Let's break down the problem step-by-step to find the number of moles of [tex]\( \text{BaCl}_2 \)[/tex] present in 200 mL of a 0.10 M [tex]\( \text{BaCl}_2 \)[/tex] solution:
1. Understanding Molarity:
- Molarity (M) is defined as the number of moles of solute per liter of solution.
- Therefore,
[tex]\[
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{volume of solution in liters}}
\][/tex]
2. Given Values:
- Volume of the [tex]\( \text{BaCl}_2 \)[/tex] solution ([tex]\( \text{V}_{\text{solution}} \)[/tex]) = 200 mL
- First, we need to convert this volume into liters because the molarity is given in terms of liters.
- There are 1000 mL in 1 liter, so:
[tex]\[
200 \, \text{mL} = \frac{200}{1000} = 0.2 \, \text{L}
\][/tex]
- Molarity of the [tex]\( \text{BaCl}_2 \)[/tex] solution (M) = 0.10 M
3. Calculating Moles of [tex]\( \text{BaCl}_2 \)[/tex]:
- Now, use the molarity formula to find the number of moles of [tex]\( \text{BaCl}_2 \)[/tex]:
[tex]\[
\text{Moles of } \text{BaCl}_2 = \text{Molarity (M)} \times \text{Volume (L)}
\][/tex]
- Plugging in the given values:
[tex]\[
\text{Moles of } \text{BaCl}_2 = 0.10 \, \text{M} \times 0.2 \, \text{L}
\][/tex]
4. Performing the Multiplication:
- Simply multiply the two numbers to get the number of moles:
[tex]\[
\text{Moles of } \text{BaCl}_2 = 0.10 \times 0.2 = 0.020
\][/tex]
Therefore, the number of moles of [tex]\( \text{BaCl}_2 \)[/tex] present in 200 mL of a 0.10 M [tex]\( \text{BaCl}_2 \)[/tex] solution is:
[tex]\[
0.020 \text{ moles}
\][/tex]
