\(1^{\text {st }} \)ઘટકના \(n_{1}\) મોલ્સ અને \(2^{\text {nd }}\) ઘટકના \(n_{2}\) મોલ્સ ધરાવતા બે ઘટકોનો દ્રાવણ તૈયાર છે. ઘટક \(1\) અને \(2\) ના આણ્વિય દળ અનુક્રમે \(M _{1}\) અને \(M _{2}\) છે જો \(2^{\text {nd }}\) ઘટકમાં \( d \) એ દ્રાવણમાં ઘનતા \(g\, mL ^{-1}\) માં છે ,\(C _{2}\) એ મોલારિટી છે અને \(x _{2}\)એ મોલ અંશ છે તો \(C_{2}\) ............તરીકે વ્યક્ત કરી શકાય છે

A \(C _{2}=\frac{1000 x _{2}}{ M _{1}+ x _{2}\left( M _{2}- M _{1}\right)}\)
B \(C _{2}=\frac{ d x _{2}}{ M _{2}+ x _{2}\left( M _{2}- M _{1}\right)}\)
C \(C _{2}=\frac{ d x _{1}}{ M _{2}+ x _{2}\left( M _{2}- M _{1}\right)}\)
D \(C _{2}=\frac{1000 dx _{2}}{ M _{1}+ x _{2}\left( M _{2}- M _{1}\right)}\)

Verified Solution

Answer & Solution

Correct Answer

(D) \(C _{2}=\frac{1000 dx _{2}}{ M _{1}+ x _{2}\left( M _{2}- M _{1}\right)}\)

Step-by-step Solution

Detailed explanation

\(C_{2}=\frac{x_{2}}{\left[x_{2} M_{2}+\left(1-x_{2}\right) M_{2}\right] / C l} \times 1000\) \(C_{2}=\frac{1000 d x_{2}}{M_{1}+\left(M_{2}-M_{1}\right) x_{2}}\)

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.

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