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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Chemistry
Chapter
Surface Chemistry

NTA Abhyas 2020 · Chemistry · Surface Chemistry

The critical micelle concentration (CMC) of a cationic colloidal...

The critical micelle concentration (CMC)\left(\text{CMC}\right) of a cationic colloidal electrolyte is 10−3M{10}^{- 3}\text{M} . If 1mm31{\text{mm}}^{3} contains 1013{10}^{13} micelles, the number of cations making one micelle is
(Given, NA=6.0×1023mol−1{\text{N}}_{A} = 6.0 \times {10}^{23}{\text{mol}}^{- 1} )

Correct answer

60.00

Step-by-step solution

At CMC,CMC, the number of cationic colloidal particles =10−3×6.0×1023= {10}^{- 3} \times 6.0 \times {10}^{23}=6.0×1020= 6.0 \times {10}^{20} per L

Therefore, number of particles per mm3m{m}^{3}
=6.0×1020106(∵1L=106mm3)= \dfrac{6.0 \times {10}^{20}}{{10}^{6}}\left(∵ 1\text{L} = {10}^{6}{\text{mm}}^{3}\right)
=6.0×1014= 6.0 \times {10}^{14} particles/ mm3m{m}^{3}

Number of micelles in 1mm3= 10131m{m}^{3}{\text{= 10}}^{13} (given)
Number of cations forming one micelle
=6.0×10141013= \dfrac{6.0 \times {10}^{14}}{{10}^{13}}
=60= 60 cations
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