Sure, let's solve the problem step-by-step to find the concentration of the unknown NaOH.
Given Values:
- Volume of hydrochloric acid (HCl), [tex]\( V_{\text{HCl}} = 10.0 \)[/tex] mL
- Molarity of HCl, [tex]\( M_{\text{HCl}} = 1.00 \)[/tex] M
- Volume of sodium hydroxide (NaOH), [tex]\( V_{\text{NaOH}} = 25.0 \)[/tex] mL
- We need to find the molarity of NaOH, [tex]\( M_{\text{NaOH}} \)[/tex].
Chemical Equation:
[tex]\[ \text{HCl} + \text{NaOH} \rightarrow \text{NaCl} + \text{H}_2\text{O} \][/tex]
This equation tells us that HCl and NaOH react in a 1:1 molar ratio.
Step-by-Step Solution:
1. Identify the titration formula:
When a solution of known concentration (HCl) is used to determine the concentration of another solution (NaOH), we use the titration formula:
[tex]\[
M_1 \times V_1 = M_2 \times V_2
\][/tex]
Where:
[tex]\( M_1 \)[/tex] = Molarity of HCl
[tex]\( V_1 \)[/tex] = Volume of HCl
[tex]\( M_2 \)[/tex] = Molarity of NaOH
[tex]\( V_2 \)[/tex] = Volume of NaOH
2. Substitute the given values into the titration formula:
[tex]\[
(1.00 \, \text{M}) \times (10.0 \, \text{mL}) = M_{\text{NaOH}} \times (25.0 \, \text{mL})
\][/tex]
3. Calculate the unknown concentration:
[tex]\[
10.0 \, \text{M} \cdot \text{mL} = M_{\text{NaOH}} \times 25.0 \, \text{mL}
\][/tex]
[tex]\[
M_{\text{NaOH}} = \frac{10.0 \, \text{M} \cdot \text{mL}}{25.0 \, \text{mL}}
\][/tex]
[tex]\[
M_{\text{NaOH}} = \frac{10.0}{25.0}
\][/tex]
[tex]\[
M_{\text{NaOH}} = 0.4 \, \text{M}
\][/tex]
So, the concentration of the unknown NaOH is [tex]\( 0.4 \, \text{M} \)[/tex].
The correct answer is:
[tex]\[ \boxed{0.4 \, \text{M}} \][/tex]
