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Answer :
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Part 1: Calculate the moles of [tex]\( KNO_3 \)[/tex] needed to produce 99.8 kg of [tex]\( O_2 \)[/tex]
1. Determine the mass of [tex]\( O_2 \)[/tex] in grams:
- Convert 99.8 kg of [tex]\( O_2 \)[/tex] to grams: [tex]\( 99.8 \, \text{kg} = 99,800 \, \text{g} \)[/tex].
2. Find the number of moles of [tex]\( O_2 \)[/tex]:
- The molar mass of [tex]\( O_2 \)[/tex] is 32.00 g/mol.
- Moles of [tex]\( O_2 = \frac{\text{99,800 g}}{\text{32.00 g/mol}} = 3,118.75 \, \text{mol} \)[/tex].
3. Use the balanced equation to find moles of [tex]\( KNO_3 \)[/tex]:
- From the equation, 5 moles of [tex]\( O_2 \)[/tex] are produced from 4 moles of [tex]\( KNO_3 \)[/tex].
- Moles of [tex]\( KNO_3 = \frac{4}{5} \times 3,118.75 \, \text{mol} = 2,495.0 \, \text{mol} \)[/tex].
Part 2: Calculate the grams of [tex]\( KNO_3 \)[/tex] needed to produce 20.2 kg of [tex]\( O_2 \)[/tex]
1. Determine the mass of [tex]\( O_2 \)[/tex] in grams:
- Convert 20.2 kg of [tex]\( O_2 \)[/tex] to grams: [tex]\( 20.2 \, \text{kg} = 20,200 \, \text{g} \)[/tex].
2. Find the number of moles of [tex]\( O_2 \)[/tex]:
- Moles of [tex]\( O_2 = \frac{20,200 \, \text{g}}{32.00 \, \text{g/mol}} = 631.25 \, \text{mol} \)[/tex].
3. Use the balanced equation to find moles of [tex]\( KNO_3 \)[/tex]:
- Moles of [tex]\( KNO_3 = \frac{4}{5} \times 631.25 \, \text{mol} = 505.0 \, \text{mol} \)[/tex].
4. Convert moles of [tex]\( KNO_3 \)[/tex] to grams:
- The molar mass of [tex]\( KNO_3 \)[/tex] is 101.10 g/mol.
- Grams of [tex]\( KNO_3 = 505.0 \, \text{mol} \times 101.10 \, \text{g/mol} = 51,055.5 \, \text{g} \)[/tex].
Thus, to produce 99.8 kg of [tex]\( O_2 \)[/tex], you need 2,495.0 moles of [tex]\( KNO_3 \)[/tex], and to produce 20.2 kg of [tex]\( O_2 \)[/tex], you need 51,055.5 grams of [tex]\( KNO_3 \)[/tex].
Part 1: Calculate the moles of [tex]\( KNO_3 \)[/tex] needed to produce 99.8 kg of [tex]\( O_2 \)[/tex]
1. Determine the mass of [tex]\( O_2 \)[/tex] in grams:
- Convert 99.8 kg of [tex]\( O_2 \)[/tex] to grams: [tex]\( 99.8 \, \text{kg} = 99,800 \, \text{g} \)[/tex].
2. Find the number of moles of [tex]\( O_2 \)[/tex]:
- The molar mass of [tex]\( O_2 \)[/tex] is 32.00 g/mol.
- Moles of [tex]\( O_2 = \frac{\text{99,800 g}}{\text{32.00 g/mol}} = 3,118.75 \, \text{mol} \)[/tex].
3. Use the balanced equation to find moles of [tex]\( KNO_3 \)[/tex]:
- From the equation, 5 moles of [tex]\( O_2 \)[/tex] are produced from 4 moles of [tex]\( KNO_3 \)[/tex].
- Moles of [tex]\( KNO_3 = \frac{4}{5} \times 3,118.75 \, \text{mol} = 2,495.0 \, \text{mol} \)[/tex].
Part 2: Calculate the grams of [tex]\( KNO_3 \)[/tex] needed to produce 20.2 kg of [tex]\( O_2 \)[/tex]
1. Determine the mass of [tex]\( O_2 \)[/tex] in grams:
- Convert 20.2 kg of [tex]\( O_2 \)[/tex] to grams: [tex]\( 20.2 \, \text{kg} = 20,200 \, \text{g} \)[/tex].
2. Find the number of moles of [tex]\( O_2 \)[/tex]:
- Moles of [tex]\( O_2 = \frac{20,200 \, \text{g}}{32.00 \, \text{g/mol}} = 631.25 \, \text{mol} \)[/tex].
3. Use the balanced equation to find moles of [tex]\( KNO_3 \)[/tex]:
- Moles of [tex]\( KNO_3 = \frac{4}{5} \times 631.25 \, \text{mol} = 505.0 \, \text{mol} \)[/tex].
4. Convert moles of [tex]\( KNO_3 \)[/tex] to grams:
- The molar mass of [tex]\( KNO_3 \)[/tex] is 101.10 g/mol.
- Grams of [tex]\( KNO_3 = 505.0 \, \text{mol} \times 101.10 \, \text{g/mol} = 51,055.5 \, \text{g} \)[/tex].
Thus, to produce 99.8 kg of [tex]\( O_2 \)[/tex], you need 2,495.0 moles of [tex]\( KNO_3 \)[/tex], and to produce 20.2 kg of [tex]\( O_2 \)[/tex], you need 51,055.5 grams of [tex]\( KNO_3 \)[/tex].
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