$\text{A constant current was passed through a solution of AuCl}_4^- \text{ ion between gold electrodes. After a} \\\text{period of 10.0 minutes, the increase in mass of cathode was 1.314 g. The total charge passed} \\$$\text{through the solution is \_\_\_\_\_\_\_\_} \times 10^{-2} \, \text{F.} \\$$\text{(Given atomic mass of Au = 197)}$
Correct Answer: 2
Approach Solution - 1
1. **Understanding the Reaction**:
The electrochemical reaction at the cathode involves the reduction of AuCl4- ions to gold (Au), where each ion gains 3 electrons:
$$\text{AuCl}_4^- + 3e^- \rightarrow \text{Au} + 4\text{Cl}^-$$
2. **Calculate Moles of Au Deposited**:
The molar mass of Au is given as 197 g/mol. The mass of Au deposited is 1.314 g. The number of moles of Au deposited is:
$$\text{Moles of Au} = \frac{1.314 \text{ g}}{197 \text{ g/mol}} = 0.00667 \text{ mol}$$
3. **Electrons Transferred**:
Since each Au atom corresponds to the transfer of 3 electrons, the total moles of electrons (n) is:
$$n = \text{Moles of Au} \times 3 = 0.00667 \times 3 = 0.02001 \text{ mol e}^-$$
4. **Calculate Total Charge**:
The total charge (Q) transferred is given by Faraday's constant (F = 96485 C/mol), where:
$$Q = n \times F = 0.02001 \times 96485 = 1930.34985 \text{ C}$$
5. **Express Charge in Faradays**:
Since 1 Faraday (F) is 96485 Coulombs, the charge in Faradays is:
$$\text{Charge in F} = \frac{1930.34985 \text{ C}}{96485 \text{ C/F}} = 0.02002 \text{ F}$$
6. **Express in Given Format**:
The charge expressed in the given format is:
$$0.02002 \times 10^{-2} \text{ F} = 2.002 \times 10^{-2} \text{ F}$$
7. **Verification Against Range**:
The computed charge, 2.002, indeed falls within the given range of 2 to 2.
Thus, the total charge passed through the solution is 2.002 × 10-2 F.
Approach Solution -2
Solution:
\(\frac{W}{E} = \frac{\text{charge}}{1F}\)
Substitute the values:
\(\frac{1.314}{\frac{197}{3}} = \frac{Q}{1F}\)
\(Q = 2 \times 10^{-2} F\)
The Correct Answer is: 2
Top JEE Main Chemistry Questions
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- At equilibrium the concentrations of and in a sealed vessel at . What will be for the reaction
- Find out the major products from the following reactions
Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are
- The correct order of atomic radii is:
Top JEE Main Electrolysis Questions
- Find out charge (in C) required for electrolysis of \(1\) mole of \(H_2O\) to produce \(O_2\) on one of the electrodes. \((F = 96500 \;C)\)
Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12. The current in Amperes used for the given electrolysis is ….. (Nearest integer).
A solution of aluminium chloride is electrolyzed for 30 minutes using a current of 2A. The amount of the aluminium deposited at the cathode is _________
O\(_2\) gas will be evolved as a product of electrolysis of:
(A) an aqueous solution of AgNO3 using silver electrodes.
(B) an aqueous solution of AgNO3 using platinum electrodes.
(C) a dilute solution of H2SO4 using platinum electrodes.
(D) a high concentration solution of H2SO4 using platinum electrodes.
Choose the correct answer from the options given below :- The molar conductivity of a conductivity cell filled with $10$ moles of $20\, mL\, NaCl$ solution is $\Lambda_{ m 1}$ and that of $20$ moles another identical cell heaving $80 \, mL \, NaCl$ solution is $\Lambda_{ m 2}$, The conductivities exhibited by these two cells are same The relationship between $\Lambda_{ m 2}$ and $\Lambda_{ m 1}$ is
Top JEE Main Questions
- In a hydrogen like atom, when an electron jumps from the $M$ - shell to the $L$ - shell, the wavelength of emitted radiation is $\lambda$. If an electron jumps from $N$-shell to the $L$-shell, the wavelength of emitted radiation will be :
- Two masses $m$ and $\frac{m}{2}$ are connected at the two ends of a massless rigid rod of length $l$. The rod is suspended by a thin wire of torsional constant $k$ at the centre of mass of the rod-mass system(see figure). Because of torsional constant $k$, the restoring torque is $\tau =k\theta$ for angular displacement $\theta$. If the rod is rota ted by $\theta_0$ and released, the tension in it when it passes through its mean position will be:
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)- The value of is
- The number of terms of an is even. The sum of the odd terms is and of the even terms is . The last term exceeds the first by . Then the number of terms in the series is ______.