What is the mass of #9.76xx10^12# atoms of nitrogen?

Question

Serenity Allen · Accepted Answer

#2.27 * 10^(-10)"g"#

To make this problem more interesting, let's calculate the mass of a single atom of nitrogen first, then use that value as a conversion factor to determine the mass of #9.76 * 10^(12)# atoms of nitrogen.

The starting point here will be the molar mass of nitrogen, which is listed as

#M_("M N") = "14.00674 g mol"^(-1)#

This tells you that one mole of nitrogen has a mass of #"14.00674 g"#. Since one mole of any element contains #6.022 * 10^(23)# atoms of that element, you can say that the mass of a single atom of nitrogen will be

#1 color(red)(cancel(color(black)("atom N"))) * "14.00674 g"/(6.022 * 10^(23)color(red)(cancel(color(black)("atoms N")))) = 2.326 * 10^(-23)"g"#

Now all you have to do is multiply this value by the number of atoms given to you to find

#9.76 * 10^(12) color(red)(cancel(color(black)("atoms N"))) * (2.326 * 10^(-23)"g")/(1color(red)(cancel(color(black)("atom N")))) = color(green)(|bar(ul(color(white)(a/a)color(black)(2.27 * 10^(-10)"g")color(white)(a/a)|)))#

The answer is rounded to three sig figs.

Henry Antrim · Answer

undefined The molar mass of nitrogen (N), which is approximately 14.01 grams per mole, must be known in order to calculate the mass of 9.76 x 10^12 atoms of nitrogen. Next, using Avogadro's number, which is 6.022 x 10^23 atoms per mole, find the mass of 9.76 x 10^12 atoms of nitrogen: Mass = (9.76 x 10^12 atoms) * (1 mole / 6.022 x 10^23 atoms) * (14.01 grams / 1 mole) Mass ≈ 2.31 x 10^-10 grams