The values of \(K_{sp}\) of \(CaCO_3\) and \(CaC_2O_4\) are \(4.7 \times 10^{-9}\) and \(1.3 \times 10^{-9}\) respectively at \(25\,^oC.\) If the mixture of these two is washed with water, what is the concentration of \(Ca^{2+}\) ions in water ..............\( \times 10^{-5}\, M\)?

A \(5.831\)
B \(6.856\)
C \(3.606\)
D \(7.746\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(7.746\)

Step-by-step Solution

Detailed explanation

\(\mathrm{CaCO}_{3} \rightarrow \mathrm{Ca}^{2+}+\mathrm{CO}_{3}^{2-}\) \(\quad \quad \quad \quad \quad \quad x \quad \quad x\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Match List I with List II :

List I (Order of reaction)	List II (Unit of rate constant)
(A) Zero order	(I) \(mol ^{-1} Ls ^{-1}\)
(B) First order	(II) \(mol ^{-2} L^2 s^{-1}\)
(C) Second order	(III) \(s ^{-1}\)
(D) Third order	(IV) \(mol L ^{-1} s^{-1}\)

Choose the correct answer from the options given below:

NEET 2026 Easy

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From NEET

Column \(- I\) gives certain physical terms associated with flow of current through a metallic conductor. Column \(- II\) gives some mathematical relations involving electrical quantities. Match Column \(- I\) and Column \(- II\) with appropriate relations.

Column \(- I\)	Column \(- II\)
\((A)\) Drift Velocity	\((P)\) \(\frac{m}{n e^{2} \rho}\)
\((B)\) Electrical Resistivity	\((Q)\) \(\mathrm{ne} v_{\mathrm{d}}\)
\((C)\) Relaxation Period	\((R)\) \(\frac{\mathrm{eE}}{\mathrm{m}} \tau\)
\((D)\) Current Density	\((S)\) \(\frac{E}{J}\)

NEET 2021 Medium

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