Question #1caee

The question essentially wants you to figure out the molar mass, i.e. the mass of exactly `1` mole, of this compound.

Now, the important thing to keep in mind here is that `1` mole of a molecular substance contains `6.022 * 10^(23)` molecules of that substance `->` this is known as Avogadro's constant.

In other words, in order to have `1` mole of a molecular substance, you need to have a sample that contains `.6022 * 10^(23)` molecules of that substance.

This means that the molar mass of the compound will give you the mass of `6.022 * 10^(23)` molecules.

Since you already know that `4.67 * 10^(16)` molecules have a mass of `3.41 * 10^(-6)` `"g"`, you can use this as a conversion factor to find the mass of `6.022 * 10^(23)` molecules.

`6.022 * 10^(23) color(red)(cancel(color(black)("molecules"))) * (3.41 * 10^(-6)color(white)(.)"g")/(4.67 * 10^(16)color(red)(cancel(color(black)("molecules"))))= "44.0 g"`

You can thus say that you have `"44.0 g"` for every `6.022 * 10^(23)` molecules, i.e. `1` mole of this compound, which means that you have

`"molar mass" = "44.0 g mol"^(-1) ->` three sig figs

Based on the options given to you, the closest match is carbon dioxide, `"CO"_2`, which has a molar mass of `"44.01 g mol"^(-1)`

The mole is related to the mass by the molecular weight. We can calculate the ratio of molecules to those of a mole and compare that to the ratio of compound molecular weights to the sample mass. The one with the equal ratios is the answer.

Ratio of molecules to a Mole: `(4.67 xx 10^16)/(6.022 xx 10^23)`
`= 7.75 xx 10^(-8)`

`(Mass)/("Molecular Weight") = (3.41 xx 10^(-6))/("M.W.")`

`CO_2 = (3.41 xx 10^(-6))/44 = 7.75 xx 10^(-8)`
`CH_4 = (3.41 xx 10^(-6))/16 = 2.13 xx 10^(-8)`
`NH_3 = (3.41 xx 10^(-6))/17 = 2.01 xx 10^(-8)`
`H_2O = (3.41 xx 10^(-6))/18 = 1.89 xx 10^(-8)`