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# Find out no. of molecules of ##"SO"_2## (sulphate) in 1) ##"6.4g"## 2) ##"640 u"##?

Here's what I got.

For starters, it's important to note that you're dealing with sulfur dioxide, ##"SO"_2##, **not** with "sulfate".

Now, the problem wants you to find the number of molecules of sulfur dioxide present in ##"6.4 g"## and in ##"640 u"## of sulfur dioxide.

In order to find the number of molecules present in ##"6.4 g"## of sulfur dioxide, you will need to use

- sulfur dioxide's
**molar mass**, which is listed as ##"64.064 g mol"^(-1)## **Avogadro's number**, which gives you the number of molecules**per mole**of a given substance

So, the first thing to do here is figure out how many moles of sulfur dioxide you have in that ##"6.4-g"## sample. The compound's molar mass tells you that **every mole** of sulfur dioxide has a mass of ##"64.064 g"##.

This means that you'll have

##6.4 color(red)(cancel(color(black)("g"))) * "1 mole SO"_2/(64.064color(red)(cancel(color(black)("g")))) = "0.0999 moles SO"_2##

Now use the fact that

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

to calculate how many molecules you get in that many moles of sulfur dioxide

##0.0999color(red)(cancel(color(black)("moles SO"_2))) * (6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole SO"_2)))) = color(green)(|bar(ul(color(white)(a/a)6.0 * 10^(22)"molec."color(white)(a/a)|)))##

In order to find the number of molecules of sulfur dioxide in ##"640 u"##, you need to use the definition of the unified unit, ##"u"##.

The unified atomic mass unit was defined as the mass of ##1/12"th"## of the mass of an unbound carbon-12 atom in its ground state, and is equivalent to ##"1 g mol"^(-1)##. Keep this in mind for later.

The approximate value of a unified atomic mass unit is

##color(purple)(|bar(ul(color(white)(a/a)color(black)("1 u" = 1.66054 * 10^(-24)"g")color(white)(a/a)|)))##

This means that the ##"640 u"## sample will be equivalent to

##640 color(red)(cancel(color(black)("u"))) * (1.66054 * 10^(-24)"g")/(1color(red)(cancel(color(black)("u")))) = 1.063 * 10^(-21)"g"##

Use sulfur dioxide's **molar mass** to determine how many moles would be present in this sample

##1.063 * 10^(-21)color(red)(cancel(color(black)("g"))) * "1 mole SO"_2/(64.064color(red)(cancel(color(black)("g")))) = 1.66 * 10^(-23)"moles SO"_2##

Once again, use Avogadro's number to find

##1.66 * 10^(-23)color(red)(cancel(color(black)("moles SO"_2))) * (6.022 * 10^(23)"molec.")/(1color(red)(cancel(color(black)("mole SO"_2)))) ~~ color(green)(|bar(ul(color(white)(a/a)"10. molec. SO"_2color(white)(a/a)|)))##

**ALTERNATIVE APPROACH**

You can get the same result by using the fact that

##color(purple)(|bar(ul(color(white)(a/a)color(black)("1 u" = "1 g mol"^(-1))color(white)(a/a)|)))##

The unified atomic mass unit tells you the mass of **one nucleon**, i.e. one proton or one neutron. Take a look at the molar mass of sulfur dioxide, which as you know tells you the mass of **one mole** of sulfur dioxide.

In essence, you can use the unified atomic mass unit as conversion factor between the mass of a **single molecule** and the mass of a **mole** of sulfur dioxide.

##64.064 color(red)(cancel(color(black)("g mol"^(-1)))) * "1 u"/(1color(red)(cancel(color(black)("g mol"^(-1))))) = "64.064 u"##

So, if **one molecule** has a mass of ##"64.064 u"##, it follows that your ##"640 u"## sample will contain

##640 color(red)(cancel(color(black)("u"))) * ("1 molec. SO"_2)/(64.064color(red)(cancel(color(black)("u")))) = 9.99 ~~ color(green)(|bar(ul(color(white)(a/a)"10. molec. SO"_2color(white)(a/a)|)))##