Question

A 5.0 g sample of a pure compound containing H, C, and N contains .19 g of H and 2.22 g of C. Another smaller sample of this pure compound is analyzed. How many grams of N should be found in the new 2.0 g pure sample?

Answer 1

`"1.0 g N"`

Explanation:

The idea here is that you need to use the amount of hydrogen and the amount of carbon found in the `"5.0-g"` sample of this unknown compound to determine the percent composition of nitrogen.

Once you know the percent composition of nitrogen, you can determine the amount of nitrogen present in the `"2.0-g"` sample.

So, if your compound contains only hydrogen, `"H"`, carbon, `"C"`, and nitrogen, `"N"`, then you can write the mass of the compound as the sum of the masses of these elements

`m_"compound" = m_(H) + m_(C) + m_(N)`

This means that the `"5.0-g"` sample will contain

`m_(N) = "5.0 g" - "0.19 g" - "2.22 g" = "2.59 g N"`

If you divide the mass of nitrogen by the total mass of the compound and multiply the result by `100`, you will get the compound's percent composition of nitrogen

`(2.59 color(red)(cancel(color(black)("g"))))/(5.0color(red)(cancel(color(black)("g")))) xx 100 = "51.8% N"`

So, what does this tell you?

For every `"100 g"` of this unknown compound, `"51.8 g"` will be nitrogen.

This means that the `"2.0-g"` sample will contain

`2.0 color(red)(cancel(color(black)("g compound"))) * overbrace("51.8 g N"/(100color(red)(cancel(color(black)("g compound")))))^(color(purple)("% composition of N")) = "1.036 g N"`

Rounded to two sig figs, the answer will be

`m_(N) = color(green)("1.0 g")`