Chapter 12: Problem 30

Calculate the number of Frenkel defects per cubic meter in silver chloride at 350C. The energy for defect formation is 1.1 eV, whereas the density for AgCl is 5.50 g/cm3 at 350C.

Short Answer

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Question: Calculate the number of Frenkel defects per cubic meter in silver chloride (AgCl) at 350°C, given that the energy for defect formation is 1.1 eV and the density of AgCl at 350°C is 5.50 g/cm^3. Answer: The number of Frenkel defects per cubic meter in silver chloride at 350°C is approximately 1.28 x 10^9 defects/m^3.

Step by step solution

Convert the temperature to Kelvin

To work with the temperature in our calculations, we first need to convert the given temperature from Celsius to Kelvin. T(K) = T(°C) + 273.15 T(K) = 350°C + 273.15 = 623.15 K Now, we have the temperature in Kelvin as 623.15 K.

Calculate the number of AgCl molecules per cubic meter

Given the density of AgCl at 350°C is 5.50 g/cm^3, we will convert this to kg/m^3 and then use Avogadro's number and the molar mass of AgCl to find the number of AgCl molecules per cubic meter. Density of AgCl = 5.50 g/cm^3 * (1000 kg/m^3 / 1 g/cm^3) = 5500 kg/m^3 Molar mass of AgCl = Molar mass of Ag + Molar mass of Cl = (107.87 + 35.45) g/mol = 143.32 g/mol Number of moles of AgCl per cubic meter = Density / Molar mass = 5500 kg/m^3 / (143.32 g/mol * 0.001 kg/g) = 38364.82 mol/m^3 Number of AgCl molecules per cubic meter = Number of moles * Avogadro's number = 38364.82 mol/m^3 * 6.022 x 10^23 molecules/mol = 2.309 x 10^28 molecules/m^3

Calculate the equilibrium concentration of Frenkel defects

Now, using the energy for defect formation (1.1 eV) and the Boltzmann constant (k = 8.617 x 10^{-5} eV/K), we can calculate the equilibrium concentration of Frenkel defects. Equilibrium concentration of defects = N * exp(-E / kT) Here, N is the number of lattice sites or, in this case, AgCl molecules per cubic meter, E is the energy for defect formation in eV, k is the Boltzmann constant in eV/K, and T is the temperature in Kelvin. Plugging in the values: Equilibrium concentration of defects = 2.309 x 10^28 molecules/m^3 * exp(-1.1 eV / (8.617 x 10^{-5} eV/K * 623.15 K)) = 2.309 x 10^{28} molecules/m^3 * exp(-17.92)