To solve the problem, we need to determine the number of moles of [tex]\( \text{BaCl}_2 \)[/tex] present in a [tex]\( 200 \, \text{mL} \)[/tex] solution of [tex]\( 0.10 \, \text{M} \text{BaCl}_2 \)[/tex].
Let's go through the calculations step-by-step:
1. Convert Volume to Liters:
The volume given is [tex]\( 200 \, \text{mL} \)[/tex]. We need to convert this volume from milliliters (mL) to liters (L) because molarity (M) is defined in terms of liters.
[tex]\[
\text{Volume of } \text{BaCl}_2 \text{ solution} = 200 \, \text{mL} = \frac{200}{1000} \, \text{L} = 0.2 \, \text{L}
\][/tex]
2. Calculate Moles of [tex]\(\text{BaCl}_2\)[/tex]:
Molarity (M) is defined as the number of moles of solute per liter of solution. Therefore, to find the moles of [tex]\( \text{BaCl}_2 \)[/tex], we use the formula:
[tex]\[
\text{Moles of } \text{BaCl}_2 = \text{Molarity} \times \text{Volume (in L)}
\][/tex]
Given the molarity of [tex]\( \text{BaCl}_2 \)[/tex] is [tex]\( 0.10 \, \text{M} \)[/tex]:
[tex]\[
\text{Moles of } \text{BaCl}_2 = 0.10 \, \text{M} \times 0.2 \, \text{L} = 0.02 \, \text{moles}
\][/tex]
Therefore, there are [tex]\( 0.02 \)[/tex] moles of [tex]\(\text{BaCl}_2\)[/tex] present in [tex]\( 200 \, \text{mL} \)[/tex] of [tex]\( 0.10 \, \text{M} \text{BaCl}_2\)[/tex].
