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Chapter 10: Problem 38

(a) If the pressure exerted by ozone, \(\mathrm{O}_{3}\), in the stratosphere is \(304 \mathrm{~Pa}\) and the temperature is \(250 \mathrm{~K}\), how many ozone molecules are in a liter? (b) Carbon dioxide makes up approximately \(0.04 \%\) of Earth's atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level \((101.33 \mathrm{kPa})\) on a warm day $\left(27^{\circ} \mathrm{C}\right)\(, how many \)\mathrm{CO}_{2}$ molecules are in your sample?

Short Answer

Expert verified
(a) The number of ozone molecules in a liter is: \(n_{molecules} = n \times (6.022\times 10^{23}\ \text{molecules/mol})\) where \(n = \frac{(0.003 \text{ atm})(1 \text{ L})}{(0.08206\ \text{atm L}\,\text{mol}^{-1}\,\text{K}^{-1})(250\text{ K})}\) (b) The number of CO2 molecules in a 2.0-L sample is: \(n_{molecules} = n \times (6.022\times 10^{23}\ \text{molecules/mol})\) where \(n = \frac{(3.998\times10^{-4} \text{ atm})(2 \text{ L})}{(0.08206\ \text{atm L}\,\text{mol}^{-1}\,\text{K}^{-1})(300.15\ \text{K})}\)

Step by step solution

01

Convert pressure to atm and volume to liters

: We are given the pressure in Pascals and the temperature in Kelvin. Convert the pressure to atm: \(\frac{1\ \text{atm}}{101325\ \text{Pa}} \times 304\ \text{Pa} = 0.003 \text{atm}\) The volume is given in liters, which is 1 L.
02

Calculate number of moles (n)

: Rearrange the ideal gas law equation for n: \(n = \frac{PV}{RT}\) Plugging in the given values and the gas constant (R) = 0.08206 atm L mol\(^{-1}\) K\(^{-1}\): \(n = \frac{(0.003 \text{ atm})(1 \text{ L})}{(0.08206\ \text{atm L}\,\text{mol}^{-1}\,\text{K}^{-1})(250\text{ K})}\)
03

Compute the number of molecules

: Calculate the number of ozone molecules by multiplying the number of moles by Avogadro's number: \(n_{molecules} = n \times (6.022\times 10^{23}\ \text{molecules/mol})\) (b) Number of CO2 molecules in a 2.0-L sample:
04

Calculate the partial pressure of CO2

: Given that carbon dioxide makes up approximately 0.04% of Earth's atmosphere, calculate the partial pressure of CO2 by multiplying the percentage by the total atmospheric pressure: \((0.0004) \times 101.33\ \text{kPa} = 0.040532\ \text{kPa} \) Convert this partial pressure from kPa to atm: \(0.040532\ \text{kPa} \times \frac{1\ \text{atm}}{101325\ \text{Pa}} = 3.998\times 10^{-4} \text{atm}\)
05

Convert temperature to Kelvin

: Given the temperature in Celsius, convert it to Kelvin: \(27 ^{\circ}\ \text{C} + 273.15\ = 300.15\ \text{K}\)
06

Calculate number of moles (n)

: Rearrange the ideal gas law equation for n: \(n = \frac{PV}{RT}\) Plugging in the given values and R = 0.08206 atm L mol\(^{-1}\) K\(^{-1}\): \(n = \frac{(3.998\times10^{-4} \text{ atm})(2 \text{ L})}{(0.08206\ \text{atm L}\,\text{mol}^{-1}\,\text{K}^{-1})(300.15\ \text{K})}\)
07

Compute the number of molecules

: Calculate the number of CO2 molecules by multiplying the number of moles by Avogadro's number: \(n_{molecules} = n \times (6.022\times 10^{23}\ \text{molecules/mol})\)

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Most popular questions from this chapter

The atmospheric concentration of \(\mathrm{CO}_{2}\) gas is presently 407 ppm (parts per million, by volume; that is, \(407 \mathrm{~L}\) of every $10^{6} \mathrm{~L}\( of the atmosphere are \)\mathrm{CO}_{2}$ ). What is the mole fraction of \(\mathrm{CO}_{2}\) in the atmosphere?

Consider the following gases, all at STP: $\mathrm{Ne}, \mathrm{SF}_{6}, \mathrm{~N}_{2}, \mathrm{CH}_{4}$. (a) Which gas is most likely to depart from the assumption of the kinetic- molecular theory that says there are no attractive or repulsive forces between molecules? (b) Which one is closest to an ideal gas in its behavior? (c) Which one has the highest root-mean-square molecular speed at a given temperature? (d) Which one has the highest total molecular volume relative to the space occupied by the gas? (e) Which has the highest average kinetic- molecular energy? (f) Which one would effuse more rapidly than $\mathrm{N}_{2} ?\( (g) Which one would have the largest van der Waals \)b$ parameter?

A piece of dry ice (solid carbon dioxide) with a mass of \(20.0 \mathrm{~g}\) is placed in a 25.0-L vessel that already contains air at \(50.66 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant \(\mathrm{CO}_{2}\) gas, and the total pressure in the container at \(25^{\circ} \mathrm{C} ?\)

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. \(\mathrm{Hg}\). (a) Convert this pressure to torr. (b) Convert this pressure to atm.

A sample of \(5.00 \mathrm{~mL}\) of diethylether $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OC}_{2} \mathrm{H}_{5},\right.\( density \)=0.7134 \mathrm{~g} / \mathrm{mL}\( ) is introduced into a \)6.00-\mathrm{L}$ vessel that already contains a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), whose partial pressures are \(R_{\mathrm{N}_{2}}=21.08 \mathrm{kPa}\) and \(P_{\mathrm{O}_{2}}=76.1 \mathrm{kPa}\). The temperature is held at \(35.0^{\circ} \mathrm{C},\) and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container.
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