Consider the following two half-cell reactions along with the standard reduction potential given :
$\mathrm{CO}_2 + 6\mathrm{H}^+ + 6e^- \longrightarrow \mathrm{CH}_3\mathrm{OH} + \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 0.02\ \mathrm{V}$
$\dfrac{1}{2} \mathrm{O}_2 + 2\mathrm{H}^+ + 2e^- \longrightarrow \mathrm{H}_2\mathrm{O}\qquad E_{\text{red}}^{\circ} = 1.23\ \mathrm{V}$
A fuel cell was set up using the above two reactions such that the cell operates under the standard condition of 1 bar pressure and 298 K temperature. The fuel cell works with 80% efficiency. If the work derived from the cell using 1 mol of $\mathrm{CH}_3\mathrm{OH}$ is used to compress an ideal gas isothermally against a constant pressure of 1 kPa, then the change in the volume of the gas,
$\Delta V = \underline{\hspace{2cm}}$ m$^3$. (nearest integer)
Given : $\mathrm{F} = 96500~\mathrm{C~mol}^{-1}$
A volume of x mL of 5 M NaHCO3 solution was mixed with 10 mL of 2 M H2CO3 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 mV, then the value of x = ______ mL (nearest integer).
Sn(s) | Sn(OH)62− (0.5 M) | HSnO2− (0.05 M) | OH− | Bi2O3(s) | Bi(s)
Consider up to one place of decimal for intermediate calculations
$\left[\begin{array}{ll}\text { Given: } & E_{Sn\left( {OH} \right)_6^{2 - } |HSnO_2^ -}^o = - 0.9V \\ & \mathrm{E}^{\mathrm{o}}{ }_{\mathrm{Bi}_2 \mathrm{O}_3 \mid \mathrm{Bi}}=-0.44 \mathrm{~V} \\ & \mathrm{pKa}_{\left(\mathrm{H}_2 \mathrm{CO}_3\right)}=6.11 \\ & \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059 \mathrm{~V} \\ & \text { Antilog }(1.29)=19.5\end{array}\right]$
For strong electrolyte $\Lambda_m$ increases slowly with dilution and can be represented by the equation
$$\Lambda_m = \Lambda_m^\circ - A c^{1/2}$$
Molar conductivity values of the solutions of strong electrolyte AB at 18°C are given below :
| c [mol L-1] | 0.04 | 0.09 | 0.16 | 0.25 |
|---|---|---|---|---|
| $\Lambda_m$ [S cm2 mol-1] | 96.1 | 95.7 | 95.3 | 94.9 |
The value of constant A based on the above data [in S cm2 mol-1/(mol/L)1/2] unit is ________.
Consider the following redox reaction taking place in acidic medium
$$ \mathrm{BH}_4^{-}(a q)+\mathrm{ClO}_3^{-}(a q) \longrightarrow \mathrm{H}_2 \mathrm{BO}_3^{-}(a q)+\mathrm{Cl}^{-}(a q) $$
If the Nernst equation for the above balanced reaction is
$$ \mathrm{E}_{\mathrm{cell}}=\mathrm{E}_{\mathrm{cell}}^{\circ}-\frac{\mathrm{RT}}{\mathrm{nF}} \ln \mathrm{Q}, $$
then the value of $n$ is $\_\_\_\_$ .(Nearest integer)
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