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JEE Main 202628 JanuaryEvening Shift
Exam
JEE Main
Year
2026
Date
28 January
Shift
Evening Shift
Subject
Chemistry
Chapter
Electrochemistry

JEE Main 2026 · 28 January · Evening Shift · Chemistry · Electrochemistry

A volume of x\,mL of 5\,M\,NaHCO_3 solution was mixed with 10\,mL...

A volume of x mLx\,\mathrm{mL} of 5 M NaHCO35\,\mathrm{M}\,\mathrm{NaHCO_3} solution was mixed with 10 mL10\,\mathrm{mL} of 2 M H2CO32\,\mathrm{M}\,\mathrm{H_2CO_3} solution to make an electrolytic buffer. If the same buffer was used in the following electrochemical cell to record a cell potential of 235.3 mV235.3\,\mathrm{mV}, then the value of x=____x = \_\_\_\_ mL (nearest integer).

Sn(s)  ∣  Sn(OH)62−(0.5 M)  ∣  HSnO2−(0.05 M)  ∣  OH−  ∣  Bi2O3(s)  ∣  Bi(s)\mathrm{Sn(s)} \; \big| \; \mathrm{Sn(OH)_6^{2-}}(0.5\,\mathrm{M}) \; \big| \; \mathrm{HSnO_2^-}(0.05\,\mathrm{M}) \; \big| \; \mathrm{OH^-} \; \big| \; \mathrm{Bi_2O_3(s)} \; \big| \; \mathrm{Bi(s)}

Consider up to one place of decimal for intermediate calculations.

Given:E[Sn(OH)6]2−/HSnO2−∘=−0.90 VEBi2O3/Bi∘=−0.44 VpKa(H2CO3)=6.112.303 RTF=0.059 VAntilog(1.29)=19.5\begin{array}{ll}\text{Given:} & E^\circ_{\mathrm{[Sn(OH)_6]^{2-}/HSnO_2^-}} = -0.90\,\mathrm{V} \\[4pt]& E^\circ_{\mathrm{Bi_2O_3/Bi}} = -0.44\,\mathrm{V} \\[4pt]& \mathrm{p}K_a(\mathrm{H_2CO_3}) = 6.11 \\[4pt]& \dfrac{2.303\,RT}{F} = 0.059\,\mathrm{V} \\[6pt]& \text{Antilog}(1.29) = 19.5\end{array}

Correct answer

0

Step-by-step solution

We have considered
E[Sn(OH)6]2−/HSnO2−∘=−0.9 VE^{\circ}_{[Sn(OH)_6]^{2-}/HSnO_2^-} = -0.9 \text{ V}
Pt∣HSnO2−(aq),[Sn(OH)6]2−(aq),OH−(aq)∣Bi2O3(s)∣Bi(s)∣Pt | HSnO_2^-(aq), [Sn(OH)_6]^{2-}(aq), OH^-(aq) | Bi_2O_3(s) | Bi(s) |
0.5M0.05M0.5M \quad 0.05M
Ecell∘=+0.9−0.44=0.46 VE^{\circ}_{cell} = +0.9 - 0.44 = 0.46 \text{ V}
Oxidation Half :
HSnO2−+H2O+3OH−→[Sn(OH)6]2−+2e−HSnO_2^- + H_2O + 3OH^- \rightarrow [Sn(OH)_6]^{2-} + 2e^-
Reduction Half :
Bi2O3+3H2O+6e−→2Bi+6OH−Bi_2O_3 + 3H_2O + 6e^- \rightarrow 2Bi + 6OH^-
---------------------------------------
3HSnO2−(aq)+Bi2O3(s)+6H2O+3OH−(aq)→3[Sn(OH)6]2−(aq)+2Bi(s)3HSnO_2^-(aq) + Bi_2O_3(s) + 6H_2O + 3OH^-(aq) \rightarrow 3[Sn(OH)_6]^{2-}(aq) + 2Bi(s)
Ecell=Ecell∘−0.0596log⁡(0.5)3(0.05)3×[OH−]3E_{cell} = E^{\circ}_{cell} - \dfrac{0.059}{6} \log \dfrac{(0.5)^3}{(0.05)^3 \times [OH^-]^3}
0.2353=0.46−0.0596×3log⁡[10[OH−]]0.2353 = 0.46 - \dfrac{0.059}{6} \times 3 \log \left[ \dfrac{10}{[OH^-]} \right]
log⁡[10OH−]=2×0.22470.059=7.6\log \left[ \dfrac{10}{OH^-} \right] = \dfrac{2 \times 0.2247}{0.059} = 7.6
1+pOH=7.61 + pOH = 7.6
pOH=6.6pOH = 6.6
pH=14−6.6=7.4pH = 14 - 6.6 = 7.4
pH=pKa1+log⁡[HCO3−][H2CO3]pH = pK_{a_1} + \log \dfrac{[HCO_3^-]}{[H_2CO_3]}
7.4=6.11+log⁡5x207.4 = 6.11 + \log \dfrac{5x}{20}
1.29=log⁡x41.29 = \log \dfrac{x}{4}
x4=19.5\dfrac{x}{4} = 19.5
x=78x = 78
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