The temperature-dependent form of the extended Debye-Hückel equation is (-1.825 x 10°) (€T) z² va log (y) = 1+ 2.00VCT where y is the activity coefficient, e is the dielectric constant of water (a unitless quantity), T is the temperature (in Kevin), z is the charge of the ion, µ is the ionic strength (in moles per liter), and a is the ion size parameter (in picometers). The temperature- dependence of the dielectric constant is given by the equation e = 79.755e(-4.6x10~')(T–293.15) where the temperature is in Kelvin. What is the value of the activity coefficient of Pb2+ at 70.00 °C when the ionic strength is 0.014 M?
The temperature-dependent form of the extended Debye-Hückel equation is (-1.825 x 10°) (€T) z² va log (y) = 1+ 2.00VCT where y is the activity coefficient, e is the dielectric constant of water (a unitless quantity), T is the temperature (in Kevin), z is the charge of the ion, µ is the ionic strength (in moles per liter), and a is the ion size parameter (in picometers). The temperature- dependence of the dielectric constant is given by the equation e = 79.755e(-4.6x10~')(T–293.15) where the temperature is in Kelvin. What is the value of the activity coefficient of Pb2+ at 70.00 °C when the ionic strength is 0.014 M?
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![The extended Debye-Hückel equation, which incorporates temperature dependence, is expressed as follows:
\[
\log (\gamma) = \frac{(-1.825 \times 10^6) (\epsilon T)^{-\frac{1}{2}} z^2 \sqrt{\mu}}{1 + \frac{\alpha \sqrt{\mu}}{2.00\sqrt{\epsilon T}}}
\]
In this equation:
- \(\gamma\) is the activity coefficient.
- \(\epsilon\) represents the dielectric constant of water (a unitless quantity).
- \(T\) is the temperature in Kelvin.
- \(z\) denotes the charge of the ion.
- \(\mu\) signifies the ionic strength in moles per liter.
- \(\alpha\) is the ion size parameter in picometers.
The temperature dependence of the dielectric constant is given by:
\[
\epsilon = 79.755e^{(-4.6 \times 10^{-3})(T - 293.15)}
\]
where the temperature is in Kelvin.
**Problem:**
Calculate the value of the activity coefficient of \( \text{Pb}^{2+} \) at 70.0°C when the ionic strength is 0.014 M.
\[
\gamma =
\]
This exercise requires finding the activity coefficient, \(\gamma\), for lead ions at a specified temperature and ionic strength using the provided equations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6184893-1e67-4ed8-9784-fdd0cf2ed60a%2F6c9dbb73-e6f3-4232-9cf4-df669892e180%2Fenyfs2w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The extended Debye-Hückel equation, which incorporates temperature dependence, is expressed as follows:
\[
\log (\gamma) = \frac{(-1.825 \times 10^6) (\epsilon T)^{-\frac{1}{2}} z^2 \sqrt{\mu}}{1 + \frac{\alpha \sqrt{\mu}}{2.00\sqrt{\epsilon T}}}
\]
In this equation:
- \(\gamma\) is the activity coefficient.
- \(\epsilon\) represents the dielectric constant of water (a unitless quantity).
- \(T\) is the temperature in Kelvin.
- \(z\) denotes the charge of the ion.
- \(\mu\) signifies the ionic strength in moles per liter.
- \(\alpha\) is the ion size parameter in picometers.
The temperature dependence of the dielectric constant is given by:
\[
\epsilon = 79.755e^{(-4.6 \times 10^{-3})(T - 293.15)}
\]
where the temperature is in Kelvin.
**Problem:**
Calculate the value of the activity coefficient of \( \text{Pb}^{2+} \) at 70.0°C when the ionic strength is 0.014 M.
\[
\gamma =
\]
This exercise requires finding the activity coefficient, \(\gamma\), for lead ions at a specified temperature and ionic strength using the provided equations.
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