Joyce combines 9 atoms of hydrogen and 3 atoms of nitrogen to make 3 molecules of ammonia.
write a direct variation equation which relates atoms of hydrogen to atoms of nitrogen.
How many nitrogen atoms does Joyce need to form ammonia molecules using 51 hydrogen atoms?
To write a direct variation equation, we need to find the ratio between the number of atoms of hydrogen and the number of atoms of nitrogen. In this case, we can see that for every 9 atoms of hydrogen, there are 3 atoms of nitrogen. This can be written as:
Hydrogen atoms/Nitrogen atoms = 9/3
Simplifying the ratio, we have:
Hydrogen atoms/Nitrogen atoms = 3/1
Now, to find the number of nitrogen atoms Joyce needs to form ammonia molecules using 51 hydrogen atoms, we can set up a proportion using the direct variation equation we derived:
Hydrogen atoms/Nitrogen atoms = 3/1
Plugging in the known values, we have:
51/Nitrogen atoms = 3/1
To solve for Nitrogen atoms, we can cross-multiply and solve the equation:
3 * Nitrogen atoms = 51 * 1
3 * Nitrogen atoms = 51
Dividing both sides by 3:
Nitrogen atoms = 51 / 3
Nitrogen atoms = 17
Therefore, Joyce needs 17 nitrogen atoms to form ammonia molecules using 51 hydrogen atoms.