Explain the difference between an electrochemical cell and electrolytic cell. State Kohlrausch's law and write its applications.
Step 1: Difference Between Electrochemical and Electrolytic Cells: Feature & Electrochemical Cell & Electrolytic Cell
Energy Conversion & Chemical to electrical & Electrical to chemical
Spontaneity & Spontaneous reaction & Non-spontaneous reaction
Example & Galvanic/Daniel cell & Electrolysis of NaCl
Step 2: Kohlrausch's Law: \[ \Lambda_m^0 = \lambda^0_+ + \lambda^0_- \] where \( \lambda^0_+ \) and \( \lambda^0_- \) are the limiting molar conductivities of cations and anions, respectively.
Step 3: Applications: - Used to calculate the molar conductivity of weak electrolytes. - Helps in determining dissociation constants of weak acids and bases.
List-I (Symbol of electrical property) | List-II (Units) |
---|---|
A) \( \Omega \) | I) S cm\(^{-1}\) |
B) G | II) m\(^{-1}\) |
C) \( \kappa \) | III) S cm\(^2\) mol\(^{-1}\) |
D) G\(^*\) | IV) S |
Find the values of \( x, y, z \) if the matrix \( A \) satisfies the equation \( A^T A = I \), where
\[ A = \begin{bmatrix} 0 & 2y & z \\ x & y & -z \\ x & -y & z \end{bmatrix} \]
(b) Order of the differential equation: $ 5x^3 \frac{d^3y}{dx^3} - 3\left(\frac{dy}{dx}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^4 + y = 0 $