Given that the quantity of ozone in the stratosphere is equivalent to a 3.0-mm-thick layer of ozone on Earth at STP, calculate the number of ozone molecules in the stratosphere and their mass in kilograms. (Hint: The radius of Earth is 6371 km and the surface area of a sphere is 4 pi r^2, where r is the radius).
The radius of earth (r) = 6371 km
Surface area of a sphere (S.A) = 4πr² = "4\u00d7 \\dfrac{22}7 \u00d7 (6371 \u00d710^3)^2" = 5.1 × 10¹⁴ m²
Volume of the atmosphere volume of atmosphere = S.A × thickness = 5.1 × 10¹⁴ × 3 × 10-³ = 15.3 × 10¹¹ m³
Since 1m³ = 1000L
15.3 × 10¹¹ m³= 15.3 × 10¹⁴L
Since 22.4 L contains 6.023 × 10²³ Ozone molecules,
Thus, 15.3 × 10¹⁴ L = "\\dfrac{6.023\u00d710\u00b2\u00b3 \u00d7 15.3 \u00d7 10\u00b9\u2074L}{22.4}" = 4.11 × 10³⁷ molecules of Ozone
1 mole of Ozone (O3) = 48g (16×3g)
6.023 × 10²³ molecules of Ozone = 48g
4.11 × 10³⁷ molecules of Ozone = "\\dfrac{4.11 \u00d7 10\u00b3\u2077 \u00d7 48}{6.023\u00d7 10\u00b2\u00b3}" = 3.275 × 10¹⁵g = 3.275 × 10¹² kg
Therefore, the number of ozone molecules in their stratosphere and their mass in kilograms is 4.11 × 10³⁷ molecules and 3.275 × 10¹² kg respectively.
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