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What is the diffusion coefficient of oxygen in air at a temperature of 298 K and a pressure of 1 atm? Show the calculation and units used.

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To calculate the diffusion coefficient of oxygen in air at a given temperature and pressure, we can use the Chapman-Enskog equation, which is derived from the kinetic theory of gases. The equation is as follows:D =  3/16  *  k * T /   *   ^0.5 *  1 / P where:D = diffusion coefficient  m/s k = Boltzmann constant  1.38064852  10 J/K T = temperature  K  = pi  3.14159265359  = reduced mass of the gas pair  kg P = pressure  Pa First, we need to find the reduced mass    of the gas pair, which is given by: =  m1 * m2  /  m1 + m2 where m1 and m2 are the molar masses of the two gases. In this case, we are considering the diffusion of oxygen  O  in air, which is primarily composed of nitrogen  N . The molar masses of O and N are 32 g/mol and 28 g/mol, respectively. We need to convert these values to kg/mol:m1 = 32 g/mol *  1 kg / 1000 g  = 0.032 kg/molm2 = 28 g/mol *  1 kg / 1000 g  = 0.028 kg/molNow, we can calculate the reduced mass: =  0.032 kg/mol * 0.028 kg/mol  /  0.032 kg/mol + 0.028 kg/mol  = 0.000448 kg/molNext, we need to convert the pressure from atm to Pa:1 atm = 101325 PaNow, we can plug all the values into the Chapman-Enskog equation:D =  3/16  *  1.38064852  10 J/K * 298 K /  3.14159265359 * 0.000448 kg  ^0.5 *  1 / 101325 Pa D  2.12  10 m/sTherefore, the diffusion coefficient of oxygen in air at a temperature of 298 K and a pressure of 1 atm is approximately 2.12  10 m/s.
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