Estimate how many molecules of air are in each 2.5 L breath you take that were also in the last breath Einstein took (assumed to be the same volume). (Hint: Assume the atmosphere is about 11 km high and of constant density. Take the temperature of the air to be 27°C.)
To estimate the number of molecules of air in each breath, we need to calculate the total number of molecules in the volume of air you breathe in and compare it to the total number of molecules in the volume of air Einstein breathed in. Here's how you can calculate this:
1. Calculate the number of molecules in each breath:
- Convert the temperature from Celsius to Kelvin:
27°C + 273.15 = 300.15 K
- Use the ideal gas law to calculate the number of moles of gas in each breath:
PV = nRT, where:
P = pressure (atmospheric pressure)
V = volume of breath (2.5 L)
n = number of moles
R = gas constant (8.314 J/(mol·K))
T = temperature (300.15 K)
- Rearrange the equation to solve for n:
n = PV / RT
- Substitute the values to calculate n.
- The number of molecules (N) in each breath can be found by multiplying the number of moles (n) by Avogadro's number (6.022 x 10^23 mol^-1):
N = n * Avogadro's number
2. Calculate the number of molecules in the volume of air Einstein breathed in:
- Assume that Einstein's breath had the same volume as yours (2.5 L).
- Use the same steps as above to calculate the number of molecules (N).
3. Compare the number of molecules in each breath:
- Divide the number of molecules in Einstein's breath by the number of molecules in your breath to find the ratio:
Ratio = N(Einstein) / N(You)
Please note that this estimation assumes that the atmosphere is of constant density and the same composition throughout its height. However, in reality, these conditions may vary, and this is a simplified estimation based on the given information.