At $298 \, K$, the standard Gibbs free energy of formation for $H_2O_{(l)}$, $CO_{2(g)}$, and $C_5H_{12(g)}$ are $-237.2$, $-394.4$, and $-8.2 \, kJ \, mol^{-1}$ respectively. What is the potential of a pentane-oxygen fuel cell in $V$?

For a saturated solution of $Ag_{2}CrO_{4}$ at infinite dilution,$\lambda_{m}^{\infty}(Ag^{+}) = 127 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$ and $\lambda_{m}^{\infty}(CrO_{4}^{2-}) = 246 \ \Omega^{-1} \ cm^{2} \ mol^{-1}$. If the specific conductance of the solution is $2 \times 10^{-2} \ \Omega^{-1} \ cm^{-1}$,calculate the solubility product $(K_{sp})$ of $Ag_{2}CrO_{4}$.

If the molar conductivity $(\Lambda_{m})$ of a $0.050 \ mol \ L^{-1}$ solution of a monobasic weak acid is $90 \ S \ cm^{2} \ mol^{-1}$,its extent (degree) of dissociation will be. [Assume $\Lambda_{+}^{\circ} = 349.6 \ S \ cm^{2} \ mol^{-1}$ and $\Lambda_{-}^{\circ} = 50.4 \ S \ cm^{2} \ mol^{-1}$.]

Consider the strong electrolytes $Z_{m}X_{n}$,$U_{m}Y_{p}$ and $V_{m}X_{n}$. Limiting molar conductivity $(\Lambda^0)$ of $U_{m}Y_{p}$ and $V_{m}X_{n}$ are $250 \ S \ cm^2 \ mol^{-1}$ and $440 \ S \ cm^2 \ mol^{-1}$,respectively. The value of $(m + n + p)$ is . . . . . Given:

$Ion$	$\lambda^0 \ (S \ cm^2 \ mol^{-1})$
$U^{p+}$	$50.0$
$Y^{m-}$	$50.0$
$V^{n+}$	$60.0$
$X^{m-}$	$50.0$
$Z^{n+}$	$40.0$

$\lambda^0$ is the limiting molar conductivity of ions. The plot of molar conductivity $(\Lambda)$ of $Z_{m}X_{n}$ $vs$ $c^{1/2}$ is given below.

Which of the following statements is not correct?

Consider the following redox reaction :
$MnO_4^{-} + H^{+} + H_2C_2O_4 \rightleftharpoons Mn^{2+} + H_2O + CO_2$
The standard reduction potentials are given as below $(E_{red}^{\circ})$ :
$E_{MnO_4^{-} / Mn^{2+}}^{\circ} = +1.51 \ V$
$E_{CO_2 / H_2C_2O_4}^{\circ} = -0.49 \ V$
If the equilibrium constant of the above reaction is given as $K_{eq} = 10^x$,then the value of $x = $ . . . . . . (nearest integer).