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Chapter 6: Problem 65

A 4.0 L sample of \(\mathrm{O}_{2}\) gas has a pressure of 1.0 atm. A 2.0 L sample of \(\mathrm{N}_{2}\) gas has a pressure of 2.0 atm. If these two samples are mixed and then compressed in a 2.0 L vessel, what is the final pressure of the mixture? Assume that the temperature remains unchanged.

Short Answer

Expert verified
The final pressure of the mixture is 4.0 atm

Step by step solution

01

Determine the number of moles of each gas

Initially, we assume an ideal behavior for gases. Therefore, we can use the Ideal Gas Law \(PV=nRT\) to determine the number of moles. It's given that R (the gas constant) and T (temperature) are constant. So, we can simplify the formula to \(PV=n\). We calculate the number of moles for O\(_2\) and N\(_2\) gases using their initial pressures and volumes: Moles of O\(_2\) = \(P_{O_2}V_{O_2} = 1.0 atm * 4.0 L = 4.0 atm*L\) and moles of N\(_2\) = \(P_{N_2}V_{N_2} = 2.0 atm * 2.0 L = 4.0 atm*L\)
02

Calculate the total number of moles

We determine the total moles of the mixed gases by adding the moles of O\(_2\) and the moles of N\(_2\): Total moles = \(moles_{O_2} + moles_{N_2} = 4.0 atm*L + 4.0 atm*L = 8.0 atm*L\)
03

Determine the final pressure

To determine the final pressure, we use the modified Gas Law since volume and temperature are constant after the gases are mixed: \(P = n/V\), where n is the total number of moles and V is the final volume: Final Pressure = \(P = n/V = 8.0 atm*L / 2.0 L = 4.0 atm\).

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Most popular questions from this chapter

In research that required the careful measurement of gas densities, John Rayleigh, a physicist, found that the density of \(\mathrm{O}_{2}(\mathrm{g})\) had the same value whether the gas was obtained from air or derived from one of its compounds. The situation with \(\mathrm{N}_{2}(\mathrm{g})\) was different, however. The density of \(\mathrm{N}_{2}(\mathrm{g})\) had the same value when the \(\mathrm{N}_{2}(\mathrm{g})\) was derived from any of various compounds, but a different value if the \(\mathrm{N}_{2}(\mathrm{g})\) was extracted from air. In \(1894,\) Rayleigh enlisted the aid of William Ramsay, a chemist, to solve this apparent mystery; in the course of their work they discovered the noble gases. (a) Why do you suppose that the \(\mathrm{N}_{2}(\mathrm{g})\) extracted from liquid air did not have the same density as \(\mathrm{N}_{2}(\mathrm{g})\) obtained from its compounds? (b) Which gas do you suppose had the greater density: \(\mathrm{N}_{2}(\mathrm{g})\) extracted from air or \(\mathrm{N}_{2}(\mathrm{g})\) prepared from nitrogen compounds? Explain. (c) The way in which Ramsay proved that nitrogen gas extracted from air was itself a mixture of gases involved allowing this nitrogen to react with magnesium metal to form magnesium nitride. Explain the significance of this experiment. (d) Calculate the percent difference in the densities at \(0.00^{\circ} \mathrm{C}\) and 1.00 atm of Rayleigh's \(\mathrm{N}_{2}(\mathrm{g})\) extracted from air and \(\mathrm{N}_{2}(\mathrm{g})\) derived from nitrogen compounds. [The volume percentages of the major components of air are \(78.084 \% \mathrm{N}_{2}, 20.946 \% \mathrm{O}_{2}, 0.934 \% \mathrm{Ar},\) and \(0.0379 \% \mathrm{CO}_{2} .\)

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is sometimes used as a chlorinating agent for water treatment. It can be prepared from the reaction below: \(\mathrm{Cl}_{2}(\mathrm{g})+4 \mathrm{NaClO}(\mathrm{aq}) \longrightarrow 4 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{ClO}_{2}(\mathrm{g})\) In an experiment, \(1.0 \mathrm{L} \mathrm{Cl}_{2}(\mathrm{g}),\) measured at \(10.0^{\circ} \mathrm{C}\) and 4.66 atm, is dissolved in 0.750 L of 2.00 M \(\mathrm{NaClO}(\mathrm{aq}) .\) If \(25.9 \mathrm{g}\) of pure \(\mathrm{ClO}_{2}\) is obtained, then what is the percent vield for this experiment?

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(24^{\circ} \mathrm{C}\) The volume of gas is 1.16 L. In a subsequent experiment, it is determined that the mass of \(\mathrm{O}_{2}\) present is 1.46 g. What must have been the barometric pressure at the time the gas was collected? (Vapor pressure of water \(=22.4 \text { Torr. })\)

A 35.8 L cylinder of \(\mathrm{Ar}(\mathrm{g})\) is connected to an evacuated 1875 L tank. If the temperature is held constant and the final pressure is \(721 \mathrm{mmHg}\), what must have been the original gas pressure in the cylinder, in atmospheres?

A particular coal sample contains \(3.28 \%\) S by mass. When the coal is burned, the sulfur is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) What volume of \(\mathrm{SO}_{2}(\mathrm{g}),\) measured at \(23^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg},\) is produced by burning \(1.2 \times 10^{6} \mathrm{kg}\) of this coal?
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