Final answer:
To find the grams of each element in a 1 Liter bottle of pure vinegar, we calculate 5% of its mass to find the amount of acetic acid, then determine the moles of acetic acid and calculate the mass of hydrogen, carbon, and oxygen.
Step-by-step explanation:
To calculate the grams of each element present in a 1 Liter (1050g) bottle of pure vinegar (acetic acid), we need to know the composition of acetic acid and the concentration of acetic acid in vinegar. Acetic acid, which has the chemical formula HC₂H₃O₂, is composed of hydrogen (H), carbon (C), and oxygen (O). Since commercial vinegar is typically a 5% by mass solution of acetic acid in water, with a density of 1.007 g/cm³, we can calculate the mass of acetic acid in 1 liter of vinegar.
First, we convert the volume of vinegar to mass using the density (1 liter = 1000 mL):
1000 mL × 1.007 g/mL = 1007 g of vinegar
Next, we find the mass of acetic acid in 1 liter of vinegar:
5% of 1007 g = 0.05 × 1007 g = 50.35 g of acetic acid
Using the molecular weight of acetic acid (60.05 g/mol), we can calculate the number of moles of acetic acid in 50.35 g:
Moles of acetic acid = 50.35 g / 60.05 g/mol = 0.838 moles
The molecular formula of acetic acid shows that it contains 2 carbons, 4 hydrogens, and 2 oxygens. By calculating the mass of each atom type in moles of acetic acid, we can find the mass of each element:
Hydrogen: 4 atoms H × 1.008 g/mol × 0.838 moles = 3.37 g H
Carbon: 2 atoms C × 12.01 g/mol × 0.838 moles = 20.10 g C
Oxygen: 2 atoms O × 16.00 g/mol × 0.838 moles = 26.81 g O
In summary, in a 1 Liter bottle of vinegar, we would have approximately 3.37 grams of hydrogen, 20.10 grams of carbon, and 26.81 grams of oxygen.