The size of the ionic atmosphere, called the Debye radius, is 1/K, where K is given bye2 NA 1/2VIE0 ɛkBTK =where e is the electronic charge, NA Avogadro's constant, ɛo the permittivity of vacuum (8.854×10-12 c²·n-1.m-2), ɛ the dielectric constant of the solvent, kB the Boltzmann constant, T the absolutetemperature, and I the ionic strength. Calculate the Debye radius in a 0.036 m aqueous Na2S203 solution at 25°C. (Assume the density of the solution at 25°C is 1.0029 g•cm-3.)4.0 4.208Å

Answered: Image /qna-images/answer/2de140b5-64a2-4393-b354-c1c38dcf702a.jpgk=e2NAε0εkBT1/2IHere, medium is water since the solution is aqueous. Thus, ε for water at 250C = 78.2k=(1.6×10-19 C)2×6.02×1023 mol-1(8.854×10-12 C2N-1.m-2×78.2×1.38×10-23 J.K-1×(25+273) K1/2108.3 mol1/2m3/2k=765617137.4 mol-1/2J1/2m-1N-1/2×mol1/2m3/2k=765617137.4 N1/2m-1/2J-1/2Since, 1 J = 1 N.m1 J1/2=1 N1/2.m1/2So,k=765617137.4 N1/2m-1/2N1/2.m1/2k=765617137.4 m-1Debye length=1k=1765617137.4 m-1=1.31×10-9 mDebye length=1.31×10-9 m×1010 Angstrom/mDebye length=13.1 Angstrom

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The size of the ionic atmosphere, called the Debye radius, is 1/K, where k is given by e2 NA 1/2 where e is the electronic charge, NA Avogadro's constant, ɛn the permittivity of vacuum (8.854x10-12 c2.N-1.m-2), e the dielectric constant of the solvent, kg the Boltzmann constant, T the absolute temperature, and I the ionic strength. Calculate the Debye radius in a 0.036 m aqueous Nazs203 solution at 25°C. (Assume the density of the solution at 25°C is 1.0029 g.cm-3.) 4 4.208

The size of the ionic atmosphere, called the Debye radius, is 1/K, where k is given by e2 NA 1/2 where e is the electronic charge, NA Avogadro's constant, ɛn the permittivity of vacuum (8.854x10-12 c2.N-1.m-2), e the dielectric constant of the solvent, kg the Boltzmann constant, T the absolute temperature, and I the ionic strength. Calculate the Debye radius in a 0.036 m aqueous Nazs203 solution at 25°C. (Assume the density of the solution at 25°C is 1.0029 g.cm-3.) 4 4.208

Chemistry

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ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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Kinetic-Theory of Gases

Kinetic theory of gases is the model or method which was developed in the 19th century by Maxwell and Boltzmann. This is possible as the interatomic force which is of short-range forces that are important for solids and liquids can be neglected for gases. This theory or gas law gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. This theory is very helpful to correctly explain the specific heat capacities of many gases, kinetic energy and it also explains the transport qualities such as viscosity, thermal conductivity, and diffusion with molecular parameters. As stated in the kinetic-molecular theory, the temperature of a substance or gas particle is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles, called average kinetic energy.

Question

The size of the ionic atmosphere, called the Debye radius, is 1/K, where K is given by
e2 NA 1/2
VI
E0 ɛkBT
K =
where e is the electronic charge, NA Avogadro's constant, ɛo the permittivity of vacuum (8.854×10-12 c²·n-1.m-2), ɛ the dielectric constant of the solvent, kB the Boltzmann constant, T the absolute
temperature, and I the ionic strength. Calculate the Debye radius in a 0.036 m aqueous Na2S203 solution at 25°C. (Assume the density of the solution at 25°C is 1.0029 g•cm-3.)
4.0 4.208
Å

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