Answer
Reactions (a) and (d) occur spontaneously at standard conditions.
Work Step by Step
The standard reduction potentials of species involved in a reaction are used to predict the spontaneity of reactions under standard conditions.
The species with higher reduction potential values act as good oxidizing agents and get reduced
(a) $ Ca^{2+}(aq) → Ca_{(s)} $ $ E^{\circ} = -2.87 V $
$ Cd^{2+}(aq) → Cd_{(s)} $ $ E^{\circ} = -0.40 V $
So in this reaction $ Cd^{2+}(aq)$ is the oxidizing agent and itself gets reduced as given in the equation. So it is spontaneous.
(b)$ Br_{2(g)} → Br^{-}(aq)$ $ E^{\circ} = +1.07V $
$ Sn^{2+}(aq) → Sn{(s)} $ $ E^{\circ} = -0.14 V $
Here $ Br_{2(g)}$ is the oxidizing agent but in the reaction this is not the case, so this reaction is not possible.
(c) $ Ag^{+}(aq) → Ag_{(s)} $ $ E^{\circ} = +0.80 V $
$ Ni^{2+}(aq) → Ni_{(s)} $ $ E^{\circ} =-0.25 V $
Here $ Ag^{+}(aq)$ is the oxidizing agent but in the reaction it's not, so this reaction is not possible.
(d)$ Cu^{2+}(aq) → Cu^{+}(aq) $ $ E^{\circ} = +0.15 V $
$ Fe^{3+}(aq) → Fe^{2+}(aq) $ $ E^{\circ} =+0.77 V $
So in this reaction, $ Fe^{3+}(aq)$ is the oxidizing agent and itself gets reduced as given in the equation. So it is spontaneous.
