Question

How many atoms of carbon can be found in `"90 g"` of glucose?

Answer 1

`2 * 10^(24)`

Explanation:

In order to determine how many atoms of carbon you get in `90` grams of glucose you need to know two things

• how many molecules you have in `90` grams of glucose
• how many atoms of carbon you have per molecule of glucose

So, glucose's molecular formula is `"C"_6"H"_12"O"_6`, which means that every molecule of glucose contains

• six carbon atoms
• twelve hydrogen atoms
• six oxygen atoms

Now that you know how many atoms of carbon you get per molecule of glucose, all you need to figure out is how many molecules of glucose you get in that sample.

To do that, use glucose's molar mass, which tells you what the mass of one mole of glucose molecules is. Glucose has a molar mass of `"180.156 g/mol"`, which means that one mole of glucose molecules has a mass of `"180.156 g"`.

Therefore, your `"90-g"` sample will contain

`90 color(red)(cancel(color(black)("g"))) * ("1 mole C"_6"H"_12"O"_6)/(180.156color(red)(cancel(color(black)("g")))) = "0.4996 moles C"_5"H"_12"O"_6`

As you know, the number of molecules you get per mole is given by Avogadro's number. More specifically, one mole of any substance contains exactly `6.022 * 10^(23)` molecules of that substance.

This means that you have

`0.4996 color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = 3.009 * 10^(23)"molecules"`

So, if you know how many molecules of glucose you have, and how many atoms of carbon you have per molecule, you can say that

`3.009 * 10^(23)color(red)(cancel(color(black)("molecules C"_6"H"_12"O"_6))) * "6 atoms of C"/(1color(red)(cancel(color(black)("molecule C"_6"H"_12"O"_6)))) = 1.81 * 10^(24)"atoms of C"`

You should round this off to one sig fig, the number of sig figs you have for the mass of glucose

`"no. of atoms of C" = 2 * 10^(24)`