Question

You have a freshly prepared .01 M ascorbic acid (vitamin C) solution. Each liter of this solution contains how many ascorbic acid molecules?

Answer 1

`6 * 10^(21) "molecules"`

Explanation:

In order to be able to find the number of molecules of ascorbic acid you get per liter of that solution, you need to know how many moles of ascorbic acid you have per liter of solution.

Notice that the problem gives you the molarity of the solution, which is defined as the moles of solute, in your case ascorbic acid, divided by liters of solution.

`color(blue)("molarity" = "moles of solute"/"liters of solution")`

Since your solution has a molarity of `"0.01 moles/L"`, it follows that every liter will contain exactly `"0.01 moles"` of ascorbic acid.

Now, you know that one mole of any substance contains exactly `6.022 * 10^(23)` molecules of that substance - this is known as Avogadro's number.

In your case, `0.01` moles would contain

`0.01color(red)(cancel(color(black)("moles"))) * (6.022 * 10^(23)"molecules")/(1color(red)(cancel(color(black)("mole")))) = 6.022 * 10^(21)"molecules"`

Rounded to one sig fig, the answer will be

`"no. of molecules" = color(green)(6 * 10^(21)"molecules")`