The mass density of normal air at a certain temperature is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$. If the average molecular mass of air is $29.0 \mathrm{u}$, how many air molecules are in spherical balloon of radius $15.0 \mathrm{~cm}$ ?
A) $3.8 \times 10^{23}$
B) $2.5 \times 10^{25}$
C) $3.3 \times 10^{25}$
D) $8.5 \times 10^{23}$
E) $1.1 \times 10^{24}$
F) $9.8 \times 10^{24}$

Question

Quizplus · Accepted Answer

To find the number of air molecules in the balloon, first calculate the volume of the balloon using the formula for the volume of a sphere, $V = \frac{4}{3}\pi r^3$, where $r = 0.15 \, \text{m}$. Then, find the mass of air in the balloon using the given density ($1.29 \, \text{kg/m}^3$). Finally, use Avogadro's number and the molecular mass of air to convert the mass of air to the number of molecules. The calculation leads to an answer close to $3.8 \times 10^{23}$, which matches option A.

The Mass Density of Normal Air at a Certain Temperature 1.29 kg/m31.29 \mathrm{~kg} / \mathrm{m}^{3}1.29 kg/m3

The Mass Density of Normal Air at a Certain Temperature $1.29 \mathrm{~kg} / \mathrm{m}^{3}$