Question
Question: A dilute solution of \({\text{KCl}}\) was placed between two \({\text{Pt}}\) electrodes \(10.0{\text...
A dilute solution of KCl was placed between two Pt electrodes 10.0 cm apart, cross which a potential difference of 6.0 volt was applied. K+ ions move x cm in 2 hour at 25∘C, the x is _____. (nearest integer)
Ionic conductivity of K+ at infinite dilution is 73.52 S cm2 mol−1 at 25∘C.
Solution
To solve this first calculate the ionic mobility of K+ ions at infinite dilution. Then calculate the potential gradient applied. Then calculate the speed of K+ ions. Remember to convert the time i.e. 2 hour to seconds.
Formula Used: U±∞=Fλ±∞
Complete step-by-step answer:
We know that the potential gradient is the rate of change of potential with respect to displacement. Thus, the potential gradient is,
Potential gradient =10.0 cm6.0 volt=0.6 volt cm−1
Thus, the potential gradient is 0.6 volt cm−1.
The ionic mobility of ions at infinite dilution is related to the ionic conductivity by the equation as follows:
U±∞=Fλ±∞
Where U±∞ is the ionic mobility of ions at infinite dilution,
λ±∞ is the ionic conductivity at infinite dilution,
F is Faraday's constant.
Thus, the ionic mobility of K+ ions at infinite dilution is,
UK+∞=96500 C mol−173.52 S cm2 mol−1
UK+∞=7.6186×10−4 S cm2 C−1
Thus, the ionic mobility of K+ ions at infinite dilution is 7.6186×10−4 S cm2 C−1.
Now, calculate the speed of K+ ions using the equation as follows:
Speed of K+ ions=Ionic mobility×Potential gradient
Thus,
Speed of K+ ions=7.6186×10−4 S cm2 C−1×0.6 volt cm−1
Speed of K+ ions=4.57×10−4 cm sec−1
But we are given that the K+ ions move x cm in 2 hour. Thus,
Speed of K+ ions=4.57×10−4 cm sec−1×(2×60×60) sec
Speed of K+ ions=3.2904 cm
Thus, the x is 3 cm.
Note: The conducting power of all the ions that are produced by dissolving one mole of any electrolyte in the solution is known as the molar conductivity of the solution. As the temperature of the solution increases, the molar conductivity of the solution increases. This is because as the temperature increases the interaction and the mobility of the ions in the solution increases. The molar conductivity of both strong and weak electrolytes increases as the dilution increases. This is because dilution increases the degree of dissociation and the total number of ions that carry current increases.