To determine the mass of [tex]\( \text{NaOH} \)[/tex] needed to make [tex]\( 2.500 \, \text{L} \)[/tex] of a [tex]\( 2.000 \, \text{M} \, \text{NaOH} \)[/tex] solution, we will proceed with the following steps:
1. Understand Molarity: Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
[tex]\[
\text{Molarity (M)} = \frac{\text{moles of solute}}{\text{liters of solution}}
\][/tex]
2. Given Values:
- Molarity (M) = [tex]\( 2.000 \, \text{M} \)[/tex]
- Volume of solution (V) = [tex]\( 2.500 \, \text{L} \)[/tex]
- Molar Mass of [tex]\( \text{NaOH} \)[/tex] = [tex]\( 40.00 \, \text{g/mol} \)[/tex]
3. Calculate the Moles of NaOH Required:
Using the molarity formula, we need to find the number of moles of [tex]\( \text{NaOH} \)[/tex]:
[tex]\[
\text{Moles of NaOH} = \text{Molarity} \times \text{Volume of solution}
\][/tex]
Substituting the given values:
[tex]\[
\text{Moles of NaOH} = 2.000 \, \text{M} \times 2.500 \, \text{L} = 5.000 \, \text{moles}
\][/tex]
4. Convert Moles to Mass:
To find out the mass of [tex]\( \text{NaOH} \)[/tex] required, we need to use the molar mass.
[tex]\[
\text{Mass of NaOH} = \text{Moles of NaOH} \times \text{Molar mass of NaOH}
\][/tex]
Substituting the values:
[tex]\[
\text{Mass of NaOH} = 5.000 \, \text{moles} \times 40.00 \, \text{g/mol} = 200.0 \, \text{g}
\][/tex]
Therefore, the mass of [tex]\( \text{NaOH} \)[/tex] needed to make [tex]\( 2.500 \, \text{L} \)[/tex] of a [tex]\( 2.000 \, \text{M} \)[/tex] solution is [tex]\( 200.0 \, \text{g} \)[/tex].
From the given options, the correct answer is:
[tex]\[
\boxed{200.0 \, \text{g}}
\][/tex]
