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Answer:

The reaction [tex]\rm Zn\, (s) + 2\, HCl \, (aq) \to ZnCl_2\, (aq) + H_2\, (g)[/tex] is spontaneous (under standard conditions) because the cell potential is positive.

Explanation:

In this reaction:

  • Metallic zinc [tex]\rm Zn\, (s)[/tex] is oxidized to produce zinc ions [tex]\rm Zn^{2+}[/tex].
  • Hydrogen ions [tex]\rm H^{+}[/tex] is reduced to produce hydrogen gas [tex]\rm H_2\, (g)[/tex].

The anode is where the oxidation half-reaction takes place. In this case, the anode half-reaction is [tex]\rm Zn\, (s) \to Zn^{2+} \, (aq) + 2\, e^{-}[/tex].

The cathode is where the reduction half-reaction takes place. In this case, the cathode half-reaction is [tex]\rm 2\, H^{+}\, (aq) + 2\, e^{-} \to H_2\, (g)[/tex].

Look up the standard reduction potential for these two half-reactions:

  • [tex]E^{\circ}_{\text{reduction, anode}} = \rm -0.7618\; V[/tex] for the reaction [tex]\rm Zn^{2+} \, (aq) + 2\, e^{-} \rightleftharpoons Zn\, (s)[/tex].
  • [tex]E^{\circ}_{\text{reduction, cathode}} = \rm 0\; V[/tex] for the reaction [tex]\rm H^{+} \, (aq) + e^{-} \rightleftharpoons \dfrac{1}{2}H_2\, (g)[/tex].

The standard cell potential is equal to the standard reduction potential at the cathode minus that at the anode:

[tex]E^{\circ}_\text{cell} = E^{\circ}_{\text{reduction, cathode}} - E^{\circ}_{\text{reduction, anode}} = \rm 0.7618\; V[/tex].

The electrochemical reaction in the cell is spontaneous if and only if the cell potential is positive. Therefore, the reaction  [tex]\rm Zn\, (s) + 2\, HCl \, (aq) \to ZnCl_2\, (aq) + H_2\, (g)[/tex] is spontaneous under standard conditions.

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