Standard EMF of a Cell from Standard Electrode Potentials

With every electrode's standard reduction potential tabulated against the common SHE reference, the standard EMF of any galvanic cell formed from any two of those electrodes can be predicted directly, without ever physically constructing the cell.

The rule is: $E^{\circ}_{cell} = E^{\circ}_{cathode} - E^{\circ}_{anode}$ where $E^{\circ}_{cathode}$ and $E^{\circ}_{anode}$ are both taken directly from the standard reduction-potential table, with no sign changes. The electrode with the higher (more positive, or less negative) tabulated value is reduced and is therefore the cathode; the electrode with the lower value is oxidized and is therefore the anode — the calculation itself tells you which electrode plays which role, so the roles do not need to be assumed in advance.

For the Daniell cell, comparing $E^{\circ}(\text{Cu}^{2+}/\text{Cu}) = +0.34\ \text{V}$ against $E^{\circ}(\text{Zn}^{2+}/\text{Zn}) = -0.76\ \text{V}$, copper has the higher value and is the cathode, zinc has the lower value and is the anode, giving $E^{\circ}_{cell} = 0.34 - (-0.76) = 1.10\ \text{V}$. A positive $E^{\circ}_{cell}$ confirms that the reaction, as identified (copper reduced, zinc oxidized), is thermodynamically spontaneous under standard conditions; had the calculation instead produced a negative value for some proposed pairing/direction, that would signal the reverse reaction is the spontaneous one. …