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NEET CHEMISTRYMedium

In the electrochemical cell: ZnZnSO4(0.01 M)CuSO4(1.0 M)Cu\text{Zn}|\text{ZnSO}_4(0.01 \text{ M}) || \text{CuSO}_4(1.0 \text{ M})|\text{Cu}, the emf of this Daniel cell is E1E_1. When the concentration of ZnSO4\text{ZnSO}_4 is changed to 1.0 M1.0 \text{ M} and that of CuSO4\text{CuSO}_4 is changed to 0.01 M0.01 \text{ M}, the emf changes to E2E_2. The relationship between E1E_1 and E2E_2 is : (Given, RTF=0.059\frac{RT}{F} = 0.059)

A

E1=E2E_1 = E_2

B

E1<E2E_1 < E_2

C

E1>E2E_1 > E_2

D

E2=0E1E_2 = 0 \neq E_1

Step-by-Step Solution

According to the Nernst equation for the Daniell cell: Ecell=Ecell2.303RTnFlog[Zn2+][Cu2+]E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{2.303RT}{nF} \log \frac{[\text{Zn}^{2+}]}{[\text{Cu}^{2+}]} For the first case (E1E_1), [Zn2+]=0.01 M[\text{Zn}^{2+}] = 0.01 \text{ M} and [Cu2+]=1.0 M[\text{Cu}^{2+}] = 1.0 \text{ M}, n=2n=2. E1=Ecell0.0592log(0.011.0)=Ecell0.0592(2)=Ecell+0.059 VE_1 = E^\circ_{\text{cell}} - \frac{0.059}{2} \log \left(\frac{0.01}{1.0}\right) = E^\circ_{\text{cell}} - \frac{0.059}{2} (-2) = E^\circ_{\text{cell}} + 0.059 \text{ V} For the second case (E2E_2), [Zn2+]=1.0 M[\text{Zn}^{2+}] = 1.0 \text{ M} and [Cu2+]=0.01 M[\text{Cu}^{2+}] = 0.01 \text{ M}. E2=Ecell0.0592log(1.00.01)=Ecell0.0592(2)=Ecell0.059 VE_2 = E^\circ_{\text{cell}} - \frac{0.059}{2} \log \left(\frac{1.0}{0.01}\right) = E^\circ_{\text{cell}} - \frac{0.059}{2} (2) = E^\circ_{\text{cell}} - 0.059 \text{ V} Comparing the two equations, it is clear that E1>E2E_1 > E_2.

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