# One of the chlorophylls, chlorophyll a, has four nitrogen atoms in a molecule, and the mass fraction of nitrogen is 6.27%. What is the relative molar mass of chlorophyll a?

## How many magnesium atoms are in the molecule if the mass fraction of magnesium in chlorophyll is 2.72%?

Mar 23, 2018

Here's what I got.

#### Explanation:

The idea here is that you need to use the percent composition of nitrogen in chlorophyll a to figure out the molar mass of the compound.

You know that chlorophyll a is 6.27% by mass nitrogen, which means for every $\text{100 g}$ of chlorophyll a, you get $\text{6.27 g}$ of nitrogen, $\text{N}$.

To make the calculations easier, let's pick a sample of chlorophyll a that has a mass of exactly $\text{100. g}$. Since you know that this sample contains $\text{6.27 g}$ of nitrogen, you can use the molar mass of nitrogen to convert the mass to moles.

6.27 color(red)(cancel(color(black)("g"))) * "1 mole N"/(14.0067 color(red)(cancel(color(black)("g")))) = "0.44764 moles N"

Now, you also know that every molecule of chlorophyll a contains $4$ atoms of nitrogen. This is equivalent to saying that every mole of chlorophyll a contains $4$ moles of nitrogen.

This means that the total number of moles of chlorophyll a present in the sample is equal to

0.44764 color(red)(cancel(color(black)("moles N"))) * "1 mol chlorophyll a"/(4color(red)(cancel(color(black)("moles N")))) = "0.11191 moles chlorophyll a"

To find the molar mass of chlorophyll a, calculate the mass of exactly $1$ mole of chlorophyll a. Since you know that $0.11191$ moles have a mass of $\text{100. g}$, you can say that $1$ mole will have a mass of

1color(red)(cancel(color(black)("mole chlorophyll a"))) * "100. g"/(0.11191color(red)(cancel(color(black)("mole chlorophyll a")))) = "893.58 g"

Therefore, the molar mass of chlorophyll a is

"molar mass chlorophyll a" = color(darkgreen)(ul(color(black)("894 g mol"^(-1))))

The answer is rounded to three sig figs, the number of sig figs you have for the percent composition of nitrogen.

For the second question, you need to use the fact that every $\text{100. g}$ of chlorophyll a contain $\text{2.72 g}$ of magnesium.

You've already calculated that $\text{100. g}$ of chlorophyll a are equivalent to $0.11191$ moles of chlorophyll a, so now use the molar mass of magnesium to convert the mass of magnesium present in $\text{100. g}$ of chlorophyll a to moles.

2.72 color(red)(cancel(color(black)("g"))) * "1 mole Mg"/(24.305color(red)(cancel(color(black)("g")))) = "0.11191 moles Mg"

Notice that for every $0.11191$ moles of chlorophyll a, you get $0.11191$ moles of magnesium. Since each mole of chlorophyll a contains $1$ mole of magnesium, you can say that each molecule of chlorophyll a contains $1$ atom of magnesium.