To find out how many moles of [tex]\( Ba(NO_3)_2 \)[/tex] are in 0.25 L of a 2.00 M [tex]\( Ba(NO_3)_2 \)[/tex] solution, we need to use the formula for molarity, which is defined as:
[tex]\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Given:
- Molarity ([tex]\(M\)[/tex]) of the solution is 2.00 M
- Volume ([tex]\(V\)[/tex]) of the solution is 0.25 L
We can rearrange the formula to solve for the moles of solute:
[tex]\[ \text{moles of solute} = \text{Molarity} \times \text{liters of solution} \][/tex]
Plugging in the given values:
[tex]\[ \text{moles of solute} = 2.00 \, \text{M} \times 0.25 \, \text{L} \][/tex]
[tex]\[ \text{moles of solute} = 0.50 \, \text{moles} \][/tex]
Thus, there are [tex]\(0.50\)[/tex] moles of [tex]\( Ba(NO_3)_2 \)[/tex] in the 0.25 L of the 2.00 M [tex]\( Ba(NO_3)_2 \)[/tex] solution.
Therefore, the correct answer is [tex]\( \boxed{0.50 \, \text{mol}} \)[/tex].
