Question

Carbon dioxide makes up approximately 0.04% of Earth's atmosphere. If you collect a 2.5 L sample from the atmosphere at sea level (1.00 atm) on a warm day (27 ∘C), how many CO2 molecules are in your sample?

Answer 1

First calculate total mole of gas in gas sample

Use ideal gas equation for calculation of mole of gas

Ideal gas equation

PV = nRT             where, P = atm pressure = 1 atm,

V = volume in Liter = 2.5 L

n = number of mole = ?

R = 0.08205L atm mol^-1 K^-1 =Proportionality constant = gas constant,

T = Temperature in K = 27⁰ = 273.15+ 27 = 300.15 K

We can write ideal gas equation

n = PV/RT

Substitute the value

n = (12.5)/(0.08205300.15) = 0.1015 mole

total mole of gas = 0.1015 mole

0.1015 mole = 100% then 0.04% = 0.1015 0.04/100 = 0.0000406 mole of CO₂

According to avogadro's law 1 mole of gas contain 6.022 10²³ molecule then 0.0000406 mole of CO₂ contain

6.022 10²³ 0.0000406 = 2.444932 10¹⁹ molecule of CO₂