Of all the atoms in caffeine, 1/12 are oxygen atoms, 1/6 are nitrogen atoms, and 1/3 are carbon atoms. The rest of the atoms are hydrogen. What fraction of the atoms in caffeine are oxygen, nitrogen, or hydrogen?
Since 1/3 are carbon, 2/3 are everything else.
can some one help me
To determine the fraction of atoms in caffeine that are oxygen, nitrogen, or hydrogen, we need to find the sum of the fractions for each type of atom.
Given:
- 1/12 of the atoms in caffeine are oxygen.
- 1/6 of the atoms in caffeine are nitrogen.
- 1/3 of the atoms in caffeine are carbon.
To find the fraction of atoms that are hydrogen, we subtract the sum of the fractions of oxygen, nitrogen, and carbon from 1.
Fraction of hydrogen atoms = 1 - (1/12 + 1/6 + 1/3)
To simplify the expression, let's find a common denominator for the fractions.
Fraction of hydrogen atoms = 1 - (1/12 + 2/12 + 4/12)
Adding the fractions:
Fraction of hydrogen atoms = 1 - (7/12)
To subtract the fractions, we need to find a common denominator.
Fraction of hydrogen atoms = (12/12) - (7/12)
Fraction of hydrogen atoms = 5/12
Therefore, the fraction of atoms in caffeine that are oxygen, nitrogen, or hydrogen is:
Fraction of oxygen, nitrogen, or hydrogen atoms = Fraction of oxygen atoms + Fraction of nitrogen atoms + Fraction of hydrogen atoms
= 1/12 + 1/6 + 5/12
= (1 + 2 + 5)/12
= 8/12
Simplifying the fraction:
Fraction of oxygen, nitrogen, or hydrogen atoms = 2/3
So, 2/3 of the atoms in caffeine are oxygen, nitrogen, or hydrogen.
To find the fraction of atoms in caffeine that are oxygen, nitrogen, or hydrogen, we first need to determine the fraction of hydrogen atoms.
Given that 1/12 of the atoms are oxygen, 1/6 are nitrogen, and 1/3 are carbon, we can calculate the fraction of hydrogen atoms by subtracting the sum of these fractions from 1.
Fraction of hydrogen atoms = 1 - (1/12 + 1/6 + 1/3)
To simplify the expression, we need to find a common denominator for 12, 6, and 3, which is 12.
Fraction of hydrogen atoms = 1 - (2/24 + 4/24 + 8/24)
Now, we can combine the numerators and subtract them from 24.
Fraction of hydrogen atoms = 1 - (14/24)
To subtract fractions, we need to make sure they have a common denominator.
Fraction of hydrogen atoms = 1 - (14/24) * (1/1) = 1 - 14/24
To subtract fractions, the denominators must be the same, so we multiply (14/24) by 1 in the form of (24/24).
Fraction of hydrogen atoms = 1 - (14/24) * (1/1) = 1 - 14/24 * 24/24
Now, we can multiply the numerators together.
Fraction of hydrogen atoms = 1 - (14 * 24)/(24 * 24)
Simplifying further,
Fraction of hydrogen atoms = 1 - 336/576
To calculate the fraction, subtract the numerators.
Fraction of hydrogen atoms = (576 - 336)/576
Fraction of hydrogen atoms = 240/576
The fraction of hydrogen atoms in caffeine is 240/576.
To find the fraction of oxygen and nitrogen atoms, we can simply add their respective fractions:
Fraction of oxygen and nitrogen atoms = 1/12 + 1/6 = 2/24 + 4/24 = 6/24
Since 24 is the common denominator, we can simplify the fraction:
Fraction of oxygen and nitrogen atoms = 6/24 = 1/4
So, the fraction of atoms in caffeine that are oxygen, nitrogen, or hydrogen is 1/4 + 240/576.