Answer :
To solve the problem of finding the maximum mass of [tex]\(Ag_2S\)[/tex] produced from the reaction, follow these steps:
1. Write down the balanced chemical equation:
[tex]\[
2 \, \text{AgNO}_3 + \text{Na}_2\text{S} \rightarrow \text{Ag}_2\text{S} + 2 \, \text{NaNO}_3
\][/tex]
From the equation, you can see that 1 mole of [tex]\( \text{Na}_2\text{S} \)[/tex] reacts to produce 1 mole of [tex]\( \text{Ag}_2\text{S} \)[/tex].
2. Find the molar masses:
- Molar mass of [tex]\( \text{Na}_2\text{S} \)[/tex] is approximately [tex]\( 78.04 \, \text{g/mol} \)[/tex].
- Molar mass of [tex]\( \text{Ag}_2\text{S} \)[/tex] is approximately [tex]\( 247.80 \, \text{g/mol} \)[/tex].
3. Calculate moles of [tex]\( \text{Na}_2\text{S} \)[/tex]:
Using the given mass of [tex]\( \text{Na}_2\text{S} \)[/tex]:
[tex]\[
\text{moles of Na}_2\text{S} = \frac{\text{mass of Na}_2\text{S}}{\text{molar mass of Na}_2\text{S}} = \frac{45.00 \, \text{g}}{78.04 \, \text{g/mol}} \approx 0.5766 \, \text{moles}
\][/tex]
4. Use stoichiometry to find moles of [tex]\( \text{Ag}_2\text{S} \)[/tex]:
According to the reaction, 1 mole of [tex]\( \text{Na}_2\text{S} \)[/tex] produces 1 mole of [tex]\( \text{Ag}_2\text{S} \)[/tex]. Therefore:
[tex]\[
\text{moles of Ag}_2\text{S} = 0.5766 \, \text{moles}
\][/tex]
5. Calculate the mass of [tex]\( \text{Ag}_2\text{S} \)[/tex]:
Use the moles of [tex]\( \text{Ag}_2\text{S} \)[/tex] to find its mass:
[tex]\[
\text{mass of Ag}_2\text{S} = \text{moles of Ag}_2\text{S} \times \text{molar mass of Ag}_2\text{S} = 0.5766 \, \text{moles} \times 247.80 \, \text{g/mol} \approx 142.89 \, \text{g}
\][/tex]
Therefore, the maximum mass of [tex]\( \text{Ag}_2\text{S} \)[/tex] produced is approximately 142.9 grams. The correct answer to the question is (A) 142.9 g.
1. Write down the balanced chemical equation:
[tex]\[
2 \, \text{AgNO}_3 + \text{Na}_2\text{S} \rightarrow \text{Ag}_2\text{S} + 2 \, \text{NaNO}_3
\][/tex]
From the equation, you can see that 1 mole of [tex]\( \text{Na}_2\text{S} \)[/tex] reacts to produce 1 mole of [tex]\( \text{Ag}_2\text{S} \)[/tex].
2. Find the molar masses:
- Molar mass of [tex]\( \text{Na}_2\text{S} \)[/tex] is approximately [tex]\( 78.04 \, \text{g/mol} \)[/tex].
- Molar mass of [tex]\( \text{Ag}_2\text{S} \)[/tex] is approximately [tex]\( 247.80 \, \text{g/mol} \)[/tex].
3. Calculate moles of [tex]\( \text{Na}_2\text{S} \)[/tex]:
Using the given mass of [tex]\( \text{Na}_2\text{S} \)[/tex]:
[tex]\[
\text{moles of Na}_2\text{S} = \frac{\text{mass of Na}_2\text{S}}{\text{molar mass of Na}_2\text{S}} = \frac{45.00 \, \text{g}}{78.04 \, \text{g/mol}} \approx 0.5766 \, \text{moles}
\][/tex]
4. Use stoichiometry to find moles of [tex]\( \text{Ag}_2\text{S} \)[/tex]:
According to the reaction, 1 mole of [tex]\( \text{Na}_2\text{S} \)[/tex] produces 1 mole of [tex]\( \text{Ag}_2\text{S} \)[/tex]. Therefore:
[tex]\[
\text{moles of Ag}_2\text{S} = 0.5766 \, \text{moles}
\][/tex]
5. Calculate the mass of [tex]\( \text{Ag}_2\text{S} \)[/tex]:
Use the moles of [tex]\( \text{Ag}_2\text{S} \)[/tex] to find its mass:
[tex]\[
\text{mass of Ag}_2\text{S} = \text{moles of Ag}_2\text{S} \times \text{molar mass of Ag}_2\text{S} = 0.5766 \, \text{moles} \times 247.80 \, \text{g/mol} \approx 142.89 \, \text{g}
\][/tex]
Therefore, the maximum mass of [tex]\( \text{Ag}_2\text{S} \)[/tex] produced is approximately 142.9 grams. The correct answer to the question is (A) 142.9 g.