Question

How many molecules are there in 4.00 mol of glucose?

Answer 1

`2.49 * 10^(24)"molecules"`

Explanation:

What you're looking for here is a conversion factor that will take you from moles of glucose, `"C"_6"H"_12"O"_6`, to molecules of glucose.

A useful information to have would be the number of molecules in one mole of any substance, since knowing how many molecules you get in one mole will allow you to calculate how many you'd get in `4.00` moles.

As it turns out, chemists have a special number that designates how many molecules you get in one mole of a substance - this is known as Avogadro's number.

More specifically, Avogadro's number tells you that one mole of any substance contains `6.022 * 10^(23)` molecule of that substance

`color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"molecules"color(white)(a/a)|))) ->` Avogadro's number

This will act as the conversion factor that will take you from moles to molecules.

So, if one mole of glucose contains `6.022 * 10^(23)` molecules of glucose, it follows that `4.00` moles of glucose will contain

`4.00 color(red)(cancel(color(black)("moles"))) * overbrace((6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole")))))^(color(purple)("Avogadro's number")) = color(green)(|bar(ul(color(white)(a/a)2.49 * 10^(24)"molecules"color(white)(a/a)|)))`

The answer is rounded to three sig figs, the number of sig figs you have for the number of moles of glucose.