Question

8. A coal plant emits 0.40% SO2 by volume at a temperature of 145oC and 101.3 kPa from the stack. The total volume of gas emitted is 2.5 x104 m3/min. How many m3 of SO2 are emitted per minute at these conditions? How many moles of SO2 are emitted per minute at these conditions? How many kgs of SO2 are emitted per minute at these conditions? How many kgs of SO2 are emitted per minute at 25oC?

Answer 1

Answer – We are given, percent of SO₂ gas = 0.40 % , T = 145^oC , P = 101.3 kPa

Total volume of gas emitted = 2.5 x 10⁴ m³/min

We know for 1 min there is 2.5 x 10⁴ m³ volume gas emitted and out of that 0.40 % is SO₂

So, for each min, SO₂ emitted as follow –

100 % = 2.5 x 10⁴ m³

0.40 %= ?

= 100 m³

100 m³ of SO₂ are emitted per minute at these conditions.

Now we calculated volume of SO₂ gas and we are given temperature and pressure

We know, 101.3 kPa = 1 atm

1 m³ = 1000 L

So, 100 m³ = ? L

= 1.0 x 10⁵ L

T= 145 + 273.15 = 418.15 K

We know idea gas law

P x V = n x R x T

n = PV / RT

   = 1.0 x 10⁵ L x 1 atm / 0.0821 L.atm.mol^-1.K^-1 x 418.15 K

   = 2913 moles of SO₂

2913 moles of SO₂ are emitted per minute at these conditions.

Now we need to convert this moles to mass

We know formula

Mass = moles x molar mass

         = 2913 moles x 64.066 g/mol

         = 1.87 x 10⁵ g

We know

1.0 g = 0.001 kg

1.87 x 10⁵ g = ? kg

= 187 kg

187 kgs of SO₂ are emitted per minute at these conditions.

Now we need to calculate how many kgs of SO2 are emitted per minute at 25oC?

T = 25 +273.15 = 298.15 K

We know idea gas law

P x V = n x R x T

n = PV / RT

   = 1.0 x 10⁵ L x 1 atm / 0.0821 L.atm.mol^-1.K^-1 x 298.15 K

   = 4085.3 moles of SO₂

Now we need to convert this moles to mass

We know formula

Mass = moles x molar mass

         = 4085.3 moles x 64.066 g/mol

         = 2.62 x 10⁵ g

We know

1. g = 0.001 kg
2. 62 x 10⁵ g = ? kg

= 262 kg

262 kgs of SO₂ are emitted per minute at these 25^o C.