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The general requirement of simultaneous (and often implied localized) oxidation and reduction is based on the principle of no accumulation of excess or deficit of electrons. But this can be managed on different places as well, if charge exchange is managed by other means, like by wire in context of electrochemical cells and circuits.

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

One can this way

$$\ce{red1 + ox2 -> ox1 + red2}$$

avoid formal half-reactions like

\begin{align} \ce{red1 &->[anode] ox1 + n e-}\\ \ce{ox2 + n e- &->[cathode] red2} \end{align}

that are generally more illustrative, unless one has any understanding problem with them.

Taking electrons away is oxidation. Providing electrons is reduction. As both happen at different places, oxidation and reduction occur separately.

The general requirement of simultaneous (and often implied localized) oxidation and reduction is based on the principle of no accumulation of excess or deficit of electrons. But this can be managed on different places as well, if charge exchange is managed by other means, like by wire in context of electrochemical cells and circuits.

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

One can this way

$$\ce{red1 + ox2 -> ox1 + red2}$$

avoid formal half-reactions like

\begin{align} \ce{red1 &->[anode] ox1 + n e-}\\ \ce{ox2 + n e- &->[cathode] red2} \end{align}

that are generally more illustrative, unless one has any understanding problem with them.

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

One can this way

$$\ce{red1 + ox2 -> ox1 + red2}$$

avoid formal half-reactions like

\begin{align} \ce{red1 &->[anode] ox1 + n e-}\\ \ce{ox2 + n e- &->[cathode] red2} \end{align}

The general requirement of simultaneous (and often implied localized) oxidation and reduction is based on the principle of no accumulation of excess or deficit of electrons. But this can be managed on different places as well, if charge exchange is managed by other means, like by wire in context of electrochemical cells and circuits.

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

One can this way

$$\ce{red1 + ox2 -> ox1 + red2}$$

avoid formal half-reactions like

\begin{align} \ce{red1 &->[anode] ox1 + n e-}\\ \ce{ox2 + n e- &->[cathode] red2} \end{align}

that are generally more illustrative, unless one has any understanding problem with them.

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

For the example of the Daniell cell $\ce{Zn|ZnSO4||CuSO4|Cu}$, it can be separated in 3 processes, each being a very formal redox reaction:

\begin{align} \ce{Zn + anode &-> Zn^2+ + anode^2-}\\ \ce{Cu^2+ + cathode &-> Cu + cathode^2+}\\ \ce{anode^2- + cathode^2+ &->[via the wire] anode + cathode} \end{align}

One can this way

$$\ce{red1 + ox2 -> ox1 + red2}$$

avoid formal half-reactions like

\begin{align} \ce{red1 &->[anode] ox1 + n e-}\\ \ce{ox2 + n e- &->[cathode] red2} \end{align}