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?

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