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Chapter 5: Problem 118

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at \(22^{\circ} \mathrm{C},\) what is the mass (in grams) of \(\mathrm{O}_{2}\) present? How many liters of \(\mathrm{O}_{2}\) gas at 1.00 atm and \(22^{\circ} \mathrm{C}\) could the cylinder produce? (Assume ideal behavior.)

Short Answer

Expert verified
The mass of oxygen gas contained in the cylinder is 20742.72 grams. The volume of the gas it can produce at 1.00 atm and 22 degrees Celsius is 15633.19 liters.

Step by step solution

01

Understand the Ideal Gas Law

The ideal gas law can be defined as PV=nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature. The gas constant value to be used here will be 0.0821 L.atm/(mol.K) and the temperature must be converted into Kelvin by adding 273 to the Celsius temperature. Here, P=132 atm, V=120 L, and T= 295K (22 + 273).
02

Calculate number of moles using Ideal Gas Law

Rearranging the ideal gas law to n=P*V/(R*T), we substitute the given values to find n=(132*120)/(0.0821*295). Upon calculating, we find n= 648.21 moles of O2.
03

Find Mass of O2

We know the molar mass of oxygen is 32 g/mol. So, we multiply the number of moles by the molar mass to get the mass of the gas. Therefore mass = n * molar mass = 648.21 * 32 = 20742.72 grams.
04

Determine the volume the gas can occupy at standard conditions

We now use the ideal gas law again to find the volume the gas will occupy at standard conditions. We substitute the given conditions for P=1.00 atm, T=295K, n= 648.21, and R= 0.0821 as before. So, V=nRT/P =(648.21*0.0821*295)/1. Calculating, we find volume V=15633.19 liters.

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Most popular questions from this chapter

A stockroom supervisor measured the contents of a partially filled 25.0 -gallon acetone drum on a day when the temperature was \(18.0^{\circ} \mathrm{C}\) and atmospheric pressure was \(750 \mathrm{mmHg}\), and found that 15.4 gallons of the solvent remained. After tightly sealing the drum, an assistant dropped the drum while carrying it upstairs to the organic laboratory. The drum was dented and its internal volume was decreased to 20.4 gallons. What is the total pressure inside the drum after the accident? The vapor pressure of acetone at \(18.0^{\circ} \mathrm{C}\) is \(400 \mathrm{mmHg} .\)

What are the basic assumptions of the kinetic molecular theory of gases? How does the kinetic molecular theory explain Boyle's law, Charles' law, Avogadro's law, and Dalton's law of partial pressures?

The following apparatus can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at \(850^{\circ} \mathrm{C}\) some bismuth (Bi) atoms struck the target at a point \(2.80 \mathrm{~cm}\) from the spot directly opposite the slit. The diameter of the cylinder is \(15.0 \mathrm{~cm}\) and it is rotating at 130 revolutions per second. (a) Calculate the speed (m/s) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r,\) where \(r\) is the radius. \()\) (b) Calculate the time (in seconds) it takes for the target to travel \(2.80 \mathrm{~cm} .\) (c) Determine the speed of the Bi atoms. Compare your result in (c) with the \(u_{\mathrm{rms}}\) of \(\mathrm{Bi}\) at \(850^{\circ} \mathrm{C}\). Comment on the difference.

Apply your knowledge of the kinetic theory of gases to the following situations. (a) Two flasks of volumes \(V_{1}\) and \(V_{2}\left(V_{2}>V_{1}\right)\) contain the same number of helium atoms at the same temperature. (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures \(T_{1}\) and \(T_{2}\left(T_{2}>T_{1}\right) .\) (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is \(74^{\circ} \mathrm{C}\). Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\)

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?
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