A biomass power station burns forestry residue which has 2000 ppm potassium in it and produces 2% ash by weight (think Ive worded that right). I need to find the fraction of K2O in the ash, but only the fraction of K in the fuel as a whole is given.
To find the fraction of K2O in the ash, we need to know the total amount of potassium (K) in the fuel and the amount of ash produced.
Given information:
- Potassium concentration in the forestry residue (fuel): 2000 ppm (parts per million)
- Ash content in the fuel: 2% by weight
First, let's calculate the amount of potassium (K) in the fuel.
1. Convert the parts per million (ppm) concentration to a fraction:
- 2000 ppm = 2000/1,000,000 = 0.002 (fraction)
This means that for every kilogram of the fuel, there are 0.002 kilograms (2 grams) of potassium.
Now, let's calculate the amount of ash produced.
2. Assume we have 1 kilogram of the fuel.
- Ash content: 2% by weight
- Ash content = 2/100 * 1 kg = 0.02 kg
Next, we need to find the fraction of K2O in the ash.
3. Calculate the fraction of K2O in the ash:
- To do this, we need to know the molar mass of K2O, which is 94.2 g/mol.
- Since K2O has one potassium atom (K), the molar mass of potassium (K) is 39.1 g/mol.
The molar ratio between K2O and K is 2:1. This means that for every 2 moles of K2O, there is 1 mole of K.
4. Calculate the amount of potassium (K) in the ash:
- Ash content = 0.02 kg of ash
- Convert kg to grams: 0.02 kg * 1000 = 20 grams
5. Determine the moles of potassium (K) in the ash:
- Moles of K = Mass of K / Molar mass of K
- Moles of K = 20 g / 39.1 g/mol ≈ 0.511 moles of K
6. Calculate the moles of K2O:
- Since the molar ratio between K2O and K is 2:1, there will be half as many moles of K2O.
- Moles of K2O = 0.511 moles of K / 2 ≈ 0.2555 moles of K2O
Finally, we can find the fraction of K2O in the ash:
7. Fraction of K2O in the ash:
- Fraction = Moles of K2O / Total moles
- Since the total moles are given by the moles of K2O, the fraction is 1.
So, the fraction of K2O in the ash is 1.