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Chapter 5: Problem 45

The ozone molecules present in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are \(250 \mathrm{~K}\) and \(1.0 \times 10^{-3} \mathrm{~atm},\) respectively. How many ozone molecules are present in \(1.0 \mathrm{~L}\) of air under these conditions?

Short Answer

Expert verified
The number of ozone molecules present in 1.0 L of air under these conditions is approximately \(2.91 \times 10^{19} \mathrm{~molecules}\)

Step by step solution

01

Convert units to match ideal gas law

First of all, ensure your units are consistent with the gas law. Here, pressure is given in atm and will be left as is, volume is given in L and will also be left as is, the gas constant \(R\) is \(0.0821 \mathrm{~L·atm/K·mol}\) and the temperature is given in Kelvin and will therefore remain the same.
02

Rearrange Ideal Gas Law equation

Rearrange the Ideal Gas Law equation to find n (number of moles). It will look like this: \(n = \frac{PV}{RT}\)
03

Plug in the values into the Ideal Gas Law equation

Plug known values into the rearranged Ideal Gas Law equation: \(n = \frac{1.0 \times 10^{-3} \mathrm{~atm} \times 1.0 \mathrm{~L}}{0.0821 \mathrm{~L·atm/K·mol} \times 250 \mathrm{~K}}\)
04

Solve for number of moles (n)

Using a calculator, calculate the number of moles (n). The result is \(n = 4.84 \times 10^{-5} \mathrm{~moles}\)
05

Convert to the number of Ozone molecules

The number of molecules is equal to the number of moles times Avogadro's number (\(6.022 \times 10^{23}\)). So, the number of ozone molecules is \( 4.84 \times 10^{-5} \mathrm{~moles} \times 6.022 \times 10^{23} \mathrm{~molecules/mole} = 2.91 \times 10^{19} \mathrm{~molecules}\)

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Most popular questions from this chapter

Dry air near sea level has the following composition by volume: \(\mathrm{N}_{2}, 78.08\) percent; \(\mathrm{O}_{2}, 20.94\) percent; \(\mathrm{Ar},\) 0.93 percent; \(\mathrm{CO}_{2}, 0.05\) percent. The atmospheric pressure is \(1.00 \mathrm{~atm} .\) Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at \(0^{\circ} \mathrm{C}\).

Define pressure and give the common units for pressure.

Why is it that if the barometer reading falls in one part of the world, it must rise somewhere else?

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is \(0.0050 \mathrm{~cm}\) and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is \(37^{\circ} \mathrm{C},\) calculate the number of oxygen molecules in one of the alveoli.

What are standard temperature and pressure (STP)? What is the significance of STP in relation to the volume of 1 mole of an ideal gas?
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