Sure, let's walk through the solution step by step.
1. Balanced Chemical Equation:
The chemical reaction for the decomposition of sodium chloride (NaCl) can be written as:
[tex]\[
2 \text{NaCl} \rightarrow 2 \text{Na} + \text{Cl}_2
\][/tex]
This equation is balanced as there are 2 sodium (Na) atoms and 2 chlorine (Cl) atoms on both sides of the equation.
2. Given Information:
- Mass of sodium produced: 19.5 grams.
3. Molar Masses:
- Molar mass of Sodium (Na): 22.99 g/mol.
- Molar mass of Chlorine (Cl): 35.45 g/mol.
- Molar mass of Sodium Chloride (NaCl): 22.99 + 35.45 = 58.44 g/mol.
4. Calculate Moles of Sodium (Na) Produced:
We use the molar mass to convert the given mass of sodium to moles:
[tex]\[
\text{Moles of Na produced} = \frac{\text{mass of Na}}{\text{molar mass of Na}} = \frac{19.5 \text{ g}}{22.99 \text{ g/mol}} \approx 0.848 \text{ moles}
\][/tex]
5. Stoichiometric Relationships:
According to the balanced chemical equation, 2 moles of NaCl produce 2 moles of Na and 1 mole of [tex]\( \text{Cl}_2 \)[/tex].
Therefore, the moles of [tex]\( \text{Cl}_2 \)[/tex] produced will be:
[tex]\[
\text{Moles of } \text{Cl}_2 \text{ produced} = \frac{\text{Moles of Na produced}}{2} = \frac{0.848 \text{ moles}}{2} \approx 0.424 \text{ moles}
\][/tex]
6. Calculate the Mass of Chlorine Gas ([tex]\( \text{Cl}_2 \)[/tex]) Produced:
The molar mass of [tex]\( \text{Cl}_2 \)[/tex] is twice the molar mass of a single chlorine atom:
[tex]\[
\text{Molar mass of } \text{Cl}_2 = 2 \times 35.45 \text{ g/mol} = 70.90 \text{ g/mol}
\][/tex]
Hence, the mass of [tex]\( \text{Cl}_2 \)[/tex] produced can be calculated as:
[tex]\[
\text{Mass of } \text{Cl}_2 \text{ produced} = \text{moles of } \text{Cl}_2 \text{ produced} \times \text{molar mass of } \text{Cl}_2 = 0.424 \text{ moles} \times 70.90 \text{ g/mol} \approx 30.07 \text{ grams}
\][/tex]
Thus, approximately 30.07 grams of chlorine gas ([tex]\( \text{Cl}_2 \)[/tex]) are produced when sodium chloride decomposes to produce 19.5 grams of sodium.
