How much air did Julius Caesar breathe in his lifetime?
Fact: He was killed at the age of 56 (Et tu Brute?).
Fact: On average, a human being uses between 1 and 2 m³ of air per hour. A part of the exhaled air will be re-inhaled, so let's say it is 1 m³/hour.
Conclusion: In a 56 year lifetime that is 56×365.25×24 = ca. 500000 m³.

What fraction of the Earth's atmosphere is that?
Fact: The Earth's circumference is 40000 km, so its surface is 40000²/pi = ca. 5×10⁸ km².
Fact: The air pressure at ground level is 1 kg/cm² and the density of air at ground level is 1.225 kg/m³.
Conclusion: The air column above 1 cm² is 1/(1.225 kg/m³) = ca. 0.82 m³ effectively, and (0.82 m³)/(1 cm²) = 8200 m, so the effective thickness of the atmosphere is 8.2 km. This leads to a total effective atmospheric volume of 8.2×(5×10⁸) = 4.1×10⁹ km³ = 4.1×10¹⁸ m³. Thus, the fraction of the atmosphere breathed by Julius Caesar is (5×10⁵)/(4.1×10¹⁸) = 1.2×10^-13, so about every 1.2 in 10,000,000,000,000 molecules of the Earth's atmosphere have been inhaled and exhaled by Julius Caesar. The Oxygen component of the air is an essential part of biological cycles, but the 80% Nitrogen is chemically inert, so let's reduce this result to 10^-13 = 1 in 10,000,000,000,000.

What does this mean?
Since the weather is a very turbulent global phenomenon (it takes only a week for a Caribbean hurricane to become a European depression), all of Julius Caesar's exhaled air has been very homogeneously mixed with the atmosphere in the (Julian) years that passed since he died.
Your own lungs contain ca. 3 to 4 litres of air right now, let's calculate with 4 litres. That is (using Avogadro's law: 6×10²³ molecules is ca. 25 litres at room temperature) a total of 6×10²³×4/25 = ca. 10²³ molecules. Combining these results leads to the following conclusion: