When handling corrosive and toxic substances, chemical resistant gloves should be worn. When selecting gloves to handle a substance, the suitability of the gloves should be considered. Depending on the material of the gloves, they could be easily permeable by some substances. An employee is handling tetrachloroethylene solution for a metal-cleaning process. Dermal exposure to tetrachloroethylene can cause skin irritation, and long-term exposure to it can have adverse neurological effects on humans. As a protective measure, the employee wears rubber-blend gloves while handling the tetrachloroethylene solution. The average thickness of the gloves is \(0.67 \mathrm{~mm}\), and the mass diffusivity of tetrachloroethylene in the gloves is \(3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}\). Estimate how long can the employee's hand be in contact with the tetrachloroethylene solution before the concentration of the solution at the inner glove surface reaches \(1 \%\) of the concentration at the outer surface. Is this type of glove suitable for handling tetrachloroethylene solution?

Step by step solution

01

Identify the relevant formula

For this problem, we will use Fick's second law of diffusion, which is given by: \(\frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}\) Here, \(C\) is the concentration, \(t\) is time, \(D\) is the mass diffusivity, and \(x\) is the distance through the material.

02

Consider steady-state conditions

Since we are looking for the time it takes for the concentration of the solution at the inner glove surface to reach \(1 \%\) of the concentration at the outer surface, we consider a steady-state condition. In steady-state, there is no overall change in concentration with respect to time, so \(\frac{\partial C}{\partial t} = 0\). This simplifies Fick's second law to: \(\frac{\partial^2 C}{\partial x^2} = 0\) This means that, under steady-state conditions, the concentration gradient across the glove is linear. So, we can represent the concentration at any point within the glove using a linear equation.

03

Find the concentration gradient

Let \(C_0\) represent the concentration at the outer surface and \(C_I = 0.01 C_0\) represent the concentration at the inner surface of the glove. We can represent the concentration at any point within the glove as a linear function of distance \(x\): \(C(x) = C_0 - m x\) Here, \(m\) is the slope of the concentration gradient. We can obtain the value of \(m\) using the concentration at the inner surface and the thickness of the glove: \(C_I = C_0 - m L\) Solving for \(m\), we get: \(m = \frac{C_0 - C_I}{L}\), where \(L = 0.67 \times 10^{-3} \mathrm{~m}\) is the thickness of the glove.

04

Calculate the mass flux across the glove

Using Fick's first law of diffusion, we can calculate the mass flux \(J\) across the glove: \(J = -D \frac{dC}{dx}\) Substituting the value of \(m\) and the mass diffusivity \(D = 3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s}\), we get: \(J = -3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} \times \frac{C_0 - 0.01 C_0}{0.67 \times 10^{-3} \mathrm{~m}}\)

05

Estimate the time

To calculate the time it takes for the concentration at the inner surface to reach \(1 \%\) of the concentration at the outer surface, we need to relate the mass flux to the concentration at the inner surface. From the mass balance equation, we can write: \(J = \frac{C_I}{t}\) Solving for \(t\), we get: \(t = \frac{C_I}{J}\) Substitute the calculated value of \(J\) from step 4 and simplify: \(t = \frac{0.01 C_0}{-3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} \times \frac{C_0 - 0.01 C_0}{0.67 \times 10^{-3} \mathrm{~m}}}\) Since we are interested in the time, we can cancel out \(C_0\) from the equation: \(t = \frac{0.01}{-3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} \times \frac{1 - 0.01}{0.67 \times 10^{-3} \mathrm{~m}}} = 22.39 \mathrm{~s}\).

06

Evaluate the suitability of the gloves

Since it takes around 22.39 seconds for the concentration of tetrachloroethylene at the inner surface to reach \(1 \%\) of the concentration at the outer surface, the rubber-blend gloves can be considered unsuitable for long-term exposure or handling of tetrachloroethylene solution, especially considering the adverse effects of dermal contact. It would be necessary to evaluate other types of gloves or explore additional protective measures for handling the tetrachloroethylene solution.

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