Calculate the mass of H2O produced by metabolism of 2.6kg of fat, assuming the fat consists entirely of tristearin (C57H110O6), a typical animal fat, and assuming that during metabolism, tristearin reacts with O2 to form only CO2 and H2O.
This is not physics.
write the chemical reaction, and balance it.
Then look at how many moles of H20 one gets from one mole of tristearin.
fugure the moles of fat from 2.6kg
then use the mole ratio to figure the moles of water.
Well, let's get down to some metabolic math! To calculate the mass of H2O produced, we'll need to consider the molecular formula of tristearin (C57H110O6) and the reaction with O2.
First, we determine the molecular weight of tristearin:
C: 57 * 12.01 g/mol = 684.57 g/mol
H: 110 * 1.01 g/mol = 111.1 g/mol
O: 6 * 16.00 g/mol = 96.00 g/mol
Summing these up, we get the molecular weight of tristearin:
684.57 g/mol + 111.1 g/mol + 96.00 g/mol = 891.67 g/mol
Now, we know that during metabolism, tristearin reacts with O2 to form CO2 and H2O. To balance this reaction, we need to determine the number of moles of tristearin consumed.
Given that we have 2.6 kg of fat (tristearin), we convert it to grams:
2.6 kg = 2600 g
Dividing the mass of tristearin by its molar mass, we obtain the number of moles:
2600 g / 891.67 g/mol ≈ 2.916 moles
Next, we need to consider the balanced reaction of tristearin with O2. Since there are no given coefficients, let's assume a 1:1 ratio:
C57H110O6 + O2 → CO2 + H2O
So, for every mole of tristearin consumed, we'll get one mole of H2O. Therefore, the mass of H2O can be calculated by multiplying the number of moles of tristearin by the molar mass of H2O.
Molar mass of H2O = 2 * 1.01 g/mol + 16.00 g/mol = 18.02 g/mol
Mass of H2O = 2.916 moles * 18.02 g/mol ≈ 52.44 g
Therefore, the mass of H2O produced by the metabolism of 2.6 kg of fat is approximately 52.44 grams. I hope these calculations didn't "weigh you down" too much!
To determine the mass of H2O produced by the metabolism of 2.6 kg of fat, we need to calculate the amount of tristearin (C57H110O6) that will react with oxygen (O2) to form H2O.
1. Determine the molar mass of tristearin (C57H110O6):
- The molar mass of carbon (C) is 12.01 g/mol.
- The molar mass of hydrogen (H) is 1.01 g/mol.
- The molar mass of oxygen (O) is 16.00 g/mol.
- Multiply each element's atomic mass by the number of atoms present in tristearin and sum them up:
(57 * 12.01 g/mol) + (110 * 1.01 g/mol) + (6 * 16.00 g/mol) = 847.78 g/mol
2. Convert the mass of fat (2.6 kg) to grams:
2.6 kg * 1000 g/kg = 2600 g
3. Calculate the number of moles of tristearin:
Moles = mass / molar mass
Moles = 2600 g / 847.78 g/mol ≈ 3.06 mol
4. Determine the stoichiometry between tristearin, CO2, and H2O:
From the chemical formula of tristearin: C57H110O6
- One mole of tristearin will produce 57 moles of CO2.
- One mole of tristearin will produce 55 moles of H2O (since 6 H2Os are formed but there are already 5 in the tristearin structure).
5. Calculate the moles of H2O produced:
Moles of H2O = Moles of tristearin * Moles of H2O per mole of tristearin
Moles of H2O = 3.06 mol * 55 mol/mol ≈ 168.3 mol
6. Convert moles of H2O to grams:
Mass = Moles of H2O * molar mass of H2O
Mass = 168.3 mol * (2 * 1.01 g/mol + 16.00 g/mol) ≈ 5362 g
Therefore, the mass of H2O produced by the metabolism of 2.6 kg of fat would be approximately 5362 grams.
To calculate the mass of H2O produced by the metabolism of 2.6kg of fat, we first need to determine the molar mass of tristearin (C57H110O6) and then use stoichiometry to find the ratio between the moles of tristearin and the moles of H2O produced.
Let's break down the steps:
Step 1: Calculate the molar mass of tristearin:
The molar mass is the sum of the atomic masses of all the atoms in one molecule of the substance. To calculate the molar mass of tristearin, we can look up the atomic masses of carbon (C), hydrogen (H), and oxygen (O) and multiply them by the respective number of atoms.
C: 12.01 g/mol (atomic mass of carbon)
H: 1.008 g/mol (atomic mass of hydrogen)
O: 16.00 g/mol (atomic mass of oxygen)
Molar mass of tristearin (C57H110O6):
(57 * 12.01 g/mol) + (110 * 1.008 g/mol) + (6 * 16.00 g/mol) = 891.44 g/mol
Step 2: Calculate the moles of tristearin:
To convert the mass of fat (2.6kg) to moles, we need to divide it by the molar mass of tristearin.
Moles of tristearin:
2.6kg × (1000 g/kg) / 891.44 g/mol = 2916.25 mol of tristearin
Step 3: Determine the stoichiometric ratio:
The balanced equation for the reaction between tristearin and oxygen (O2) to produce carbon dioxide (CO2) and water (H2O) can be represented as follows:
C57H110O6 + O2 -> CO2 + H2O
From the balanced equation, it is clear that for each mole of tristearin consumed, we produce one mole of water (H2O). Therefore, the moles of water produced will be equal to the moles of tristearin metabolized.
Moles of H2O produced: 2916.25 mol
Step 4: Convert moles of H2O into mass:
To calculate the mass of water produced, we need to multiply the moles of H2O by the molar mass of water.
Molar mass of water (H2O):
(2 * 1.008 g/mol for hydrogen) + (16.00 g/mol for oxygen) = 18.02 g/mol
Mass of H2O produced:
2916.25 mol × 18.02 g/mol = 52,554.75 g or 52.55 kg
Therefore, the mass of H2O produced by the metabolism of 2.6kg of fat (tristearin) is approximately 52.55 kilograms.