An industrial plant emits sulfur dioxide (SO₂) from a stack 50 m high. At a down‑wind distance of 2 km, the ground‑level concentration is given by the simplified Gaussian plume formula
$$ C = \frac{Q}{\pi u \sigma_y \sigma_z}\,\exp\!\left(-\frac{H^{2}}{2\sigma_z^{2}}\right) $$
where $Q$ is the emission rate (g s⁻¹), $u = 3$ m s⁻¹ is the wind speed, $\sigma_y = 0.08x$ and $\sigma_z = 0.10x$ with $x = 2000$ m, and $H = 50$ m. The ambient air‑quality standard for SO₂ is $0.05$ ppm; the background concentration is $0.01$ ppm. (At 25 °C, 1 ppm SO₂ = $ \dfrac{64}{24.45}$ mg m⁻³.)\n\n(a) What is the maximum permissible emission rate $Q_{\max}$ (in g s⁻¹) from the plant?\n\n(b) If the plant currently emits $50$ g s⁻¹, what percentage reduction in emissions is required to meet the standard?

Question

An industrial plant emits sulfur dioxide (SO₂) from a stack 50 m high. At a down‑wind distance of 2 km, the ground‑level concentration is given by the simplified Gaussian plume formula  
$$ C = \frac{Q}{\pi u \sigma_y \sigma_z}\,\exp\!\left(-\frac{H^{2}}{2\sigma_z^{2}}\right) $$
where $Q$ is the emission rate (g s⁻¹), $u = 3$ m s⁻¹ is the wind speed, $\sigma_y = 0.08x$ and $\sigma_z = 0.10x$ with $x = 2000$ m, and $H = 50$ m. The ambient air‑quality standard for SO₂ is $0.05$ ppm; the background concentration is $0.01$ ppm. (At 25 °C, 1 ppm SO₂ = $ \dfrac{64}{24.45}$ mg m⁻³.)\n\n(a) What is the maximum permissible emission rate $Q_{\max}$ (in g s⁻¹) from the plant?\n\n(b) If the plant currently emits $50$ g s⁻¹, what percentage reduction in emissions is required to meet the standard?

Accepted Answer

(a) ≈ 33 g s⁻¹; (b) ≈ 35 % reduction

Neco Model Questions Vol1 2019 Chemistry Question 7

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