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Chapter 8: Problem 80

Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions \(0.78 \mathrm{N}_{2}, 0.21 \mathrm{O}_{2},\) and \(0.010 \mathrm{Ar},\) what is the density of air at standard temperature and pressure?

Short Answer

Expert verified
The density of air at standard temperature and pressure, given the mole fractions \(0.78 N_2\), \(0.21 O_2\), and \(0.010 Ar\), is approximately 1.29 g/L.

Step by step solution

01

Find the molar mass of each component

To get the molar mass of the air sample, we need to find the molar mass of each gas involved. We use the mole fraction given in the problem and use the molar masses of nitrogen, oxygen, and argon gases to have an appropriate measure. Molar mass of N2: 28.02 g/mol Molar mass of O2: 32.00 g/mol Molar mass of Ar: 39.95 g/mol
02

Calculate the molar mass of air

Now, using the mole fractions and the molar masses of each gas, we find the molar mass of air. Multiply the mole fraction of each gas by its molar mass and sum them up: M_air = (0.78 * 28.02 g/mol) + (0.21 * 32.00 g/mol) + (0.010 * 39.95 g/mol) M_air ≈ 28.97 g/mol
03

Recall the ideal gas law and standard conditions

To find the density of air, we need to use the ideal gas law (PV = nRT), where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is the temperature. We are given standard temperature and pressure (STP) conditions, which means: Temperature (T) = 273.15 K (0°C) Pressure (P) = 1 atm (101.325 kPa) Also, the ideal gas constant (R) = 0.0821 (L * atm / (mol * K))
04

Find the number of moles per volume

Rearranging the ideal gas law formula to find n/V: n/V = P / (RT) Let's plug in the values of P, R, and T: n/V = (1 atm) / (0.0821 L * atm / (mol * K) * 273.15 K) n/V ≈ 0.0446 mol/L
05

Calculate the density of air

Now let's use the calculated molar mass of air and the number of moles per volume to find density. Density = M_air * n/V Density_air ≈ (28.97 g/mol) * (0.0446 mol/L) Density_air ≈ 1.29 g/L Thus, the density of air at standard temperature and pressure is approximately 1.29 g/L.

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Most popular questions from this chapter

Calculate the pressure exerted by \(0.5000\) mole of \(\mathrm{N}_{2}\) in a \(1.0000-\mathrm{L}\) container at \(25.0^{\circ} \mathrm{C}\) a. using the ideal gas law. b. using the van der Waals equation. c. Compare the results.

The total volume of hydrogen gas needed to fill the Hindenburg was \(2.0 \times 10^{8} \mathrm{L}\) at 1.0 atm and \(25^{\circ} \mathrm{C}\). Given that \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(l)\) is \(-286 \mathrm{kJ} / \mathrm{mol},\) how much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted to form water?

Methane \(\left(\mathrm{CH}_{4}\right)\) gas flows into a combustion chamber at a rate of \(200 .\) L/min at \(1.50\) atm and ambient temperature. Air is added to the chamber at 1.00 atm and the same temperature, and the gases are ignited. a. To ensure complete combustion of \(\mathrm{CH}_{4}\) to \(\mathrm{CO}_{2}(g)\) and \(\mathrm{H}_{2} \mathrm{O}(g),\) three times as much oxygen as is necessary is reacted. Assuming air is \(21\) mole percent \(\mathrm{O}_{2}\) and \(79\) mole percent \(\mathrm{N}_{2}\), calculate the flow rate of air necessary to deliver the required amount of oxygen. b. Under the conditions in part a, combustion of methane was not complete as a mixture of \(\mathrm{CO}_{2}(g)\) and \(\mathrm{CO}(g)\) was produced. It was determined that \(95.0 \%\) of the carbon in the exhaust gas was present in \(\mathrm{CO}_{2}\). The remainder was present as carbon in \(\mathrm{CO}\). Calculate the composition of the exhaust gas in terms of mole fraction of \(\mathrm{CO}, \mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{N}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}\). Assume \(\mathrm{CH}_{4}\) is completely reacted and \(\mathrm{N}_{2}\) is unreacted.

An important process for the production of acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\right)\) is given by the following equation: $$2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ A \(150 .\)-\(\mathrm{L}\)reactor is charged to the following partial pressures at \(25^{\circ} \mathrm{C}:\) $$\begin{aligned}P_{\mathrm{C}, \mathrm{H}_{6}} &=0.500 \mathrm{MPa} \\\P_{\mathrm{NH}_{3}} &=0.800 \mathrm{MPa} \\\P_{\mathrm{O}_{2}} &=1.500 \mathrm{MPa}\end{aligned}$$ What mass of acrylonitrile can be produced from this mixture \(\left(\mathrm{MPa}=10^{6} \mathrm{Pa}\right) ?\)

Write an equation to show how sulfuric acid is produced in the atmosphere.
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