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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.
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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