To determine the molar concentration of a solution containing 16 grams of [tex]\( CH_3OH \)[/tex] (methanol) in 200 milliliters of solution, follow these steps:
1. Determine the number of moles of [tex]\( CH_3OH \)[/tex]:
The molar mass of [tex]\( CH_3OH \)[/tex] is given as 32.04 grams per mole.
The number of moles can be calculated using the formula:
[tex]\[
\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}
\][/tex]
Using the given data, the calculation is:
[tex]\[
\text{moles of } CH_3OH = \frac{16 \text{ g}}{32.04 \text{ g/mol}} \approx 0.4993757802746567 \text{ moles}
\][/tex]
2. Convert the volume of the solution from milliliters to liters:
Since concentration is often expressed in moles per liter (M), you need to convert the volume of the solution to liters:
[tex]\[
\text{volume (L)} = \frac{\text{volume (mL)}}{1000}
\][/tex]
Given that the volume is 200 milliliters,
[tex]\[
\text{volume (L)} = \frac{200 \text{ mL}}{1000} = 0.2 \text{ L}
\][/tex]
3. Calculate the molar concentration:
Molar concentration is defined as the number of moles of solute per liter of solution, expressed as M (molarity):
[tex]\[
\text{Molar concentration} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
Substituting the known values:
[tex]\[
\text{Molar concentration} = \frac{0.4993757802746567 \text{ moles}}{0.2 \text{ L}} \approx 2.4968789013732833 \text{ M}
\][/tex]
Therefore, the molar concentration of the solution is approximately 2.497 M (rounded to three decimal places).
