Question

If the Earth's ozone (O3) layer has a total volume of 1.00 × 1020 km3, a partial pressure of 1.6 × 10-9 atm, and an average temperature of 230 K, how many ozone molecules are in the Earth's ozone layer?

Answer 1

To solve this problem we will apply the ideal gas equations for which the product of pressure and volume is defined, as the equivalent between the ideal gas constant by the amount of matter and the temperature, mathematically this equation is described as

$PV = nRT$

Here,

P = Pressure

V = Volume

R = Ideal gas Constant

T = Temperature

n = Number of molecules

The pressure is in atmospheres, and considering the units of the other values we have finally that,

$R = 0.08206 \cdot atm\cdot L\cdot mol^{-1}\cdot K^{-1}$

$V = 1*10^{20}km^3 (\frac{1*10^{12}L}{1km^3 })$

$V = 1*10^{32}L$

$P = 1.6*10^{-9}atm$

$T = 230K$

Replacing,

$(1.6*10^{-9})(1*10^{32}) = n(0.08206)(230)$

$n = \frac{(1.6*10^{-9})(1*10^{32})}{(0.08206)(230)}$

$n = 8.47736*10^{-21}$

Multiplying the number of moles by Avogadro's number we have,

$M =(8.47736*10^{-21})(6.022*10^{23})$

$M = 5.1*10^{45}$

Therefore the number of ozone molecules in the Earth's ozone layer are $5.1*10^{45}$