# Percent composition of nitrogen in fertilizer

The question was posed as follows:

Fertilizers supply the essential elements, nitrogen, phosphorus and potassium for plant growth. A bag of fertilizer contains 500g of ammonium sulfate, $\small \ce{(NH4)2 SO4}$, and 500g of potassium nitrate, $\small \ce{KNO3}$. Calculate the percentage by mass of nitrogen in the bag of fertilizer.

This came in a test of mine and I got the answer wrong, now I did a redo and here's my solution:

(42 * 2)/227  * 100 = 37%


I got 17.542% by mass nitrogen.

An explanation for beginners, a refresher for the rest of us:

To make sure anyone reading knows what molar mass means: The mass of one mole of something, in our case the mass of a mole of nitrogen, or the mass of a mole of ammonium sulfate, etc. A mole is just a way of saying a really big number which is actually $6.022 * 10^{23}$. It is a word we use instead of saying that big number, like when we say a dozen of eggs, but we know it means $12$ eggs. The same concept applies to a mole of eggs (that's a lot of eggs). To calculate the molar mass you need to add the atomic masses of each atom present in the molecule. If it is water, then we must count hydrogen's atomic mass twice (two hydrogen atoms per molecule), oxygen only once, since the formula is $H_2O$. Atomic mass can be found on any respectable periodic table, be sure not to confuse the atomic mass with the atomic number! The atomic mass always represents the weight in grams of a mole of that element. This convention makes our calculations much easier.

Ultimately we need to know how many $mol$ of nitrogen exist in this bag of fertilizer, so we can find out the mass of nitrogen in said bag (atomic mass can be used both ways because it is a ratio of grams per mole). To find that we need to do this process for both of the compounds separately because they have different molar masses. If there are two $chickens$ per $hen$ and we have $4_{mols}$ of $hens$ we should be able to tell that we have $8_{mols}$ of $chickens$. The same concept is used to determine how many $mols$ of nitrogen we have, based on how many nitrogens we expect per molecule of each substance.

Here is how that calculation might look in dimensional analysis in case it surprises you:

$81_{grams} * \frac{1_{mol}}{12_{grams}}$

Notice units of grams cancel each other out, and the remainder is in moles. This is how you would find the number of moles of carbon there exist in a pure sample of 81 grams.

Notice we used the ratio $12$ $\frac{grams}{mol}$ which is carbon's atomic mass.

I highly recommend writing out the entire problem using dimensional analysis so that you can be absolutely sure you have the answer correct for whatever problem you are solving. You will know this is true when all the units cancel correctly.

To solve the problem it may be good to take a step back from the calculator and consider what we know. What is the molar mass of these two substances? It should be the summation of the atomic masses of all the atoms in the molecule. Just like a water balloon's mass is not only the mass of the water, but also the rubber. Similarly the mass of water is not just the mass of the hydrogen, but the oxygen as well.

There is $500_{grams}$ of ammonium sulfate, but if we are trying to figure out the moles based on this information, we will need to do some dimensional analysis. Use the molar mass of ammonium sulfate which has units $grams/mol$ to multiply this ratio we found by the total mass of ammonium sulfate $(500_{grams})$ in such a way that the $_{grams}$ cancel each other, leaving $mol$ units. This is how many moles of that molecule exist in a 500g sample. We need to know this because the relationship of nitrogen per molecule is not a gram to gram relationship. You could of course, go another route and figure out the percent by mass of nitrogen per molecule and your final calculation should be equivalent. You should get about $21$% nitrogen by mass in a molecule of ammonium sulfate, and therefore 21% of the mass of that substance should equal the mass of nitrogen in that substance. It will be different for the other substance in the bag.

Once you know the total moles of nitrogen, convert back into grams of nitrogen, make sure your units cancel. From there you know the mass of nitrogen in the fertilizer bag, and the total mass of the fertilizer bag.

find the answer: what percent mass is the nitrogen atoms compared to the total mass of the fertilizer bag (all the atoms/molecules)?

• I'm stuck on finding the amount of moles in nitrogen. As you said, there are 2 moles in ammonium sulfate and 1 in potassium nitrate. Since the formula for finding out the no. of moles = mass/molar mass. The molar mass in ammonium sulfate is 28 and 14 in potassium nitrate, but that would give the value of m. – Joseph Potts Sep 8 '12 at 12:08
• @Joseph Potts You are forgetting that the 500g is how much mass all of the molecules of ammonium sulfate weigh, your goal is to figure out how many molecules of both substances exist. How much does one mole of ammonium sulfate weigh? How many moles of nitrogen are in a mole of ammonium sulfate? This information for both substances will help you find the way to the right answer. – Leonardo Sep 8 '12 at 14:32