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Chemicals are stored in a laboratory with volume \(V\left(\mathrm{m}^{3}\right) .\) As a consequence of poor laboratory practices, a hazardous species, A, enters the room air (from inside the room) at a constant rate \(\dot{m}_{\mathrm{A}}(\mathrm{g} \mathrm{A} / \mathrm{h})\) The room is ventilated with clean air flowing at a constant rate \(\dot{V}_{\text {air }}\left(\mathrm{m}^{3} / \mathrm{h}\right) .\) The average concentration of A in the room air builds up until it reaches a steady-state value \(C_{\mathrm{A}, \mathrm{r}}\left(\mathrm{g} \mathrm{A} / \mathrm{m}^{3}\right)\) (a) List at least four situations that could lead to A getting into the room air. (b) Assume that the A is perfectly mixed with the room air and derive the formula $$\dot{m}_{\mathrm{A}}=\dot{V}_{\mathrm{air}} C_{\mathrm{A}}$$ (c) The assumption of perfect mixing is never justificd when the enclosed space is a room (as opposed to, say, a stirred reactor). In practice, the concentration of A varies from one point in the room to another: it is relatively high near the point where A enters the room air and relatively low in regions far from that point, including the ventilator outlet duct. If we say that \(C_{\mathrm{A}, \text { duct }}=k C_{\mathrm{A}}\) where \(k < 1\) is a nonideal mixing factor (generally between 0.1 and \(0.5,\) with the lowest value corresponding to the poorest mixing), then the equation of Part (b) becomes $$\dot{m}_{\mathrm{A}}=k \dot{V}_{\mathrm{air}} C_{\mathrm{A}}$$ Use this equation and the ideal-gas equation of state to derive the following expression for the average mole fraction of \(A\) in the room air: $$y_{\mathrm{A}}=\frac{\dot{m}_{\mathrm{A}}}{k \dot{V}_{\mathrm{air}}} \frac{R T}{M_{\mathrm{A}} P}$$ where \(M_{\mathrm{A}}\) is the molecular weight of \(\mathrm{A}\) (d) The permissible exposure level (PEL) for styrene \((M=104.14\) ) defined by the U.S. Occupational Safcty and Health Administration is 50 ppm (molar basis). \(^{21}\) An open storage tank in a polymerization laboratory contains styrene. The evaporation rate from this tank is estimated to be \(9.0 \mathrm{g} / \mathrm{h}\). Room temperature is \(20^{\circ} \mathrm{C}\). Assuming that the laboratory air is reasonably well mixed (so that \(k=0.5\) ), calculate the minimum ventilation rate \(\left(\mathrm{m}^{3} / \mathrm{h}\right)\) required to keep the average styrene concentration at or below the PEL. Then give several reasons why working in the laboratory might still be hazardous if the calculated minimum ventilation rate is used. (e) Would the hazard level in the situation described in Part (d) increase or decrease if the temperature in the room were to increase? (Increase, decrease, no way to tell.) Explain your answer, citing at least two effects of temperature in your explanation.

Step by step solution

01

Part (a) - Situations introducing hazardous species A

1. Improper handling or storage of chemical substances known to off gas hazardous species A.\n2. Accidental spillage of chemicals containing species A.\n3. Lack of proper sealing on containers holding species A.\n4. Chemical reactions taking place in the room producing species A as a byproduct.

02

Part (b) - Derivation of the formula

The rate of accumulation of species A in the room is equal to the rate of its entry \(\dot{m}_{A}\) minus its rate of removal which is given by \(\dot{V}_{air} C_{A}\). In a steady state condition, accumulation is zero, hence, \(\dot{m}_{A} = \dot{V}_{air} C_{A}\).

03

Part (c) - Modification for nonideal mixing and deriving average mole fraction

In case of nonideal mixing, the rate of removal of species A becomes \(k \dot{V}_{air} C_{A}\). Hence, the equation becomes \(\dot{m}_{A} = k \dot{V}_{air} C_{A}\). Applying the ideal gas law, express the concentration \(C_{A}\) as \(n_{A}/V_{air}\), where \(n_{A}\) is the number of moles, given as \(\dot{m}_{A}/M_{A}\). Substitute this into the equation to get \(y_{A} = \frac{\dot{m}_{A}}{k \dot{V}_{air}} \frac{R T}{M_{A} P}\), where \(y_{A}\) is the mole fraction of A.

04

Part (d) - Calculating Minimum Ventilation Rate

Given that the permissible exposure level for styrene is 50 ppm, this has to be converted into mole fraction, \(y_{styrene} = 50 parts per million = 50 x 10^{-6}\). Substitute the given values into the equation \(y_{A} = \frac{\dot{m}_{A}}{k \dot{V}_{air}} \frac{R T}{M_{A} P}\) and solve for \(\dot{V}_{air}\), the minimum ventilation rate. Working might still be hazardous due to: Variations in the concentration of styrene in different locations within the room, Other potential sources of styrene or other harmful substances, Poor assumption of perfect mixing.

05

Part (e) - Temperature Effects on Hazard Level

Increasing the temperature in the room would increase the hazard level. This is because higher temperature would: Increase the volatilization rate of styrene, hence introducing more of it into the room air. Increase the diffusion rate of styrene, potentially leading to higher exposure in regions of the room that were previously considered safe.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Hazardous Species Ventilation

When handling chemicals in a lab setting, the matter of safety is paramount. Understanding the concept of hazardous species ventilation is essential for maintaining air quality and reducing potential risks. This involves the process of removing airborne contaminants through continuous flow of fresh air. Imagine this as a dilution process where 'bad' air is replaced by 'good', clean air at a rate sufficient to keep the concentration of hazardous substances at acceptable levels.

Key to this is ensuring that there are no stagnant zones where contaminants might accumulate. Situations that can preempt the need for vigilant ventilation can include accidental spills, reactions that produce airborne byproducts, or even the off-gassing of certain materials due to improper storage. It's like having a busy and slightly messy 'roommate' in the form of a chemical compound that you have to continuously clean after to maintain a livable environment. In essence, understanding the ventilation rate hinges on balancing the introduction of hazardous species with their removal to sustain a safe indoor air quality.

Steady-State Concentration Derivation

The concept of steady-state concentration derivation can seem quite complex, but let’s break it down. A steady state is like a tug-of-war match where both teams are equally strong—there’s a lot of activity, but no movement. In our chemical 'match', the rate at which a contaminant is added to the lab air is countered by the rate at which the ventilation system removes it.

The derived steady-state equation, \(\dot{m}_{A} = \dot{V}_{\text{air}} C_{A}\), succinctly shows this balance. This formula is a snapshot of a dynamic equilibrium, meaning that even though the substances are still being emitted and ventilated, their overall concentration in the air remains constant. It’s a pivotal concept in maintaining safe lab environments, ensuring that the exposure to hazardous substances remains consistently within safe limits.

Ideal Gas Law Application

When faced with the question of how to relate the amount of a gas to volume, temperature, and pressure, the ideal gas law is the go-to tool. By applying this law, we’re equipped to solve a variety of problems, such as gases mixing in ventilation or reactions scaling from test tubes to industrial reactors. The longevity of this law lies in its simplicity and adaptability.

In the context of our lab scenario, the ideal gas law recalibrates our understanding of concentration and ventilation. Specifically, it allows us to express the concentration of a contaminant as part of the room's air mixture and defines the relationship between mass, volume, and mole fraction. Through the equation \(y_A = \frac{\dot{m}_A}{k \dot{V}_{\text{air}}} \frac{RT}{M_A P}\), the mole fraction—an indication of how 'diluted' our problematic 'roommate' is—gives a clearer picture of air quality. Always remember, this equation stands as a testament to the power of understanding basic physical relationships and applying them to complex systems.

Permissible Exposure Level Calculation

Determining the permissible exposure level (PEL) is like setting a strict curfew for the concentration of hazardous substances in the workplace: it's the maximum amount allowed, no excuses. Calculating the correct ventilation rate to stay within this 'curfew' involves not just math but a careful consideration of working conditions, like the rate at which chemicals evaporate into the air and the mixing effectiveness of the ventilation system.

In cases where you have a value in parts per million (ppm), like the PEL for styrene, you can convert it to a mole fraction. Use this mole fraction to back-calculate the minimum amount of fresh air needed per hour to 'escort out' enough of the hazardous 'guest'. Yet this number isn't the be all and end all. There could still be 'hot spots' of high concentrations, or changes in room temperature could invite our problematic 'guest' to be more 'active'. Thus, understanding the PEL and how to calculate the required ventilation provides not just a figure for engineers to aim at but also highlights the dynamic nature of maintaining safety in chemical environments.