Three liters of nitrogen combine with 9 L of hydrogen to form 6 L of ammonia. If the molecules of nitrogen and hydrogen have two atoms each, how many atoms of hydrogen and nitrogen are there in one molecule of ammonia?
____ atoms of hydrogen
____ atoms of nitrogen
To determine the number of atoms of hydrogen and nitrogen in one molecule of ammonia, we need to use the given information about the volumes of the reactants and products. Here's how we can calculate it:
1) Start by finding the mole ratio between the reactants and products. Since we are given the volumes in liters, we can assume that the volumes are directly proportional to the number of moles.
For nitrogen:
3 L nitrogen = x moles nitrogen
For hydrogen:
9 L hydrogen = x moles hydrogen
For ammonia:
6 L ammonia = x moles ammonia
2) To balance the equation, we need to find the simplest ratio between the moles of nitrogen, hydrogen, and ammonia. The balanced equation for the reaction is:
N₂ + 3H₂ → 2NH₃
This means that one mole of nitrogen reacts with three moles of hydrogen to produce two moles of ammonia. Therefore, the mole ratio of nitrogen, hydrogen, and ammonia is:
1 mole nitrogen : 3 moles hydrogen : 2 moles ammonia
3) Now, let's determine the moles of hydrogen and nitrogen required to form 2 moles of ammonia:
Since the mole ratio is 3 moles hydrogen to 2 moles ammonia, we can set up the following equation:
3 moles hydrogen = 2 moles ammonia
Using this equation, we can calculate the moles of hydrogen in one molecule of ammonia:
x moles hydrogen / 3 = 2 moles ammonia
x = 6 moles hydrogen
4) Now, we need to convert the moles of hydrogen to atoms. Since each molecule of hydrogen has two atoms, we can multiply the number of moles by Avogadro's number (6.022 x 10^23) to get the number of atoms:
6 moles hydrogen * (6.022 x 10^23 atoms/mole) = 3.613 x 10^24 atoms of hydrogen
So, there are approximately 3.613 x 10^24 atoms of hydrogen in one molecule of ammonia.
5) Similarly, let's determine the moles of nitrogen in one molecule of ammonia:
Since the mole ratio is 1 mole nitrogen to 2 moles ammonia, we can set up the following equation:
x moles nitrogen / 1 = 2 moles ammonia
x = 2 moles nitrogen
6) As with hydrogen, we need to convert the moles of nitrogen to atoms. Since each molecule of nitrogen has two atoms, we can multiply the number of moles by Avogadro's number (6.022 x 10^23) to get the number of atoms:
2 moles nitrogen * (6.022 x 10^23 atoms/mole) = 1.2044 x 10^24 atoms of nitrogen
Therefore, there are approximately 1.2044 x 10^24 atoms of nitrogen in one molecule of ammonia.
In conclusion, there are approximately 3.613 x 10^24 atoms of hydrogen and 1.2044 x 10^24 atoms of nitrogen in one molecule of ammonia.