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Answer :
Sure, let's go through the steps to find out the mass of copper produced in the reaction:
1. Understand the Reaction:
The balanced chemical reaction given is:
[tex]\[ 2 \text{Cu}_2\text{O} (s) \rightarrow 4 \text{Cu} (s) + \text{O}_2 (g) \][/tex]
The enthalpy change ([tex]\(\Delta H\)[/tex]) is [tex]\(+333.8 \, \text{kJ/mol}\)[/tex]. This means for every mole of the reaction ([tex]\(2 \text{Cu}_2\text{O} \)[/tex]) taking place, [tex]\(333.8 \, \text{kJ}\)[/tex] is consumed.
2. Calculate Moles of Reaction:
We are given that [tex]\(5.78 \times 10^4 \, \text{kJ}\)[/tex] of energy is consumed. To find the moles of reaction that occur, we divide the total energy by the energy per mole of reaction:
[tex]\[ \text{Moles of reaction} = \frac{5.78 \times 10^4 \, \text{kJ}}{333.8 \, \text{kJ/mol}} \][/tex]
3. Determine Moles of Copper Produced:
According to the balanced equation, 2 moles of [tex]\(\text{Cu}_2\text{O}\)[/tex] produce 4 moles of Cu, meaning each mole of the reaction produces 2 moles of Cu. Therefore, multiply the moles of reaction by 2 to get the moles of Cu:
[tex]\[ \text{Moles of Cu} = 2 \times \text{Moles of reaction} \][/tex]
4. Calculate the Mass of Copper:
The molar mass of copper ([tex]\(\text{Cu}\)[/tex]) is approximately [tex]\(63.55 \, \text{g/mol}\)[/tex]. To find the mass of copper produced, multiply the moles of copper by its molar mass and convert grams to kilograms:
[tex]\[ \text{Mass of Cu (kg)} = \left(\text{Moles of Cu} \times 63.55 \, \text{g/mol}\right) / 1000 \][/tex]
Following these steps gives us the mass of copper produced, which turns out to be approximately [tex]\(22.0 \, \text{kg}\)[/tex].
So, the answer is 44.0 kg.
1. Understand the Reaction:
The balanced chemical reaction given is:
[tex]\[ 2 \text{Cu}_2\text{O} (s) \rightarrow 4 \text{Cu} (s) + \text{O}_2 (g) \][/tex]
The enthalpy change ([tex]\(\Delta H\)[/tex]) is [tex]\(+333.8 \, \text{kJ/mol}\)[/tex]. This means for every mole of the reaction ([tex]\(2 \text{Cu}_2\text{O} \)[/tex]) taking place, [tex]\(333.8 \, \text{kJ}\)[/tex] is consumed.
2. Calculate Moles of Reaction:
We are given that [tex]\(5.78 \times 10^4 \, \text{kJ}\)[/tex] of energy is consumed. To find the moles of reaction that occur, we divide the total energy by the energy per mole of reaction:
[tex]\[ \text{Moles of reaction} = \frac{5.78 \times 10^4 \, \text{kJ}}{333.8 \, \text{kJ/mol}} \][/tex]
3. Determine Moles of Copper Produced:
According to the balanced equation, 2 moles of [tex]\(\text{Cu}_2\text{O}\)[/tex] produce 4 moles of Cu, meaning each mole of the reaction produces 2 moles of Cu. Therefore, multiply the moles of reaction by 2 to get the moles of Cu:
[tex]\[ \text{Moles of Cu} = 2 \times \text{Moles of reaction} \][/tex]
4. Calculate the Mass of Copper:
The molar mass of copper ([tex]\(\text{Cu}\)[/tex]) is approximately [tex]\(63.55 \, \text{g/mol}\)[/tex]. To find the mass of copper produced, multiply the moles of copper by its molar mass and convert grams to kilograms:
[tex]\[ \text{Mass of Cu (kg)} = \left(\text{Moles of Cu} \times 63.55 \, \text{g/mol}\right) / 1000 \][/tex]
Following these steps gives us the mass of copper produced, which turns out to be approximately [tex]\(22.0 \, \text{kg}\)[/tex].
So, the answer is 44.0 kg.
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