# Question #b8fcb

##### 1 Answer

Here's what I got.

#### Explanation:

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

Now, the problem wants you to find the *number of molecules* of sulfur dioxide present in

In order to find the number of molecules present in

sulfur dioxide'smolar mass, which is listed as#"64.064 g mol"^(-1)# Avogadro's number, which gives you the number of moleculesper moleof a given substance

So, the first thing to do here is figure out how many *moles* of sulfur dioxide you have in that **every mole** of sulfur dioxide has a mass of

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 *unified atomic mass unit*,

The unified atomic mass unit was defined as the mass of

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 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

#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)|)))#