Suppose you are working with a NaOH stock solution but you need a solution with a lower concentration for your experiment. Calculate the volume of the 1.224 M stock NaOH solution needed to prepare 250.0 mL of 0.1281 M dilute NaOH solution.

Respuesta :

Answer: The volume of the 1.224 M NaOH solution needed is 26.16 mL

Explanation:

In order to prepare the dilute NaOH solution, solvent is added to a given amount of the NaOH stock solution up to a final volume of 250.0 mL.

Since only solvent is added, the amount of the solute, NaOH, in the dilute solution is the same as in the volume taken from the stock solution.

Molarity (M) is calculated from the following equation:

M = n ÷ V

where n is the number of moles of the solute in the solution, and V is the volume of the solution.

Accordingly, the number of moles of the solute is given by

n = M x V

Now, let's designate the stock NaOH solution and the dilute solution as (1) and (2), respectively . The number of moles of NaOH in each of these solutions is:

n (1) = M (1) x V (1)

n (2) = M (2) x V (2)

As the amount of NaOH in the dilute solution is the same as in the volume taken from the stock solution,

n (1) = n (2)

and

M (1) x V (1) = M (2) x V (2)

For the stock solution, M (1) = 1.244 M, and V (1) is the volume needed. For the dilute solution, M (2) = 0,1281 M, and V (2) = 250.0 mL.

The volume of the stock solution needed, V (1), is calculated as follows:

V (1) = M (2) x V (2) ÷ M (1)

V (1) = 0.1281 M x 250.0 mL ÷ 1.224 M

V (1) = 26.16 mL

The volume of the 1.224 M NaOH solution needed is 26.16 mL.

The volume of 1.224 M stock NaOH solution needed to prepare 250.0 mL of 0.1281 M dilute NaOH solution is 26.16 mL

From the question given above, the following data were obtained:

Molarity of stock solution (M₁) = 1.224 M

Volume of diluted solution (V₂) = 250 mL

Molarity of diluted solution (M₂) = 0.1281 M

Volume of stock solution needed (V₁) =?

The volume of the stock solution needed can be obtained as illustrated below:

M₁V₁ = M₂V₂

1.224 × V₁ = 0.1281 × 250

1.224 × V₁ = 32.025

Divide both side by 1.224

V₁ = 32.025 / 1.224

V₁ = 26.16 mL

Thus, volume of the stock solution needed to prepare the solution is 26.16 mL

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