- Convert the mass of Na to moles: \(n_{\text{Na}} = \frac{35.0\text{ g}}{22.99\text{ g/mol}} \approx 1.5224\text{ moles}\).
- Determine the moles of \(\text{Cl}_2\) needed using the 2:1 stoichiometric ratio: \(n_{\text{Cl}_2} = \frac{1.5224\text{ moles}}{2} \approx 0.7612\text{ moles}\).
- Convert the moles of \(\text{Cl}_2\) to mass: \(53.969\text{ g}\).
- Round the result to three significant figures: \(\boxed{54.0\text{ g}}\).
Explanation
- Analyzing the chemical reaction and data
The balanced chemical equation for the reaction between sodium metal and chlorine gas is:
\[2\text{Na} + \text{Cl}_2 \rightarrow 2\text{NaCl}\]
This equation tells us that 2 moles of sodium (Na) react with 1 mole of chlorine gas (\(\text{Cl}_2\)) to form 2 moles of sodium chloride (NaCl). We are given an initial mass of \(35.0\text{ g}\) of Na and need to determine the mass of \(\text{Cl}_2\) required for a complete reaction. To solve this, we will use the molar masses of Na (\(22.99\text{ g/mol}\)) and \(\text{Cl}_2\) (\(70.90\text{ g/mol}\)). Since the initial mass is given with three significant figures (\(35.0\text{ g}\)), our final answer must also be expressed to three significant figures.
- Calculating the required mass of chlorine
First, we calculate the number of moles of sodium that we are starting with:
\[n_{\text{Na}} = \frac{\text{mass}_{\text{Na}}}{\text{Molar mass}_{\text{Na}}} = \frac{35.0\text{ g}}{22.99\text{ g/mol}} \approx 1.5224\text{ moles of Na}\]
Next, we use the stoichiometry of the balanced equation, which indicates that the required amount of \(\text{Cl}_2\) is half the number of moles of Na:
\[n_{\text{Cl}_2} = \frac{1}{2} \times n_{\text{Na}} = \frac{1}{2} \times 1.5224\text{ moles} \approx 0.7612\text{ moles of Cl}_2\]
Finally, we convert these moles of chlorine gas into grams using its molar mass:
\[\text{mass}_{\text{Cl}_2} = n_{\text{Cl}_2} \times \text{Molar mass}_{\text{Cl}_2} = 0.7612\text{ moles} \times 70.90\text{ g/mol} \approx 53.969\text{ g}\]
Rounding to three significant figures as required by the initial data, we get \(54.0\text{ g}\).
Examples
In industrial processes like the chlor-alkali process, accurately measuring the amounts of reactants is crucial. When a chemical plant needs to produce salt, calculating the exact amount of chlorine required for a known mass of sodium ensures efficiency, reduces waste, and maintains safety standards. Understanding these stoichiometric relationships is foundational for engineering, pharmacology, and material science, where precision in chemical proportions determines the quality and success of the final product.