Question

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?

Short answer

Answer: It takes 22.39 seconds for the concentration of tetrachloroethylene at the inner surface of the rubber-blend glove to reach 1% of the concentration at the outer surface.

Step-by-step solution

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.

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.

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.

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: \(J = -3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} \times \frac{C_0 - 0.01 C_0}{0.67 \times 10^{-3} \mathrm{~m}}\)

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: \(t = \frac{0.01}{-3 \times 10^{-8} \mathrm{~m}^{2} / \mathrm{s} \times \frac{1 - 0.01}{0.67 \times 10^{-3} \mathrm{~m}}} = 22.39 \mathrm{~s}\).

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.

Key concepts

Mass Diffusivity

Mass diffusivity is a key concept when evaluating how substances move through materials, like gloves. It refers to the ability of a chemical to spread or move through another medium. In this context, we're looking at how tetrachloroethylene spreads through the rubber gloves. This property is crucial because a high mass diffusivity suggests that a substance can quickly penetrate a material.
In the glove material, tetrachloroethylene has a mass diffusivity of \(3 \times 10^{-8} \mathrm{~m}^{2}/\mathrm{s}\). This value indicates how quickly the chemical can diffuse through the gloves. A higher number would mean faster penetration, putting the wearer at risk. It's important to calculate and understand these factors to ensure proper protection is provided.
Mass diffusivity affects not only glove safety but also guides which materials are most suitable for certain chemicals. For protective gear selection, choosing materials with low mass diffusivity for harmful chemicals enhances safety, reducing exposure risk.

Steady-State Conditions

In diffusion processes, understanding steady-state conditions is essential. These conditions mean that the concentrations of the diffusing substance do not change over time, resulting in a constant concentration gradient. For the gloves, this equilibrium is used to estimate the time before tetrachloroethylene reaches a certain level.
In mathematical terms, if we assume steady-state, the concentration gradient is linear across the material. In other words, there's a consistent drop in concentration from one side of the glove to the other. This simplification allows engineers to easily calculate and predict diffusion behavior, using Fick's laws.
For this glove scenario, assuming steady-state conditions helped simplify calculations to determine that the tetrachloroethylene concentration on the inside would reach 1% of the outside concentration in 22.39 seconds. Recognizing this condition helps in making informed decisions about protective gear's effectiveness.

Chemical Safety

Chemical safety is a critical consideration when working with toxic and corrosive substances. It involves implementing measures to prevent accidents and exposure, especially through skin contact. When handling tetrachloroethylene, safety measures must be taken due to the chemical's properties.
To evaluate chemical safety, factors such as the type of chemical, its concentration, and potential exposure are considered. Knowing these can guide the selection of PPE (Personal Protective Equipment), like gloves, to protect against harmful effects.
Accurate assessment, including understanding diffusion rates and material properties, contribute to ensuring safety. Chemical safety protocols demand rigorous analysis of situations to appropriately select materials that offer the right amount of resistance to chemical permeation, like gloves that prevent or minimize exposure to tetrachloroethylene.

Protective Gloves

Protective gloves are a basic yet vital form of PPE, used to shield workers from toxic chemical exposure. The choice of material is crucial. It must resist the chemical in question, such as tetrachloroethylene, to prevent it from reaching the skin.
For the gloves in this example, made from rubber-blend, understanding their suitability involves checking their thickness, material quality, and the chemical's mass diffusivity. Since these gloves allow a 1% concentration of tetrachloroethylene to penetrate in just 22.39 seconds, they are deemed unsuitable for prolonged exposure.
Choosing the right gloves demands knowledge of chemical properties and glove materials. Inadequate protection can lead to health hazards, underscoring the importance of proper glove selection based on comprehensive analysis of the interaction between the glove material and the chemicals handled.