Chapter 1, Problem 1.24NP

When Julius Caesar expired, his last exhalation had a volume of $\text{45}0.{\text{ cm}}^{\text{3}}$ and contained 1.00 mole percent argon. Assume that $\text{T}=\text{3}00$. K and $\text{P}=\text{1}.00\text{ atm}$ at the location of his demise. Assume further that T has the same value throughout Earth’s atmosphere. If all of his exhaled Ar atoms are now uniformly distributed throughout the atmosphere, how many inhalations of 450. ${\text{cm}}^{\text{3}}$ must we make to inhale one of the Ar atoms exhaled in Caesar’s last breath? Assume the radius of Earth to be $\text{6}.\text{37}\times \text{1}{0}^{\text{6}}\text{m}$. [Hint: Calculate the number of Ar atoms in the atmosphere in the simplified geometry of a plane of area equal to that of Earth’s surface. See Problem P1.20 for the dependence of the barometric pressure and the composition of air on the height above Earth’s surface.