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The initial concentration affects the conductivity of a solution in a sense that the greater the initial concentration,the greater the conductivity.increase in concentration means presence of more free moving ions in the solution.but this can only occur in the initial concentration because,after the initial concentration,an increase in concentration will mean that there are now more ions present in the solution but the same volume,hence the ions wouldn't be able to move freely an in the initial concentration,hence the conductivity would then decrease since they can't move freely now.

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Q: What kind of mathematical relationship exists between conductivity and concentration?
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