Chloropicrin, also known as PS and nitrochloroform, is a chemical compound currently used as a broad-spectrum antimicrobial, fungicide, herbicide, insecticide, and nematicide. In World War I, the Germans used it as tear gas since it is also an airway irritant. This substance is a liquid at room temperatures. Suppose there was a small spill of this material on a paved surface at a chemical plant. The spill has a width of 0.8 ft and a length of 2.5 ft. The prevailing wind is 10 miles per hour in a direction parallel to the length of the spilled material. Estimate the rate of evaporation in grams per hour of this material. Chloropicrin has a diffusivity in air of 0.088 cm2 s−1. At 25°C, its vapor pressure is such that its equilibrium concentration in air would be equal to 0.211 g L−1. The kinematic viscosity of air under these conditions is 0.157 cm2 s−1. Carefully state your assumptions.
The Correct Answer and Explanation is :
To estimate the evaporation rate of chloropicrin from a spill on a paved surface, we can use the following formula:
[ E = \frac{0.1288 \cdot A \cdot P \cdot M^{0.667} \cdot u^{0.78}}{T} ]
Where:
- ( E ) is the evaporation rate in kg/min,
- ( A ) is the surface area of the spill in m²,
- ( P ) is the vapor pressure of chloropicrin in kPa,
- ( M ) is the molecular weight of chloropicrin in g/mol,
- ( u ) is the wind speed in m/s,
- ( T ) is the absolute temperature in Kelvin.
Given Data:
- Spill dimensions: 0.8 ft (width) × 2.5 ft (length)
- Wind speed: 10 miles per hour
- Vapor pressure of chloropicrin at 25°C: 0.211 g/L
- Molecular weight of chloropicrin: 164.38 g/mol
- Temperature: 25°C (298.15 K)
Conversions:
- Surface Area: 0.8 ft × 2.5 ft = 2.0 ft²
- Converting to square meters:
- 1 ft² = 0.092903 m²
- 2.0 ft² × 0.092903 m²/ft² = 0.1858 m²
- Wind Speed: 10 miles per hour
- Converting to meters per second:
- 1 mile = 1609.34 meters
- 1 hour = 3600 seconds
- (10 miles/hour) × (1609.34 meters/mile) / (3600 seconds/hour) ≈ 4.47 m/s
- Vapor Pressure: 0.211 g/L
- Converting to kPa:
- 1 g/L = 1 kg/m³
- Using the ideal gas law:
- PV = nRT
- P = (C × R × T) / M
- Where:
- C = concentration in kg/m³
- R = 8.314 J/(mol·K)
- T = temperature in K
- M = molecular weight in kg/mol
- P = (0.211 kg/m³ × 8.314 J/(mol·K) × 298.15 K) / 0.16438 kg/mol
- P ≈ 3.19 kPa
Calculation:
[ E = \frac{0.1288 \times 0.1858 \, \text{m}^2 \times 3.19 \, \text{kPa} \times (164.38)^{0.667} \times (4.47)^{0.78}}{298.15} ]
[ E \approx \frac{0.1288 \times 0.1858 \times 3.19 \times 45.89 \times 3.72}{298.15} ]
[ E \approx \frac{35.6}{298.15} ]
[ E \approx 0.1194 \, \text{kg/min} ]
Converting to grams per hour:
[ 0.1194 \, \text{kg/min} \times 1000 \, \text{g/kg} \times 60 \, \text{min/hour} = 7164 \, \text{g/hour} ]
Assumptions:
- Temperature Uniformity: The temperature of the spilled chloropicrin is assumed to be uniform and equal to the ambient temperature of 25°C.
- Steady-State Conditions: The evaporation rate is calculated under steady-state conditions, implying that the rate remains constant over time.
- Negligible Heat Transfer Effects: Heat transfer between the liquid, air, and the paved surface is assumed to be negligible, meaning the evaporation is primarily driven by the vapor pressure and wind speed.
- Ideal Gas Behavior: The vapor behaves as an ideal gas, allowing the use of the ideal gas law for conversions.
- Consistent Wind Speed: The wind speed is constant at 10 miles per hour, and it flows parallel to the length of the spill, enhancing evaporation.
- Flat Surface: The paved surface is flat and impermeable, preventing any infiltration of the liquid.
This estimation provides a theoretical evaporation rate based on the given parameters and assumptions. In real-world scenarios, factors such as surface roughness, ambient humidity, and potential chemical interactions could influence the actual evaporation rate.