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Chapter 5: Problem 20
A gas occupying a volume of \(725 \mathrm{~mL}\) at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?
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In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) At temperatures above \(43^{\circ} \mathrm{C}\), the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.
A mixture of calcium carbonate \(\left(\mathrm{CaCO}_{3}\right)\) and magnesium carbonate \(\left(\mathrm{MgCO}_{3}\right)\) of mass \(6.26 \mathrm{~g}\) reacts completely with hydrochloric acid (HCl) to generate \(1.73 \mathrm{~L}\) of \(\mathrm{CO}_{2}\) at \(48^{\circ} \mathrm{C}\) and 1.12 atm. Calculate the mass percentages of \(\mathrm{CaCO}_{3}\) and \(\mathrm{MgCO}_{3}\) in the mixture.
Nickel forms a gaseous compound of the formula \(\mathrm{Ni}(\mathrm{CO})_{x} .\) What is the value of \(x\) given the fact that under the same conditions of temperature and pressure, methane \(\left(\mathrm{CH}_{4}\right)\) effuses 3.3 times faster than the compound?
What pressure will be required for neon at \(30^{\circ} \mathrm{C}\) to have the same density as nitrogen at \(20^{\circ} \mathrm{C}\) and \(1.0 \mathrm{~atm} ?\)
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 \(1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}\)
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