Chapter A.8, Problem 44AYU

To determine

To find: How many are oxygen?

How many are hydrogen?

Answer to Problem 44AYU

11 oxygen atoms and 22 hydrogen atoms.

Explanation of Solution

Given:

A sugar molecule has twice as many atoms of hydrogens as of oxygen and one more atom of carbon than of oxygen. If a sugar molecule has a total of 45 atoms.

Calculation:

Not counting that extra carbon atom (the “one more atom of carbon that oxygen”).

There are $45-1=44$ atoms.

Among those 44 atoms, for each oxygen atom there are 2 hydrogen atoms and one carbon atom, forming a group of 4 atoms. So among these 44 atoms, there are $\frac{44}{4}=11$.

Such groups of 4 atoms. At 1 oxygen atom per group, there is a total of 11 oxygen atoms.

At 2 hydrogen atoms per group, there is a total of $2.11=22$ hydrogen atoms.

At 1 carbon atom per group, there is a total of 11 carbon atoms in the 4-atom groups, plus that extra carbon atom, for a total of $11+1=12$ carbon atoms.