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Electrochemistry

Question
CBSEENCH12010284

The conductivity of 0.20 mol L-1 solution of KCl is 2.48 x 10-2 S cm-1. Calculate its molar conductivity and degree of dissociation  (K+) = 73.56 S cm2 mol-1 and  (Cl-)= 76.5 S

(b) What type of battery is mercury cell? Why is it more advantageous than dry cell?

Solution

Conductivity of KCl solution = 2.48 x 10-2 S cm-1

Concentration of KCl solution = 0.20 mol L-1

                                                 = 0.20 x 1000 mol cm -3

                                                = 200 mol cm-3

Molar conductivity 
straight capital lambda subscript straight m space equals space straight k over straight c

space equals fraction numerator 2.48 space straight x space 10 to the power of negative 2 end exponent space straight S space Cm to the power of negative 1 end exponent over denominator 200 space mol space cm to the power of negative 3 end exponent end fraction

Given space colon space
straight lambda subscript straight K to the power of plus end subscript superscript 0 space equals 73.5 space straight S space cm squared space mol to the power of negative 1 end exponent

straight lambda subscript Cl to the power of negative 1 end exponent end subscript superscript 0 space equals space 76.5 space straight S space cm squared space mol to the power of negative 1 end exponent

Degree space of space dissociation space

straight alpha space equals fraction numerator straight lambda subscript straight m over denominator straight lambda subscript straight m superscript 0 end fraction space............ left parenthesis straight i right parenthesis

straight lambda subscript straight m left parenthesis KCl right parenthesis end subscript superscript 0 space equals straight lambda space subscript straight K to the power of plus end subscript superscript 0 space plus straight lambda subscript Cl to the power of minus end subscript superscript 0
space equals 73.5 space plus 76.5
equals 150 space straight S space cm squared space mol to the power of negative 1 end exponent

Substituting space the space value space of space straight lambda subscript straight m space and space straight lambda subscript straight m left parenthesis KCl right parenthesis end subscript superscript 0 space in space left parenthesis straight i right parenthesis space comma space we space get space
straight alpha space equals fraction numerator 124 space straight x space 10 to the power of negative 6 end exponent space straight S space cm squared space mol to the power of negative 1 end exponent over denominator 150 space straight S space cm squared space mol to the power of negative 1 end exponent space end fraction space equals space 0.82 space straight x space 10 to the power of negative 6 end exponent

b) Mercury cell is a type of primary battery. In primary batteries , the charging  reaction occurs only once and after it has been used over a period of time , the battery becomes dead and cannot be refused mercury cell is more advantage than dry cell has a very short life span due to the conversion of zinc to zinc chloride that makes the zinc casing porous . Due to this porous casing, the substance inside the cell leaks out and corrodes the metal, reducing the lifetime of the cell. While, in the case of mercury cell, the overall reaction does not involve the formation of any ion in the solution whose concentration can change during its life time.