Certainly! Let's break down the problem step by step.
1. Understanding Molarity:
Molarity (M) is defined as the number of moles of solute per liter of solution. The formula for molarity is:
[tex]\[
M = \frac{\text{moles of solute}}{\text{liters of solution}}
\][/tex]
We are given:
- Molarity (M) of the [tex]\( \text{NaOH} \)[/tex] solution = 2.000 M
- Volume of solution = 2.500 L
2. Calculate the Moles of NaOH Needed:
Using the molarity formula, we can rearrange it to solve for the moles of [tex]\( \text{NaOH} \)[/tex] required:
[tex]\[
\text{moles of NaOH} = M \times \text{Volume of solution}
\][/tex]
Plugging in the values:
[tex]\[
\text{moles of NaOH} = 2.000 \, \text{M} \times 2.500 \, \text{L}
\][/tex]
[tex]\[
\text{moles of NaOH} = 5.0 \, \text{moles}
\][/tex]
3. Calculate the Mass of NaOH Needed:
To find the mass of [tex]\( \text{NaOH} \)[/tex], we use the molar mass of [tex]\( \text{NaOH} \)[/tex]. The molar mass (molar mass per mole) allows us to convert from moles to grams:
[tex]\[
\text{mass of NaOH} = \text{moles of NaOH} \times \text{molar mass of NaOH}
\][/tex]
We are given:
- Molar mass of [tex]\( \text{NaOH} \)[/tex] = 40.00 g/mol
Now, calculate the mass:
[tex]\[
\text{mass of NaOH} = 5.0 \, \text{moles} \times 40.00 \, \text{g/mol}
\][/tex]
[tex]\[
\text{mass of NaOH} = 200.0 \, \text{grams}
\][/tex]
4. Conclusion:
Therefore, the mass of [tex]\( \text{NaOH} \)[/tex] needed to make 2.500 L of a 2.000 M [tex]\( \text{NaOH} \)[/tex] solution is:
[tex]\[
\boxed{200.0 \, \text{g}}
\][/tex]
Among the given options, the correct answer is:
- [tex]\(0.1250 \, \text{g}\)[/tex]
- [tex]\(5.000 \, \text{g}\)[/tex]
- [tex]\(32.00 \, \text{g}\)[/tex]
- [tex]\(200.0 \, \text{g}\)[/tex]
The correct choice is [tex]\(\boxed{200.0 \, \text{g}}\)[/tex].
