The atmosphere contains about 6.8×1013 moles of ozone. If this amount of ozone gas is

compressed into a thin layer around the globe (the radius of Earth is 6370 km) at STP
(Standard Temperature (0°C) and Pressure (1.0 atm.)), how thick will the layer be in
millimeter? One hundredth of 1 mm of this layer is called a Dobson Unit (DU).

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To calculate the thickness of the ozone layer, we need to know the volume occupied by the given amount of ozone gas. From there, we can determine how many millimeters thick the layer would be.

To start, let's find the volume of the ozone gas using the ideal gas law:

PV = nRT

Where:
P = pressure (1.0 atm)
V = volume of gas
n = number of moles (6.8×10^13 moles)
R = ideal gas constant (0.0821 L∙atm/(mol∙K))
T = temperature (0°C or 273.15 K)

Rearranging the equation to solve for V, we have:

V = (nRT) / P

Substituting the given values:

V = (6.8×10^13 moles * 0.0821 L∙atm/(mol∙K) * 273.15 K) / 1.0 atm

V ≈ 1.76×10^15 L

Now, let's calculate the thickness of the layer. Since the layer is compressed into a thin layer around the globe, its volume is equal to the volume of a thin shell with an inner radius of Earth (6370 km) and a thickness of h (in millimeters):

V_layer = (4/3) * π * (R^3 - (R - h)^3)

Where:
V_layer = volume of the ozone layer
R = radius of Earth in millimeters (6370 km = 6370000 m = 6370000000 mm)

Simplifying the equation and solving for h, we get:

h = R - ( (3 * V_layer) / (4π(R^2)) )

Substituting the known values:

h = 6370000000 - ( (3 * 1.76×10^15) / (4π((6370000000)^2)) )

Calculating this expression, we find:

h ≈ 3.59 mm

Therefore, the thickness of the ozone layer, when compressed into a thin layer around the globe at STP, would be approximately 3.59 millimeters or 359 Dobson Units (DU).