Question

A sheet of polyethylene 1.5-mm thick is being used as an oxygen barrier at a temperature of 600K. If the flux is 2.48 x 10-5 kg/m2 s, what concentration of oxygen must be maintained on the high-pressure side to ensure that the concentration

Answer 1

Complete Question

The complete question is shown on the first uploaded image

Answer:

The concentration of high-pressure side is
`C_1 = 0.722 \ kg/m^3`

Step-by-step explanation:

From the question we are told that

The thickness of the polyethylene is
`d = 1.5 \ mm = 0.0015 \ m`

The temperature is
`T = 600 \ K`

The flux is
`JA = 2.48 *10^(-5) \ kg/m^2\cdot s`

The concentration on the low-pressure side is
`C_2 = 0.5 \ kg/m^3`

The initial diffusivity is
`D_o = 6.2 *10^(-4) \ m^2 /s`

The activation energy for diffusion is
`Q_d = 41 \ kJ /mol = 41*10^3 J /mol`

Generally the diffusivity of the oxygen at 600 K can be mathematically evaluated as

`D = D_o * e^{- (Q_d)/(R * T ) }`

substituting values

`D = 6.2*10^(-4) * e^{- (41 *10^3)/(8.314 * 600 ) }`

`D = 1.671 *10^(-7) \ m^2 /s`

Generally the flux is mathematically represented as

`JA = D * (C_1 -C_2)/(d)`

Where
`C_1` is the concentration of oxygen at the higher side

So

`C_1 = d * (JA)/(D) + C_2`

substituting values

`C_1 = 0.0015 * (2.48*10^(-5))/(1.671*10^(-7)) + 0.5`

`C_1 = 0.722 \ kg/m^3`