To prepare the solutions and determine the moles of each substance involved, let's follow a step-by-step approach:
### Step 1: Understand the Given Data
- Volume of NaOH solution ( [tex]\( V_{NaOH} \)[/tex] ): [tex]\( 200 \)[/tex] mL
- Concentration of NaOH solution ( [tex]\( C_{NaOH} \)[/tex] ): [tex]\( 1.0 \)[/tex] M
- Volume of acetic acid solution ( [tex]\( V_{AceticAcid} \)[/tex] ): [tex]\( 200.5 \)[/tex] mL
- Concentration of acetic acid solution ( [tex]\( C_{AceticAcid} \)[/tex] ): [tex]\( 1.0 \)[/tex] M
### Step 2: Convert Volumes from mL to Liters
> Remember, [tex]\( 1 \)[/tex] mL = [tex]\( 0.001 \)[/tex] L, so we will convert as follows:
- [tex]\( V_{NaOH} = 200 \)[/tex] mL [tex]\(=\frac{200}{1000}= 0.2 \)[/tex] L
- [tex]\( V_{AceticAcid} = 200.5 \)[/tex] mL [tex]\( =\frac{200.5}{1000}= 0.2005 \)[/tex] L
### Step 3: Calculate the Moles of NaOH
To find the moles of NaOH, use the formula:
[tex]\[ \text{Moles of NaOH} = \text{Volume of NaOH (L)} \times \text{Concentration of NaOH (M)} \][/tex]
[tex]\[ \text{Moles of NaOH} = 0.2 \, \text{L} \times 1.0 \, \text{M} \][/tex]
[tex]\[ \text{Moles of NaOH} = 0.2 \][/tex]
### Step 4: Calculate the Moles of Acetic Acid
To find the moles of acetic acid, use the formula:
[tex]\[ \text{Moles of Acetic Acid} = \text{Volume of Acetic Acid (L)} \times \text{Concentration of Acetic Acid (M)} \][/tex]
[tex]\[ \text{Moles of Acetic Acid} = 0.2005 \, \text{L} \times 1.0 \, \text{M} \][/tex]
[tex]\[ \text{Moles of Acetic Acid} = 0.2005 \][/tex]
### Summary
After going through the calculations:
- The moles of NaOH in [tex]\( 200 \)[/tex] mL of [tex]\( 1.0 \)[/tex] M NaOH solution are [tex]\( 0.2 \)[/tex].
- The moles of acetic acid in [tex]\( 200.5 \)[/tex] mL of [tex]\( 1.0 \)[/tex] M acetic acid solution are [tex]\( 0.2005 \)[/tex].
Thus, you have [tex]\( 0.2 \)[/tex] moles of NaOH and [tex]\( 0.2005 \)[/tex] moles of acetic acid.
