In this scenario, Ariel and Marcus are combining sugar (sucrose, C12H22O11) with oxygen gas (O2). The chemical equation for the combustion of sugar is as follows:
C12H22O11 + 12O2 → 12CO2 + 11H2O
Here, one molecule of sugar reacts with 12 molecules of oxygen gas to form 12 molecules of carbon dioxide (CO2) and 11 molecules of water (H2O).
To determine the expected total mass of the products, we first need to calculate the molar mass of sugar and oxygen gas:
- Molar mass of sugar:
(C × 12.01 g/mol) + (H × 1.01 g/mol × 22) + (O × 16 g/mol × 11)
= 144.32 g/mol + 22.22 g/mol + 176 g/mol
= 342.54 g/mol
- Molar mass of oxygen gas:
O2 × 32 g/mol
= 64 g/mol
Next, we need to calculate the moles of sugar and oxygen gas in the given masses:
- Moles of sugar (n1):
Mass of sugar / Molar mass of sugar
= 180 g / 342.54 g/mol
≈ 0.525 moles
- Moles of oxygen gas (n2):
Mass of oxygen gas / Molar mass of oxygen gas
= 192 g / 64 g/mol
= 3 moles
Finally, comparing the stoichiometric ratios of the reactants and products, we can determine the expected total mass of the products:
- Moles of carbon dioxide (n3):
n1 × 12
= 0.525 moles × 12
= 6.3 moles
- Total mass of carbon dioxide:
Mass of carbon dioxide = n3 × Molar mass of carbon dioxide
= 6.3 moles × (12.01 g/mol + 2 × 16 g/mol)
≈ 286.638 g
- Moles of water (n4):
n1 × 11
= 0.525 moles × 11
= 5.775 moles
- Total mass of water:
Mass of water = n4 × Molar mass of water
= 5.775 moles × (2 × 1.01 g/mol + 16 g/mol)
≈ 201.4953 g
Therefore, the expected total mass of the product (carbon dioxide + water) would be approximately 286.638 g + 201.4953 g ≈ 488.1333 g.
Note: This calculation assumes complete combustion and 100% yield. In reality, the actual mass of the products might be slightly different due to factors such as incomplete combustion and presence of impurities.
Ariel and Marcus combined 180 g of sugar with 192 g of oxygen gas. What would they expect the total mass of the product to be?Why
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