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Question 25

Which is the best way to prepare 500 mL of a 2.00 M solution of aqueous [tex]H_2SO_4[/tex] from deionized water (density [tex]= 1.00 \, g \cdot mL^{-1}[/tex]) and concentrated [tex]H_2SO_4[/tex] (density [tex]= 1.84 \, g \cdot mL^{-1}[/tex])?

A. Weigh 98.1 g concentrated sulfuric acid into a 500-mL volumetric flask, slowly add deionized water to the mark, and mix.

[tex]

\begin{array}{l}

n_{H_2SO_4} = 1 \, \text{mol} \rightarrow m_{H_2SO_4} = 1.98 \times 98 \, g = 98 \, g \\

V_{H_2SO_4} = \frac{m}{d} = \frac{98}{1.84} = 53.261 \, mL \\

\rightarrow V_{H_2O} = 500 - 53.261 = 446.7 \, mL

\end{array}

[/tex]

Answer :

To solve this problem, we need to prepare a 500 mL of 2.00 M solution of sulfuric acid (H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]) using deionized water and concentrated sulfuric acid. Here is a step-by-step solution:

1. Determine the desired amount of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] in moles:

The target molarity (M) and volume (V) of the solution are given:
- Target Molarity (M) = 2.00 M
- Final Volume (V) = 500 mL = 0.500 L (since 1 L = 1000 mL)

Using the formula:
[tex]\[
\text{Moles of H}_2\text{SO}_4 \text{ needed} = \text{Molarity} \times \text{Volume}
\][/tex]
[tex]\[
\text{Moles of H}_2\text{SO}_4 \text{ needed} = 2.00\, \text{M} \times 0.500\, \text{L} = 1.00\, \text{mol}
\][/tex]

2. Calculate the mass of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] required:

The molecular mass of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] is:
- Molecular Mass of H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] = 98.1 g/mol

Using the formula:
[tex]\[
\text{Mass of H}_2\text{SO}_4 \text{ needed} = \text{Moles of H}_2\text{SO}_4 \times \text{Molecular Mass}
\][/tex]
[tex]\[
\text{Mass of H}_2\text{SO}_4 \text{ needed} = 1.00\, \text{mol} \times 98.1\, \text{g/mol} = 98.1\, \text{g}
\][/tex]

3. Determine the volume of concentrated H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex] required:

Given the density of concentrated H[tex]\(_2\)[/tex]SO[tex]\(_4\)[/tex]:
- Density = 1.84 g/mL

Using the formula:
[tex]\[
\text{Volume of concentrated H}_2\text{SO}_4 = \frac{\text{Mass of H}_2\text{SO}_4}{\text{Density}}
\][/tex]
[tex]\[
\text{Volume of concentrated H}_2\text{SO}_4 = \frac{98.1\, \text{g}}{1.84\, \text{g/mL}} = 53.315217391304344\, \text{mL}
\][/tex]

4. Calculate the volume of deionized water to be added:

The total solution volume needed is 500 mL. Therefore:
[tex]\[
\text{Volume of deionized water} = \text{Total volume} - \text{Volume of concentrated H}_2\text{SO}_4
\][/tex]
[tex]\[
\text{Volume of deionized water} = 500\, \text{mL} - 53.315217391304344\, \text{mL} = 446.6847826086956\, \text{mL}
\][/tex]

Based on these calculations, the preparation procedure is as follows:

- Weigh 98.1 g of concentrated sulfuric acid.
- Slowly add this to a 500 mL volumetric flask.
- Carefully add deionized water to the mark (to make up the total volume to 500 mL).
- Mix the solution thoroughly.

Thus, this confirms the steps laid out in option A.

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