Question

question 13 (5 points) with each breath of air, you inhale 4.50 × 10²³ molecules of nitrogen gas. what is the mass of the inhaled nitrogen gas?

a) 10.5 g

b) 20.9 g

c) 18.7 g

d) 37.5 g

Explanation:

Step1: Find moles of \(N_2\)

Moles \(n = \frac{\text{Number of molecules}}{N_A}\), where \(N_A = 6.022\times10^{23}\) molecules/mol.
\(n=\frac{4.50\times10^{23}}{6.022\times10^{23}}\approx0.747\) mol.

Step2: Calculate molar mass of \(N_2\)

Molar mass of \(N\) is \(14.01\) g/mol, so \(N_2\) is \(2\times14.01 = 28.02\) g/mol.

Step3: Find mass of \(N_2\)

Mass \(m = n\times M\), where \(M = 28.02\) g/mol.
\(m = 0.747\space\text{mol}\times28.02\space\text{g/mol}\approx20.9\) g.

Answer:

b) 20.9 g