Question

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

Answer 1

Answer:

$6.022\cdot 10^{23}$ molecules of nitrogen gas

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, $n = \frac{m}{M}$,
• 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:

$N_{N_2} = n_{N_2}\cdot N_A = \frac{m_{N_2}}{M_{N_2}} N_A = \frac{28 g}{28.01 g/mol}\cdot 6.022\cdot 10^{23} mol^{-1} = 6.022\cdot 10^{23}$