What is the mass of sodium chloride produced when a mass of sodium is reacted with...

1. Identify the balanced chemical equation: The problem provides the balanced chemical equation for the reaction between sodium and chlorine to produce sodium chloride: $$2Na_{(s)} + Cl_{2(g)} \rightarrow 2NaCl_{(s)}$$
2. Determine the molar masses of the reactants and product: We need the molar masses of sodium (Na), chlorine (Cl), and sodium chloride (NaCl).
- Molar mass of Na = 22.99 g/mol
- Molar mass of Cl = 35.45 g/mol
- Molar mass of NaCl = Molar mass of Na + Molar mass of Cl = 22.99 g/mol + 35.45 g/mol = 58.44 g/mol
3. Calculate the moles of each reactant: Convert the given masses of sodium and chlorine into moles using their respective molar masses.
- Moles of Na = $\frac{\text{mass of Na}}{\text{molar mass of Na}} = \frac{8.3 \text{ g}}{22.99 \text{ g/mol}} \approx 0.361 \text{ mol}$ Na
- Moles of Cl$_2$ = $\frac{\text{mass of Cl}_2}{\text{molar mass of Cl}_2} = \frac{4.5 \text{ g}}{2 \times 35.45 \text{ g/mol}} = \frac{4.5 \text{ g}}{70.90 \text{ g/mol}} \approx 0.0635 \text{ mol}}$ Cl$_2$
4. Identify the limiting reactant: The limiting reactant is the one that is completely consumed first and thus limits the amount of product formed. We compare the mole ratio of reactants to the stoichiometric ratio from the balanced equation.
- From the equation, 2 moles of Na react with 1 mole of Cl$_2$. The ratio is 2:1.
- If all 0.361 mol of Na reacted, it would require $\frac{0.361 \text{ mol Na}}{2} = 0.1805 \text{ mol}}$ Cl$_2$. We only have 0.0635 mol of Cl$_2$, so Cl$_2$ is the limiting reactant.
- Alternatively, if all 0.0635 mol of Cl$_2$ reacted, it would require $0.0635 \text{ mol Cl}_2 \times \frac{2 \text{ mol Na}}{1 \text{ mol Cl}_2} = 0.127 \text{ mol}}$ Na. We have 0.361 mol of Na, which is more than enough. Therefore, Cl$_2$ is the limiting reactant.
5. Calculate the moles of sodium chloride produced: Use the moles of the limiting reactant (Cl$_2$) and the stoichiometry of the reaction to find the moles of NaCl produced.
- From the equation, 1 mole of Cl$_2$ produces 2 moles of NaCl.
- Moles of NaCl produced = $0.0635 \text{ mol Cl}_2 \times \frac{2 \text{ mol NaCl}}{1 \text{ mol Cl}_2} = 0.127 \text{ mol}}$ NaCl
6. Calculate the mass of sodium chloride produced: Convert the moles of NaCl to grams using its molar mass.
- Mass of NaCl = Moles of NaCl $\times$ Molar mass of NaCl
- Mass of NaCl = $0.127 \text{ mol} \times 58.44 \text{ g/mol} \approx 7.42 \text{ g}}$ NaCl
7. Compare with the given options: The calculated mass of sodium chloride is approximately 7.42 g. Looking at the options, 7.4 g NaCl is the closest value.