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23 March, 16:17

Atmospheric pollution is a problem that has received much attention. Not all pollution, however, is from industrial sources. Volcanic eruptions can be a significant source of air pollution. The Kilauea volcano in Hawaii emits 200-300 t (1 t = 103 kg) of SO2 each day. If this gas is emitted at 800 °C and 1.0 atm, what volume of gas is emitted?

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  1. 23 March, 20:12
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    For 200t per day, the volume of gas is 2.76*10⁵ m³

    For 300t per day, the volume of gas is 4.13*10⁵ m³

    Explanation:

    It is stated that 1t = 10³ kg

    Therefore,

    For 200t per day:

    The number of moles of SO₂ is calculated as follows,

    n (SO₂) = m / (molar mass)

    where

    m is the mass of SO₂ molar mass is the sum of the molecular masses of Sulphur (S) and Oxygen (O)

    Thus,

    n (SO₂) = (200*10³kg) / (64*10⁻³kg. mol⁻¹)

    = 3.13*10⁶ mol

    Therefore, the volume is determined as follows,

    V = nRT/P

    where

    n is the number of moles of SO₂ R is the gas constant T is the temperature in Kelvin (K) P is the pressure of the gas

    Thus,

    To convert from degrees celcius to Kelvin, we 273 to the given temperature.

    V = ((3.13*10⁶ mol) (0.08206dm³. atm. mol⁻¹. K⁻¹) (800+273K)) / 1 atm

    = 2.76*10⁸ dm³

    For the answer to be in m³, we divide by 10³. Thus,

    V = 2.76*10⁵ m³

    For 300t per day:

    The number of moles of SO₂ is calculated as follows,

    n (SO₂) = m / (molar mass)

    where

    m is the mass of SO₂ molar mass is the sum of the molecular masses of Sulphur (S) and Oxygen (O)

    Thus,

    n (SO₂) = (300*10³kg) / (64*10⁻³kg. mol⁻¹)

    = 4.69*10⁶ mol

    Therefore, the volume is determined as follows,

    V = nRT/P

    where

    n is the number of moles of SO₂ R is the gas constant T is the temperature in Kelvin (K) P is the pressure of the gas

    Thus,

    To convert from degrees celcius to Kelvin, we 273 to the given temperature.

    V = ((4.69*10⁶ mol) (0.08206dm³. atm. mol⁻¹. K⁻¹) (800+273K)) / 1 atm

    = 4.13*10⁸ dm³

    For the answer to be in m³, we divide by 10³. Thus,

    V = 4.13*10⁵ m³
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