Sure, let's go through the steps in order to determine the mass of sodium chloride that can be created when 0.013 kg of sodium metal are consumed by the reaction.
### Step-by-Step Solution:
1. Convert the mass of sodium from kilograms to grams:
- Given mass of sodium = 0.013 kg.
- Since 1 kg = 1000 g, we convert the mass to grams:
[tex]\[
0.013 \text{ kg} \times 1000 \text{ g/kg} = 13 \text{ g}
\][/tex]
2. Calculate the moles of sodium consumed:
- The molar mass of sodium ([tex]\( \text{Na} \)[/tex]) is [tex]\( 22.99 \)[/tex] g/mol.
- Using the formula:
[tex]\[
\text{Moles of Na} = \frac{\text{Mass of Na}}{\text{Molar mass of Na}}
\][/tex]
- Substitute the values:
[tex]\[
\text{Moles of Na} = \frac{13 \text{ g}}{22.99 \text{ g/mol}} \approx 0.5655 \text{ moles}
\][/tex]
3. Determine the moles of sodium chloride (NaCl) formed:
- According to the chemical equation for the formation of sodium chloride, each mole of sodium reacts with chlorine to form one mole of sodium chloride.
- Therefore, the moles of [tex]\( \text{NaCl} \)[/tex] formed will be equal to the moles of [tex]\( \text{Na} \)[/tex] consumed:
[tex]\[
\text{Moles of NaCl} = 0.5655 \text{ moles}
\][/tex]
4. Calculate the mass of sodium chloride formed:
- The molar mass of sodium chloride ([tex]\( \text{NaCl} \)[/tex]) is calculated as follows:
[tex]\[
\text{Molar mass of NaCl} = \text{Molar mass of Na} + \text{Molar mass of Cl}
\][/tex]
- The molar mass of chlorine ([tex]\( \text{Cl} \)[/tex]) is [tex]\( 35.45 \)[/tex] g/mol.
- So, the molar mass of sodium chloride is:
[tex]\[
22.99 \text{ g/mol} + 35.45 \text{ g/mol} = 58.44 \text{ g/mol}
\][/tex]
- Using the formula:
[tex]\[
\text{Mass of NaCl} = \text{Moles of NaCl} \times \text{Molar mass of NaCl}
\][/tex]
- Substitute the values:
[tex]\[
\text{Mass of NaCl} = 0.5655 \text{ moles} \times 58.44 \text{ g/mol} \approx 33.05 \text{ g}
\][/tex]
### Final Answer:
- The mass of sodium chloride that can be created from [tex]\( 0.013 \)[/tex] kg of sodium metal is approximately [tex]\( 33.05 \)[/tex] grams.
