Question

How many molecules are in 28 grams of nitrogen gas in balloons?

a.28 x 6.0 x 10 to the 23rd power molecules nitrogen gas
b.2.0 x 10 to the 23rd power molecules nitrogen gas
c.1.0 x 10 to the 23rd power molecules nitrogen gas
d.6.0 x 10 to the 23rd power molecules nitrogen gas
e.1.2 x 10 to the 24rd power molecules nitrogen gas
f.3.0 x 10 to the 23rd power molecules nitrogen gas

Answer 1

`6.022\cdot 10^(23)` molecules of nitrogen gas

Step-by-step explanation:

In order to convert the mass of a given compound into the number of molecules, we need to:

• identify the number of moles of a given compound dividing its mass by the molar mass,
  `n = (m)/(M)`,
• multiply the number of moles by the Avogadro's constant which tells us that 1 mole contains
  `N_A = 6.022\cdot 10^(23)` molecules.

In this problem:

`m_(N_2) = 28~g`

`M_(N_2) = 28.01~g/mol`

The number of particles is then found by:

`N_(N_2) = n_(N_2)\cdot N_A = (m_(N_2))/(M_(N_2)) N_A = (28 g)/(28.01 g/mol)\cdot 6.022\cdot 10^(23) mol^(-1) = 6.022\cdot 10^(23)`