gunpowder is a mixture of potassium nitrate , sulfur and carbon in th proportion (by mass) of 6:1:1 (KNO3;S:C). A typical riflr shell contains 3.2 gunpowder. How many moles of each compnent are there in our sample gunpowder?
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To determine the number of moles of each component in the sample of gunpowder, we need to follow a few steps:
Step 1: Calculate the molar masses of each component:
- Potassium nitrate (KNO3), molar mass = 39.10 g/mol (K) + 14.01 g/mol (N) + (3 * 16.00 g/mol) (O) = 101.11 g/mol
- Sulfur (S), molar mass = 32.07 g/mol
- Carbon (C), molar mass = 12.01 g/mol
Step 2: Determine the mass of each component in the sample:
- Mass of Potassium nitrate (KNO3) = (6/8) * Total mass of gunpowder
- Mass of Sulfur (S) = (1/8) * Total mass of gunpowder
- Mass of Carbon (C) = (1/8) * Total mass of gunpowder
Step 3: Calculate the number of moles for each component using the formula:
- Moles (n) = Mass (m) / Molar mass (M)
Let's perform the calculations:
Given:
- Total mass of gunpowder = 3.2 g
Step 1: Calculate the molar masses
- Molar mass of KNO3 = 101.11 g/mol
- Molar mass of S = 32.07 g/mol
- Molar mass of C = 12.01 g/mol
Step 2: Determine the mass of each component
- Mass of KNO3 = (6/8) * 3.2 g = 2.4 g
- Mass of S = (1/8) * 3.2 g = 0.4 g
- Mass of C = (1/8) * 3.2 g = 0.4 g
Step 3: Calculate the number of moles for each component
- Moles of KNO3 = Mass of KNO3 / Molar mass of KNO3
- Moles of S = Mass of S / Molar mass of S
- Moles of C = Mass of C / Molar mass of C
Plugging in the values:
- Moles of KNO3 = 2.4 g / 101.11 g/mol
- Moles of S = 0.4 g / 32.07 g/mol
- Moles of C = 0.4 g / 12.01 g/mol
Calculating:
- Moles of KNO3 ≈ 0.024 moles
- Moles of S ≈ 0.012 moles
- Moles of C ≈ 0.033 moles
Therefore, in the sample of gunpowder, there are approximately 0.024 moles of potassium nitrate (KNO3), 0.012 moles of sulfur (S), and 0.033 moles of carbon (C).