefore:

C₂ =
`(0.25 x 0.55 )/(1.25 )` = 0.11M

The diluted concentration is now 0.11M

To find the molarity of Na⁺ in Na₂SO₄:

We write the ionic form of the compound in solution:

Na₂SO₄ → 2Na⁺ + SO₄²⁻

In this solution,

1 mole of Na₂SO₄ will produce 2 moles of Na⁺ ions

From 0.11M of Na₂SO₄, we would have (2 x 0.11M) = 0.22M of Na⁺

The molarity of sodium ions will be 0.22M