Number of moles of MnO4- getting reduced to Mn2+ under acidic condition by 4.517 x 10^24 electrons is:
Understand the Problem
The question is asking for the number of moles of MnO4- that are reduced to Mn2+ under acidic conditions when a specific number of electrons (4.517 x 10^24) are involved. This requires understanding the relationship between moles of electrons and moles of the compound in a redox reaction.
Answer
The number of moles of $\text{MnO}_4^-$ reduced to $\text{Mn}^{2+}$ is $1.5 \text{ moles}$.
Answer for screen readers
The number of moles of $\text{MnO}_4^-$ getting reduced to $\text{Mn}^{2+}$ is $1.5 \text{ moles}$.
Steps to Solve
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Determine the charge transfer in the reaction
In the reduction of permanganate ion ($\text{MnO}_4^-$) to manganese ion ($\text{Mn}^{2+}$) under acidic conditions, the reaction involves the transfer of 5 electrons per mole of $\text{MnO}_4^-$.
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Calculate the number of moles of electrons
Given the total number of electrons is $4.517 \times 10^{24}$, we use Avogadro's number (approximately $6.022 \times 10^{23}$) to convert electrons to moles:
$$ \text{moles of electrons} = \frac{4.517 \times 10^{24} \text{ electrons}}{6.022 \times 10^{23} \text{ electrons/mole}} $$
Calculating the above gives:
$$ \text{moles of electrons} \approx 7.48 \text{ moles} $$
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Determine the number of moles of MnO4- reduced
Since 5 moles of electrons are required for every mole of $\text{MnO}_4^-$ reduced,
$$ \text{moles of } \text{MnO}_4^- = \frac{7.48 \text{ moles of electrons}}{5 \text{ moles of electrons/mole of } \text{MnO}_4^-} $$
Performing this calculation gives:
$$ \text{moles of } \text{MnO}_4^- \approx 1.496 \text{ moles} $$
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Round the result
Since we want the final answer in whole or half moles, we round $1.496 \text{ moles}$ to $1.5 \text{ moles}$.
The number of moles of $\text{MnO}_4^-$ getting reduced to $\text{Mn}^{2+}$ is $1.5 \text{ moles}$.
More Information
The reduction of permanganate ion to manganese ion is a common reaction in redox chemistry, particularly in analytical chemistry for titrations. The stoichiometry must be carefully understood to make accurate calculations of reactants and products.
Tips
Common mistakes include:
- Not using the correct number of moles of electrons required per mole of $\text{MnO}_4^-$ (which is 5).
- Failing to correctly convert between number of electrons and moles using Avogadro's number.
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