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Chapter 10: Problem 29

(a) Write the ideal-gas equation, and give the units used for each term in the equation when \(R=0.0821 \mathrm{~L}-\mathrm{atm} / \mathrm{mol}-\mathrm{K}\). (b) What is an ideal gas?

Short Answer

Expert verified
(a) The ideal-gas equation is \(PV = nRT\), where \(P\) has units of atm, \(V\) has units of L, \(n\) has units of mol, \(R\) is given as 0.0821 L atm / mol K, and \(T\) has units of K. (b) An ideal gas is a theoretical gas where particles move randomly and do not interact. It obeys the ideal-gas equation and serves as an approximation for real gas behavior under certain conditions, such as low pressures and high temperatures.

Step by step solution

01

(a) Ideal-gas equation and units

The ideal-gas equation is given by: \[PV = nRT\] where: - \(P\) is the pressure with units of atmospheres (atm) - \(V\) is the volume with units of liters (L) - \(n\) is the moles of the gas with units of moles (mol) - \(R\) is the gas constant, given in this case as 0.0821 L atm / mol K - \(T\) is the temperature with units of Kelvin (K)
02

(b) Definition of an ideal gas

An ideal gas is a theoretical gas composed of a large number of randomly-moving, non-interacting particles, that obey the ideal-gas equation. It is an approximation of the behavior of real gases under certain conditions, especially at low pressures and high temperatures. In an ideal gas, the volume of the gas particles can be neglected, and it is assumed that there are no intermolecular forces between them. While no real gas behaves exactly like an ideal gas, this model helps to simplify calculations and can give reasonably accurate results under certain scenarios.

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Most popular questions from this chapter

Cyclopropane, a gas used with oxygen as a general anesthetic, is composed of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\) by mass. (a) If \(1.56 \mathrm{~g}\) of cyclopropane has a volume of \(1.00 \mathrm{~L}\) at \(0.984\) atm and \(50.0^{\circ} \mathrm{C}\), what is the molecular formula of cyclopropane? (b) Judging from its molecular formula, would you expect cyclopropane to deviate more or less than Ar from ideal-gas behavior at moderately high pressures and room temperature? Explain.

(a) What conditions are represented by the abbreviation STP? (b) What is the molar volume of an ideal gas at STP? (c) Room temperature is often assumed to be \(25^{\circ} \mathrm{C}\). Calculate the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and 1 atm pressure.

(a) Place the following gases in order of increasing average molecular speed at \(25^{\circ} \mathrm{C}: \mathrm{Ne}, \mathrm{HBr}, \mathrm{SO}_{2}, \mathrm{NF}_{3}, \mathrm{CO}\). (b) Calculate the rms speed of \(\mathrm{NF}_{3}\) molecules at \(25^{\circ} \mathrm{C}\).

A gas forms when elemental sulfur is heated carefully with AgF. The initial product boils at \(15^{\circ} \mathrm{C}\). Experiments on several samples yielded a gas density of \(0.803 \pm 0.010 \mathrm{~g} / \mathrm{L}\) for the gas at \(150 \mathrm{~mm}\) pressure and \(32{ }^{\circ} \mathrm{C}\). When the gas reacts with water, all the fluorine is converted to aqueous HF. Other products are elemental sulfur, \(S_{8}\), and other sulfur-containing compounds. A 480 -mL sample of the dry gas at \(126 \mathrm{~mm}\) pressure and \(28^{\circ} \mathrm{C}\), when reacted with \(80 \mathrm{~mL}\) of water, yielded a \(0.081 \mathrm{M}\) solution of HF. The initial gaseous product undergoes a transformation over a period of time to a second compound with the same empirical and molecular formula, which boils at \(-10^{\circ} \mathrm{C}\). (a) Determine the empirical and molecular formulas of the first compound formed. (b) Draw at least two reasonable Lewis structures that represent the initial compound and the one into which it is transformed over time. (c) Describe the likely geometries of these compounds, and estimate the single bond distances, given that the \(\mathrm{S}-\mathrm{S}\) bond distance in \(\mathrm{S}_{8}\) is \(2.04 \mathrm{~A}\) and the \(\mathrm{F}-\mathrm{F}\) distance in \(\mathrm{F}_{2}\) is \(1.43 \mathrm{~A}\).

Assume that an exhaled breath of air consists of \(74.8 \% \mathrm{~N}_{2}\), \(15.3 \% \mathrm{O}_{2}, 3.7 \% \mathrm{CO}_{2}\), and \(6.2 \%\) water vapor. (a) If the total pressure of the gases is \(0.980 \mathrm{~atm}\), calculate the partial pressure of each component of the mixture. (b) If the volume of the exhaled gas is \(455 \mathrm{~mL}\) and its temperature is \(37^{\circ} \mathrm{C}\), calculate the number of moles of \(\mathrm{CO}_{2}\) exhaled. (c) How many grams of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) would need to be metabolized to produce this quantity of \(\mathrm{CO}_{2}\) ? (The chemical reaction is the same as that for combustion of \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\). See Section 3.2.)
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