To determine the number of moles of [tex]\( \text{Ba}\left( \text{NO}_3 \right)_2 \)[/tex] in 0.25 liters of a 2.00 M solution, we can use the definition of molarity (M). Molarity is expressed as:
[tex]\[ \text{Molarity} = \frac{\text{moles of solute}}{\text{liters of solution}} \][/tex]
Here, we are given:
- The volume of the solution [tex]\( V = 0.25 \, \text{L} \)[/tex]
- The molarity [tex]\( M = 2.00 \, \text{M} \)[/tex]
The formula to find the number of moles of solute is:
[tex]\[ \text{moles of solute} = \text{Molarity} \times \text{Volume of solution} \][/tex]
Plugging in the given values:
[tex]\[ \text{moles of } \text{Ba}\left( \text{NO}_3 \right)_2 = 2.00 \, \text{M} \times 0.25 \, \text{L} \][/tex]
[tex]\[ \text{moles of } \text{Ba}\left( \text{NO}_3 \right)_2 = 0.50 \, \text{mol} \][/tex]
Therefore, the number of moles of [tex]\( \text{Ba}\left( \text{NO}_3 \right)_2 \)[/tex] in 0.25 liters of a 2.00 M solution is:
[tex]\[ \boxed{0.50 \, \text{mol}} \][/tex]
So, the correct answer is 0.50 mol.
