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Chapter 5: Problem 59

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 \(0^{\circ} \mathrm{C}\).

Short Answer

Expert verified
The partial pressure and concentration of each gas: for N2 are approximately 0.780 atm and \(0.033 mol/L\), for O2 are approximately 0.209 atm and \(0.009 mol/L\), for Ar are approximately 0.009 atm and \(0.0004 mol/L\), and for CO2 are approximately 0.0005 atm and \(0.00002 mol/L\).

Step by step solution

01

Calculating the Partial Pressure

The atmospheric pressure is given as 1.00 atm. Knowing that each gas contributes to the total pressure in the ratio of its volume percent, the partial pressure of each gas can be calculated by multiplying the atmospheric pressure by their individual volume percentage divided by 100. For instance, the partial pressure of N2 can be calculated as \(P_{N_2} = 1.00 atm * 78.08/100\). Similar computations will be done for O2, Ar, and CO2.
02

Determine the Temperature in Kelvin

Conversion of the temperature from Celsius to Kelvin is essential when calculating the number of moles in the Ideal Gas Law. The temperature in Kelvin can be determined by adding 273.15 to the Celsius temperature, so \(T = 0^{\circ}C + 273.15 = 273.15K\).
03

Calculate the Concentrations

The concentration of each gas in moles per liter can be calculated by substituting the partial pressure of that specific gas and the temperature into the Ideal Gas Law, \(PV = nRT\), and solving for n/V which gives us the concentration (C). The molar gas constant (R) is \(0.0821 L.atm/K.mol\). For example, the concentration of N2 is calculated as following: \(C_{N_2} = P_{N_2}/(RT)\). Similar computations will be done for O2, Ar, and CO2.

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Most popular questions from this chapter

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