To determine the total volume in milliliters of water a chemist should add to prepare a 0.200 M aqueous solution with 30.2 grams of NaCl, let's go through the following steps:
1. Determine the number of moles of NaCl:
The mass of NaCl provided is 30.2 grams, and the molar mass of NaCl is 58.44 g/mol. We can calculate the number of moles of NaCl by dividing the mass by the molar mass:
[tex]\[
\text{Number of moles of NaCl} = \frac{\text{mass of NaCl}}{\text{molar mass of NaCl}} = \frac{30.2 \, \text{grams}}{58.44 \, \text{g/mol}}
\][/tex]
After performing the division:
[tex]\[
\text{Number of moles of NaCl} \approx 0.5168 \, \text{moles}
\][/tex]
2. Calculate the volume of the solution required:
Molarity (M) is defined as the number of moles of solute divided by the volume of the solution in liters. Re-arranging the equation to solve for volume:
[tex]\[
\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
So,
[tex]\[
\text{Volume of solution in liters} = \frac{\text{moles of solute}}{\text{Molarity}} = \frac{0.5168 \, \text{moles}}{0.200 \, \text{M}}
\][/tex]
After performing the division:
[tex]\[
\text{Volume of solution} \approx 2.584 \, \text{liters}
\][/tex]
3. Convert the volume from liters to milliliters:
There are 1000 milliliters in 1 liter. To convert the volume from liters to milliliters, we multiply by 1000:
[tex]\[
\text{Volume of solution in milliliters} = 2.584 \, \text{liters} \times 1000 \, \frac{\text{milliliters}}{\text{liters}}
\][/tex]
After performing the multiplication:
[tex]\[
\text{Volume of solution} \approx 2584 \, \text{milliliters}
\][/tex]
Therefore, the chemist should add approximately 2584 milliliters of water to prepare the 0.200 M aqueous solution with 30.2 grams of NaCl.
