A catalyst sphere with 30% voids to be used for the following dehydrogenationreaction: 2 6 2 4 2C H C H H  . At 300oC and 1 atm, the effective diffusion coefficientof ethane in a 0.5 cm sphere is 0.06 cm2/sec. Assuming a low conversion for H2 asthe by-product, determine the tortuosity of the pores? What does the value physicallysignify?The values of atomic and structural diffusion volume increments are: C=16.5;H=1.98; O=5.48; N=5.69; S=17; H2=7.07; Air=20.1; O2=16.6; H2O=12.7.In a different scenario, if the formation of H2 in the by-product is high, write ageneralized equation to find the value of diffusion coefficient

The tortuosity of the pores can be calculated using the formula:

Tortuosity (τ) = ε / D_eff

where ε is the porosity (void fraction) and D_eff is the effective diffusion coefficient.

Given that the porosity is 30% (or 0.3) and the effective diffusion coefficient is 0.06 cm^2/sec, we can substitute these values into the formula to get:

τ = 0.3 / 0.06 = 5

The tortuosity value physically signifies the complexity of the path that a molecule must take through the porous medium. A higher tortuosity means a more complex path, which can slow down the diffusion process.

In a different scenario where the formation of H2 in the by-product is high, the diffusion coefficient can be affected. A generalized equation to find the value of the diffusion coefficient in this case could be:

D = D_0 * exp(-Ea/RT)

where D is the diffusion coefficient, D_0 is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature. This equation is based on the Arrhenius equation and assumes that the diffusion process is temperature-dependent.