Determine the mass of ammonium nitrate (in g) that has the same number of nitrogen atoms as 2.2 liters of liquid nitrogen (N2). Density of liquid nitrogen is 0.808 g/mL.

The mass of ammonium nitrate that has the same number of nitrogen atoms is 5077.5 g.

Explanation:

To calculate the mass of ammonium nitrate we need to find the number of atoms in liquid nitrogen, as follows:

Where:

: is the density of liquid nitrogen = 0.808 g/mL

: is the mass of liquid nitrogen

V: is the volume of liquid nitrogen = 2.2 L

By calculating the mass of liquid nitrogen we can find the number of atoms:

Where:                

: is the Avogadro's number = 6.022x10²³ atoms/mol

n: is the number of atoms of liquid nitrogen

: is the number of moles of liquid nitrogen  

: is the molar mass of liquid nitrogen = 28.014 g/mol

Finally, the mass of ammonium nitrate is:

Where:

: is the molar mass of ammonium nitrate = 80.043 g/mol

Hence, the mass of ammonium nitrate that has the same number of nitrogen atoms is 5077.5 g.

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