Question:
If at infinite dilution, molar conductivities of BaCl\(_2\), HCl and H\(_2\)SO\(_4\) are \( x_1 \), \( x_2 \), \( x_3 \) S cm\(^2\)mol\(^{-1}\) respectively, find solubility product of BaSO\(_4\).
Given \( K_{\text{BaSO}_4} \) (Specific conductance) = \( x \) S cm\(^{-1}\)
If at infinite dilution, molar conductivities of BaCl\(_2\), HCl and H\(_2\)SO\(_4\) are \( x_1 \), \( x_2 \), \( x_3 \) S cm\(^2\)mol\(^{-1}\) respectively, find solubility product of BaSO\(_4\).
Given \( K_{\text{BaSO}_4} \) (Specific conductance) = \( x \) S cm\(^{-1}\)
Updated On: Apr 8, 2026
- \(\left( \frac{x}{x_1 + x_3 - 2x_2} \right)^2 \times 10^6 \)
- \(\left( \frac{x_1 + x_3 - 2x_2}{x} \right)^2 \times 10^6 \)
- \(\left( \frac{x}{x_1 + x_3 - x_2} \right)^2 \times 10^3 \)
- \(\left( \frac{x_1 + x_3 - x_2}{x} \right)^2 \times 10^6 \)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Step 1: Molar conductivity at infinite dilution.
At infinite dilution, the molar conductivities of the ionic compounds are related to their respective ions. The solubility product of BaSO\(_4\) can be derived from the molar conductivities at infinite dilution of BaCl\(_2\), HCl, and H\(_2\)SO\(_4\).
Step 2: Derivation of the solubility product.
For the dissociation of BaSO\(_4\), the ions produced are Ba\(^{2+}\) and SO\(_4^{2-}\). The relationship between the molar conductivity of the salt and the dissociation constants gives the solubility product. The given equation for the specific conductance \( K_{\text{BaSO}_4} = x \) allows us to compute the solubility product.
Step 3: Comparison with the options.
- (1) \(\left( \frac{x}{x_1 + x_3 - 2x_2} \right)^2 \times 10^6\) is the correct expression for the solubility product as derived from the given data and equations.
- Other options are incorrect as they do not match the derived formula for the solubility product.
Step 4: Conclusion.
Thus, the correct answer is option (A).
Final Answer: (A) \(\left( \frac{x}{x_1 + x_3 - 2x_2} \right)^2 \times 10^6 \)
At infinite dilution, the molar conductivities of the ionic compounds are related to their respective ions. The solubility product of BaSO\(_4\) can be derived from the molar conductivities at infinite dilution of BaCl\(_2\), HCl, and H\(_2\)SO\(_4\).
Step 2: Derivation of the solubility product.
For the dissociation of BaSO\(_4\), the ions produced are Ba\(^{2+}\) and SO\(_4^{2-}\). The relationship between the molar conductivity of the salt and the dissociation constants gives the solubility product. The given equation for the specific conductance \( K_{\text{BaSO}_4} = x \) allows us to compute the solubility product.
Step 3: Comparison with the options.
- (1) \(\left( \frac{x}{x_1 + x_3 - 2x_2} \right)^2 \times 10^6\) is the correct expression for the solubility product as derived from the given data and equations.
- Other options are incorrect as they do not match the derived formula for the solubility product.
Step 4: Conclusion.
Thus, the correct answer is option (A).
Final Answer: (A) \(\left( \frac{x}{x_1 + x_3 - 2x_2} \right)^2 \times 10^6 \)
Was this answer helpful?
0
0
Top JEE Main Chemistry Questions
- Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol\(^{-1}\)) in 0.5 L of water at 300 K. Its osmotic pressure is \( x \) bar. Solution B is made by dissolving 2 g of the same protein in 1 L of water at 300 K. Osmotic pressure of solution B is \( y \) bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is \( z \) bar. \( x \), \( y \), and \( z \) respectively are:
- JEE Main - 2026
- Chemistry
- Raoult's Law and Colligative Properties
- Bromine trifluoride autoionizes to form BrF$_2^+$ and BrF$_4^-$. The shapes of the cation and anion are respectively ________, and ________
- JEE Main - 2026
- Chemistry
- VSEPR theory and shape of molecules
- Solid carbon, CaO and CaCO$_3$ are mixed and allowed to attain equilibrium at T K. \[ \text{CaCO}_3(s) \rightleftharpoons \text{CaO}(s) + \text{CO}_2(g) \quad K_{P1} = 0.08 \, \text{atm} \] \[ \text{C}(s) + \text{CO}_2(g) \rightleftharpoons 2 \text{CO}(g) \quad K_{P2} = 2 \, \text{atm} \] The partial pressure of CO is _______ \(\times 10^{-1}\) atm.
- JEE Main - 2026
- Chemistry
- Chemical Equilibria and Dissociation
- ‘x’ is the product which is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride. ‘y’ is the major product obtained from the benzene by reacting it with ethanoyl chloride in the presence of anhydrous AlCl$_3$. Product (major) obtained by heating x and y in the presence of alkali is z. Total number of $\pi$ (pi) electrons in z is _______.
- JEE Main - 2026
- Chemistry
- Coordination chemistry
- Which of the following amino acid will give violet coloured complex with neutral ferric chloride solution?
View More Questions
Top JEE Main Thermodynamics Questions
- Arrange the following isothermal processes in order of the magnitude of the work (p - V) involved between states 1 and 2.
A. Expansion in single stage $w_A$
B. Expansion in multi stages $w_B$
C. Compression in single stage $w_C$
D. Compression in multi stages $w_D$
Choose the correct option.- JEE Main - 2026
- Chemistry
- Thermodynamics
- Calculate \(|\Delta H^{\circ}|\) for the following reaction (in kJ/mol):
\[ 2H_2S(g) + 3O_2(g) \rightarrow 2SO_2(g) + 2H_2O(l) \] Given data: \[ \Delta H_f^{\circ}(H_2S(g)) = -20.6 \, \text{kJ/mol}, \Delta H_f^{\circ}(SO_2(g)) = -296.8 \, \text{kJ/mol}, \Delta H_f^{\circ}(H_2O(l)) = -285.8 \, \text{kJ/mol} \]- JEE Main - 2026
- Chemistry
- Thermodynamics
- For given four processes compare magnitude of work:
- JEE Main - 2026
- Chemistry
- Thermodynamics
- For the reversible reaction at 300 K, \( \Delta H^o = 28.4 \, \text{KJ/mole} \) and equilibrium constant \( K = 1.8 \times 10^{-7} \), then calculate the magnitude of \( \Delta S^o \) in Joule/K-mole.
[Given: log 2 = 0.3, \( \ln 10 = 2.3 \), \( R = 8.314 \, \text{J/K.mole} \), log 3 = 0.47]- JEE Main - 2026
- Chemistry
- Thermodynamics
- 1 mole of He and 1 mole A are taken in a 10 L rigid container at 400 K, and equilibrium \( A \rightleftharpoons B \) is established. Calculate the partial pressure of He and B at equilibrium if \( K_c = 4 \).
- JEE Main - 2026
- Chemistry
- Thermodynamics
View More Questions
Top JEE Main Questions
- A thin half ring of radius $35 \text{ cm}$ is uniformly charged with a total charge of $Q$ coulomb. If the magnitude of the electric field at centre of the half ring is $100 \text{ V/m}$, then the value of $Q$ is ______ $\text{nC}$.
($\epsilon_o = 8.85 \times 10^{-12} \text{ C}^2/\text{Nm}^2$ and $\pi = 3.14$)- JEE Main - 2026
- Electric Field
Find the area of the region \[ R = \{(x, y) : xy \le 27,\; 1 \le y \le x^2 \}. \]
- JEE Main - 2026
- Integration and Area Calculation
- Solution A is prepared by dissolving 1 g of a protein (molar mass = 50000 g mol\(^{-1}\)) in 0.5 L of water at 300 K. Its osmotic pressure is \( x \) bar. Solution B is made by dissolving 2 g of the same protein in 1 L of water at 300 K. Osmotic pressure of solution B is \( y \) bar. Entire solution of A is mixed with entire solution of B at same temperature. The osmotic pressure of resultant solution is \( z \) bar. \( x \), \( y \), and \( z \) respectively are:
- JEE Main - 2026
- Raoult's Law and Colligative Properties
An object of uniform density rolls up the curved path with the initial velocity $v_o$ as shown in the figure. If the maximum height attained by an object is $\frac{7v_o^2}{10 g}$ ($g=$ acceleration due to gravity), the object is a _______
- JEE Main - 2026
- Rotational Motion and Torque
A body of mass $m$ is taken from the surface of earth to a height equal to twice the radius of earth ($R_e$). The increase in potential energy will be ____ ($g$ is acceleration due to gravity at the surface of earth)
- JEE Main - 2026
- Gravitation
View More Questions