How many liters of pure oxygen at STP is consumed by a human being in 24
hours if the human body requires daily energy that comes from metabolizing
816 grams of sucrose (C12H22O11)?
C12H22O11(s ) + 12 O2(g) => 12 CO2(g)+11 H2O
816 g C12H22O11 = how many moles? mol = g/molar mass.
Convert mol sucrose to mols O2 using the coefficients in the balanced equation.
Convert mol O2 to volume. mol O2 x 22.4 L/mol = ?L.
To find out how many liters of pure oxygen at STP is consumed by a human being in 24 hours, we need to use the stoichiometry of the balanced equation you provided.
First, let's convert the mass of sucrose (C12H22O11) into moles. The molar mass of sucrose is calculated by adding up the atomic masses of all the atoms involved:
C: 12.01 g/mol
H: 1.01 g/mol
O: 16.00 g/mol (there are 11 oxygen atoms in sucrose)
Molar mass of C12H22O11 = (12.01 x 12) + (1.01 x 22) + (16.00 x 11) = 342.34 g/mol
Now, let's calculate the number of moles of sucrose:
Moles of sucrose = mass of sucrose / molar mass of sucrose
Moles of sucrose = 816 g / 342.34 g/mol
Next, we can use the stoichiometry of the balanced equation to determine the moles of oxygen consumed:
From the balanced equation:
1 mole of sucrose reacts with 12 moles of oxygen.
So, Moles of oxygen = Moles of sucrose x (12 moles of O2 / 1 mole of C12H22O11)
Once we have the moles of oxygen consumed, we can convert it into liters at STP (Standard Temperature and Pressure). The molar volume of a gas at STP is 22.4 liters/mol.
Liters of oxygen = Moles of oxygen x 22.4 liters/mol
Now we can plug in the numbers to calculate the result. I'll do the calculations for you:
Moles of sucrose = 816 g / 342.34 g/mol = 2.3839 mol
Moles of oxygen = 2.3839 mol x (12 mol O2 / 1 mol C12H22O11) = 28.607 mol
Liters of oxygen = 28.607 mol x 22.4 liters/mol = 640.2056 liters
Therefore, a human being would consume approximately 640.21 liters of pure oxygen at STP in 24 hours if the daily energy requirement is met by metabolizing 816 grams of sucrose (C12H22O11).
To find out how many liters of pure oxygen are consumed by a human being in 24 hours, we first need to calculate the amount of sucrose (C12H22O11) that is metabolized.
1. Calculate the molar mass of sucrose (C12H22O11):
C = 12.01 g/mol
H = 1.008 g/mol
O = 16.00 g/mol
Molar mass of C12H22O11 = (12.01 x 12) + (1.008 x 22) + (16.00 x 11) = 342.34 g/mol
2. Calculate the number of moles of sucrose:
Number of moles = mass / molar mass = 816 g / 342.34 g/mol ≈ 2.384 mol
According to the balanced equation C12H22O11 + 12 O2 → 12 CO2 + 11 H2O, we can see that 12 moles of oxygen (O2) are required to metabolize 1 mole of sucrose.
3. Calculate the number of moles of oxygen required:
Number of moles of oxygen = 12 x 2.384 mol = 28.608 mol
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies 22.4 liters. Therefore, the number of liters of oxygen required is:
Number of liters of oxygen = number of moles x 22.4 L/mol
Number of liters of oxygen = 28.608 mol x 22.4 L/mol ≈ 640.9728 L
Therefore, a human being would consume approximately 640.9728 liters of pure oxygen at STP in 24 hours to metabolize 816 grams of sucrose.