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?

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")#