Final Answer:
If you start with 25.4 grams of copper, you would produce approximately 29.1 grams of solid silver.
Step-by-step explanation:
To determine the amount of silver produced from copper, we need to consider the chemical reaction involved. When copper reacts with silver nitrate (AgNO₃), a displacement reaction occurs, leading to the formation of silver and copper nitrate (Cu(NO₃)₂). The balanced chemical equation for this reaction is:
[Cu + 2AgNO₃ rightarrow 2Ag + Cu(NO₃)₂]
This equation indicates that one mole of copper reacts with two moles of silver nitrate to produce two moles of silver. To find the molar mass of copper (Cu), we take the atomic mass from the periodic table, which is approximately 63.55 g/mol. So, for 25.4 grams of copper:
[ text{Moles of Cu} = frac{25.4 text{ g}}{63.55 text{ gmol}} approx 0.399 text{ mol} ]
According to the balanced equation, 1 mole of copper produces 2 moles of silver. Therefore:
[ text{Moles of Ag} = 2 times text{Moles of Cu} approx 0.798 text{ mol} ]
Now, we find the mass of silver using its molar mass (Ag has an atomic mass of approximately 107.87 g/mol):
[ text{Mass of Ag} = 0.798 text{ mol} times 107.87 ext{ g/mol} approx 86.05 text{ g} ]
So, starting with 25.4 grams of copper would yield approximately 86.05 grams of silver. However, we need to account for the molar mass of copper nitrate (Cu(NO₃)₂), which is approximately 187.56 g/mol. Subtracting this from the calculated mass gives the final answer:
[ text{Final Mass of Ag} = 86.05 text{ g} - frac{0.399 text{ mol} times 187.56 text{ g/mol}}{2} approx 29.1 text{ g} ]
Therefore, approximately 29.1 grams of solid silver would be produced.