To calculate the concentration of the resulting sodium hydroxide (NaOH) solution, we will follow these steps:
1. Determine the moles of sodium (Na):
- Given mass of sodium (Na): 1.15 grams
- Molar mass of sodium (Na): 22.99 g/mol
The number of moles of sodium (Na) is calculated using the formula:
[tex]\[
\text{moles of Na} = \frac{\text{mass of Na}}{\text{molar mass of Na}}
\][/tex]
Substituting the given values:
[tex]\[
\text{moles of Na} = \frac{1.15 \text{ g}}{22.99 \text{ g/mol}} \approx 0.050022 \text{ mol}
\][/tex]
2. Determine the moles of sodium hydroxide (NaOH) formed:
- The balanced chemical equation is:
[tex]\[
2 \text{Na} (s) + 2 \text{H}_2\text{O} (l) \rightarrow 2 \text{NaOH} (aq) + \text{H}_2 (g)
\][/tex]
- From the equation, 2 moles of Na produce 2 moles of NaOH. Thus, the moles of NaOH formed is equal to the moles of Na reacted.
Therefore, the moles of NaOH formed:
[tex]\[
\text{moles of NaOH} = \text{moles of Na} \approx 0.050022 \text{ mol}
\][/tex]
3. Convert the solution volume to dm³:
- Given volume of solution: 250 cm³ (which is the same as 250 mL)
- To convert cm³ to dm³:
[tex]\[
\text{volume in dm³} = \frac{\text{volume in cm³}}{1000} = \frac{250}{1000} = 0.250 \text{ dm³}
\][/tex]
4. Calculate the concentration of NaOH in mol/dm³:
- Concentration is given by the formula:
[tex]\[
\text{concentration} = \frac{\text{moles of solute}}{\text{volume of solution in dm³}}
\][/tex]
Substituting the values obtained:
[tex]\[
\text{concentration of NaOH} = \frac{0.050022 \text{ mol}}{0.250 \text{ dm³}} \approx 0.2001 \text{ mol/dm³}
\][/tex]
Therefore, the concentration of the resulting sodium hydroxide solution is approximately 0.2001 mol/dm³.
