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?
see below.
To determine how many atoms of oxygen and hydrogen are in a sugar molecule, we can use algebraic equations and solve for the variables. Let's set up the equations based on the given information:
1) The sugar molecule has twice as many atoms of hydrogen as it does oxygen:
H = 2O
2) The sugar molecule has one more atom of carbon than oxygen:
C = O + 1
3) The total number of atoms in the sugar molecule is 45:
H + O + C = 45
We can solve this system of equations to find the values of H (hydrogen) and O (oxygen).
First, simplify equation 2) by substituting C with O + 1:
(O + 1) = O + 1
Next, substitute the value of C in equation 3) with O + 1:
H + O + (O + 1) = 45
Now, substitute the value of H in equation 1) with 2O:
(2O) + O + (O + 1) = 45
Combine like terms:
4O + 1 = 45
Subtract 1 from both sides:
4O = 44
Now divide both sides by 4:
O = 11
So, we know that there are 11 atoms of oxygen in the sugar molecule.
To find the number of hydrogen atoms, we substitute this value of O back into equation 1):
H = 2O = 2(11) = 22
Therefore, there are 11 atoms of oxygen and 22 atoms of hydrogen in the sugar molecule.