To determine the molarity of a solution containing 25 grams of HCl in 150 mL of solution, we need to follow a series of steps. Here's a detailed, step-by-step solution:
1. Find the number of moles of HCl:
- The formula used to convert grams to moles is:
[tex]\[
\text{moles of HCl} = \frac{\text{mass of HCl (in grams)}}{\text{molar mass of HCl (in g/mol)}}
\][/tex]
- Given:
[tex]\[
\text{mass of HCl} = 25 \text{ grams}
\][/tex]
[tex]\[
\text{molar mass of HCl} = 36.46 \text{ g/mol}
\][/tex]
- Therefore, the number of moles of HCl is:
[tex]\[
\text{moles of HCl} = \frac{25 \text{ g}}{36.46 \text{ g/mol}} \approx 0.6857 \text{ moles}
\][/tex]
- The correct setup to find the moles of HCl is:
[tex]\[
25 \text{ g HCl} \times \frac{1 \text{ mol HCl}}{36.46 \text{ g HCl}}
\][/tex]
2. Convert the volume of solution from mL to L:
- The formula to convert milliliters to liters is:
[tex]\[
\text{volume in liters} = \frac{\text{volume in mL}}{1000}
\][/tex]
- Given:
[tex]\[
\text{volume of solution} = 150 \text{ mL}
\][/tex]
- Therefore, the volume in liters is:
[tex]\[
\text{volume in liters} = \frac{150 \text{ mL}}{1000} = 0.15 \text{ L}
\][/tex]
- The correct setup to convert volume is:
[tex]\[
150 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}}
\][/tex]
3. Calculate the molarity of the solution:
- Molarity is defined as the number of moles of solute per liter of solution:
[tex]\[
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
- Given:
[tex]\[
\text{moles of HCl} \approx 0.6857 \text{ moles}
\][/tex]
[tex]\[
\text{volume of solution} = 0.15 \text{ L}
\][/tex]
- Therefore, the molarity of the solution is:
[tex]\[
\text{Molarity} = \frac{0.6857 \text{ moles}}{0.15 \text{ L}} \approx 4.57 \text{ M}
\][/tex]
The molarity of the solution is approximately [tex]\(4.57 \text{ M}\)[/tex].
