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What is the diffusion coefficient of a solute with a molecular weight of 100 g/mol in water at 25°C, when the solute concentration is 0.01 M and the diffusion rate is 1.5 × 10^-5 cm^2/s?

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To calculate the diffusion coefficient  D  of a solute in a solvent, we can use the Stokes-Einstein equation:D = kT /  6r where:- D is the diffusion coefficient  cm/s - k is the Boltzmann constant  1.38  10^-23 J/K - T is the temperature in Kelvin  K -  is the dynamic viscosity of the solvent  in this case, water   Pas - r is the radius of the solute molecule  m First, we need to convert the temperature from Celsius to Kelvin:T = 25C + 273.15 = 298.15 KNext, we need to find the dynamic viscosity of water at 25C. According to the literature, the dynamic viscosity of water at 25C is approximately 8.9  10^-4 Pas.Now, we need to find the radius of the solute molecule. We can use the following equation to estimate the radius based on the molecular weight  MW  of the solute:r =  3MW /  4N  ^1/3 where:- r is the radius of the solute molecule  m - MW is the molecular weight of the solute  g/mol - N is Avogadro's number  6.022  10^23 mol^-1 -  is the density of the solute  g/cm Since we don't have the density of the solute, we cannot calculate the exact radius. However, the problem states that the diffusion rate is 1.5  10^-5 cm/s. This value is already the diffusion coefficient  D  that we are looking for.Therefore, the diffusion coefficient of the solute in water at 25C is:D = 1.5  10^-5 cm/s

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