Question

Carbon dioxide makes up approximately 0.04% of Earth's atmosphere. If you collect a 2.7 L sample from the atmosphere at sea level (1.00 atm) on a warm day (25 ∘C), how many CO2 molecules are in your sample?

Answer 1

2.66x10¹⁹ molecules of CO₂

Step-by-step explanation:

Using ideal gas law (PV = nRT), it is possible to find moles of air collected thus:

PV = nRT

PV / RT = n

1.00atm×2.7L / 0.082atmL/molK×298.15K = n

Temperature in Kelvin (25°C + 273.15 = 298.15K); R is gas constant (0.082atmL/molK)

0.110moles of air you collected. From here, 0.04% is CO₂. Thus, moles of CO₂ are:

0.110moles × (0.04 / 100) = 4.42x10⁻⁵ moles of CO₂. 1 mole contains 6.022x10²³ molecules. Molecules of CO₂ are:

4.42x10⁻⁵ moles of CO₂ × (6.022x10²³ molecules / 1mol) =

2.66x10¹⁹ molecules of CO₂

Answer 2

2.66 x 10^19 CO2 molecules

Step-by-step explanation:

0.04% = 0.04 / 100 = 0.00040

2.7 L air x (0.00040 L of CO2 is in 1 L air) = 0.00108 L CO2

Use the ideal gas law to find moles of CO2.

PV = nRT

n = PV / RT = (1.00 atm)(0.0012 L) / (0.0821 L atm / K mole)(298 K) = 4.44 x 10^-5 moles CO2

One mole of anything contains 6.02 x 10^23 particles.

4.44 x 10^-5 moles CO2 x (6.02 x 10^23 CO2 molecules / 1 mole CO2) = 2.66 x 10^19 CO2 molecules