Answer:
Explanation: To calculate the mass of water produced by the metabolism of 1.0 kg of fat, we need to determine the molecular formula of tristearin (C57H110O6) and analyze the stoichiometry of its reaction with oxygen.
The molecular formula of tristearin is C57H110O6, which means it contains 57 carbon atoms, 110 hydrogen atoms, and 6 oxygen atoms.
The reaction of tristearin with oxygen can be represented as:
C57H110O6 + xO2 → yCO2 + zH2O
To determine the stoichiometric coefficients x, y, and z, we need to balance the equation. By examining the elements involved, we find that the equation is balanced when:
x = 80 (to balance the carbon atoms)
y = 114 (to balance the hydrogen atoms)
z = 117 (to balance the oxygen atoms)
Therefore, the balanced equation for the metabolism of tristearin is:
C57H110O6 + 80O2 → 114CO2 + 117H2O
From the balanced equation, we can see that for every mole of tristearin metabolized, 117 moles of water are produced.
To calculate the mass of water produced, we need to determine the molar mass of water (H2O), which is approximately 18 g/mol.
Now, let's calculate the mass of water produced by the metabolism of 1.0 kg (1000 g) of fat:
Calculate the molar mass of tristearin (C57H110O6):
Molar mass = (57 * molar mass of carbon) + (110 * molar mass of hydrogen) + (6 * molar mass of oxygen)
= (57 * 12.01 g/mol) + (110 * 1.01 g/mol) + (6 * 16.00 g/mol)
≈ 890.17 g/mol
Determine the number of moles of tristearin in 1.0 kg:
Number of moles = Mass / Molar mass
= 1000 g / 890.17 g/mol
≈ 1.123 mol
Calculate the mass of water produced:
Mass of water = Number of moles of water * Molar mass of water
= 1.123 mol * 18.02 g/mol
≈ 20.3 g
Therefore, the metabolism of 1.0 kg of tristearin would produce approximately 20.3 grams of water.