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Chapter 6: Problem 30
A 72.8 L constant-volume cylinder containing \(7.41 \mathrm{g}\) He is heated until the pressure reaches 3.50 atm. What is the final temperature in degrees Celsius?
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In order for a gas-filled balloon to rise in air, the density of the gas in the balloon must be less than that of air. (a) Consider air to have a molar mass of \(28.96 \mathrm{g} / \mathrm{mol}\) determine the density of air at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm},\) in g/L. (b) Show by calculation that a balloon filled with carbon dioxide at \(25^{\circ} \mathrm{C}\) and 1 atm could not be expected to rise in air at \(25^{\circ} \mathrm{C}\)
What is the volume, in liters, occupied by a mixture of 15.2 \(\mathrm{g} \mathrm{Ne}(\mathrm{g})\) and \(34.8 \mathrm{g} \mathrm{Ar}(\mathrm{g})\) at 7.15 atm pressure and \(26.7^{\circ} \mathrm{C} ?\)
A sounding balloon is a rubber bag filled with \(\mathrm{H}_{2}(\mathrm{g})\) and carrying a set of instruments (the payload). Because this combination of bag, gas, and payload has a smaller mass than a corresponding volume of air, the balloon rises. As the balloon rises, it expands. From the table below, estimate the maximum height to which a spherical balloon can rise given the mass of balloon, \(1200 \mathrm{g} ;\) payload, \(1700 \mathrm{g}\) : quantity of \(\mathrm{H}_{2}(\mathrm{g})\) in balloon, \(120 \mathrm{ft}^{3}\) at \(0.00^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}\); diameter of balloon at maximum height, 25 ft. Air pressure and temperature as functions of altitude are: $$\begin{array}{ccl} \hline \text { Altitude, km } & \text { Pressure, mb } & \text { Temperature, } \mathrm{K} \\ \hline 0 & 1.0 \times 10^{3} & 288 \\ 5 & 5.4 \times 10^{2} & 256 \\ 10 & 2.7 \times 10^{2} & 223 \\ 20 & 5.5 \times 10^{1} & 217 \\ 30 & 1.2 \times 10^{1} & 230 \\ 40 & 2.9 \times 10^{0} & 250 \\ 50 & 8.1 \times 10^{-1} & 250 \\ 60 & 2.3 \times 10^{-1} & 256 \\ \hline \end{array}$$
A gaseous hydrocarbon weighing \(0.231 \mathrm{g}\) occupies a volume of \(102 \mathrm{mL}\) at \(23^{\circ} \mathrm{C}\) and \(749 \mathrm{mmHg} .\) What is the molar mass of this compound? What conclusion can you draw about its molecular formula?
Explain why it is necessary to include the density of \(\mathrm{Hg}(1)\) and the value of the acceleration due to gravity, \(g,\) in a precise definition of a millimeter of mercury (page 194 ).
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