The magnitude of the change in oxidising power of the $\mathrm{MnO}_{4}^{-} / \mathrm{Mn}^{2+}$ couple is $\mathrm{x} \times 10^{-4} \mathrm{~V}$, if the $\mathrm{H}^{+}$concentration is decreased from $1 \mathrm{M}$ to $10^{-4} \mathrm{M}$ at $25^{\circ} \mathrm{C}$. (Assume concentration of $\mathrm{MnO}_{4}^{-}$and $\mathrm{Mn}^{2+}$ to be same on change in $\mathrm{H}^{+}$ concentration). The value of $x$ is (Rounded off to the nearest integer) $\left[\right.$ Given $\left.: \frac{2.303 \mathrm{RT}}{\mathrm{F}}=0.059\right]$
Eqn is-
$\mathrm{MnO}_{4}^{-}+\mathrm{H}^{\oplus}+5 \mathrm{e}^{-} \rightarrow \mathrm{Mn}^{+2}+4 \mathrm{H}_{2} \mathrm{O}$
Nernst equation:
$\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {Cell }}^{0}-\frac{0.059}{5} \log \frac{\left[\mathrm{Mn}^{+2}\right]}{\left[\mathrm{MnO}_{4}^{-}\right]}\left[\frac{1}{\mathrm{H}^{+}}\right]^{8}$
(I) Given $\left[\mathrm{H}^{\oplus}\right]=1 \mathrm{M}$
$\mathrm{E}_{1}=\mathrm{E}^{0}-\frac{0.059}{5} \log \frac{\left[\mathrm{Mn}^{+2}\right]}{\left[\mathrm{MnO}_{4}^{-}\right]}$
(II) Now : $\left[\mathrm{H}^{\oplus}\right]=10^{-4} \mathrm{M}$
$\mathrm{E}_{2}=\mathrm{E}^{0}-\frac{0.059}{5} \log \frac{\left[\mathrm{Mn}^{+2}\right]}{\left[\mathrm{MnO}_{4}^{-}\right]} \times \frac{1}{\left(10^{-4}\right)^{8}}$
$=\mathrm{E}^{0}-\frac{0.059}{5} \log \frac{\mathrm{Mn}^{+2}}{\left[\mathrm{MnO}_{4}^{-}\right]}+\frac{0.059}{5} \log 10^{-32}$
therefore : $\left|E_{1}-E_{2}\right|=\frac{0.059}{5} \times 32$
$=0.3776 \mathrm{~V}=3776 \times 10^{-4}$
$x=3776$
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,