A sugar molecule has twice as many atoms of hydrogen as it does oxygen and one more atom of carbon that oxygen. If a sugar molecule has a total of 45 atoms, how many are oxygen and how many are hydrogen?
45=2O + O + (O+1)
solve for O, oxygen molecules.
Well, let's do some clown-math here! Since we know that a sugar molecule has twice as many hydrogen atoms as oxygen atoms, let's assume that it has "x" oxygen atoms.
According to the given information, there is one more carbon atom than oxygen atoms. So there must be "x + 1" carbon atoms.
Now let's add up the atoms:
x (oxygen) + 2x (hydrogen) + (x + 1) (carbon) = 45
If we simplify this equation, we get:
4x + 1 = 45
Subtracting 1 from both sides gives us:
4x = 44
Dividing both sides by 4, we find that x = 11.
Therefore, there are 11 oxygen atoms and twice as many hydrogen atoms (so 2 x 11 = 22 hydrogen atoms) in a sugar molecule.
That's the sweet answer!
Let's assign variables to represent the number of atoms of each element in the sugar molecule. Let H be the number of hydrogen atoms, C be the number of carbon atoms, and O be the number of oxygen atoms.
From the given information, we can write two equations:
1. H = 2O (twice as many atoms of hydrogen as oxygen)
2. C = O + 1 (one more atom of carbon than oxygen)
We also know that the total number of atoms in the sugar molecule is 45, so we can write another equation:
3. H + C + O = 45
Now let's solve the system of equations to find the values of H and O.
From equation 1, we can substitute H with 2O in equation 3:
2O + C + O = 45
Combining like terms:
3O + C = 45
From equation 2, we can substitute C with O + 1:
3O + O + 1 = 45
Combining like terms:
4O + 1 = 45
Subtracting 1 from both sides:
4O = 44
Dividing both sides by 4:
O = 11
Now that we know O is 11, we can substitute this value back into equation 1 to find H:
H = 2O
H = 2(11)
H = 22
Therefore, there are 22 atoms of hydrogen and 11 atoms of oxygen in the sugar molecule.
To find out how many atoms of oxygen and hydrogen are in a sugar molecule, we'll need to set up a system of equations based on the given information. Let's denote the number of oxygen atoms as "O," the number of hydrogen atoms as "H," and the number of carbon atoms as "C."
We are given three pieces of information:
1. A sugar molecule has twice as many hydrogen atoms as oxygen atoms:
H = 2O
2. A sugar molecule has one more carbon atom than oxygen atoms:
C = O + 1
3. The total number of atoms in a sugar molecule is 45:
O + H + C = 45
Using this information, we can now solve the system of equations.
First, substitute the value of H from equation 1 into equation 3:
O + (2O) + C = 45
3O + C = 45 (equation 4)
Next, substitute the value of C from equation 2 into equation 4:
3O + (O + 1) = 45
4O + 1 = 45
4O = 44
O = 11
Now that we know the value of O, we can substitute it back into equation 2 to find the value of C:
C = O + 1
C = 11 + 1
C = 12
Finally, substitute the values of O and C into equation 1 to find the value of H:
H = 2O
H = 2(11)
H = 22
So, a sugar molecule has 11 atoms of oxygen (O) and 22 atoms of hydrogen (H).