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Chapter 10: Problem 78

Newton had an incorrect theory of gases in which he assumed that all gas molecules repel one another and the walls of their container. Thus, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure. Explain why Charles's law argues for the kineticmolecular theory and against Newton's model.

Short Answer

Expert verified
In conclusion, Charles's law supports the kinetic-molecular theory and contradicts Newton's model of gases. This is because the kinetic-molecular theory, which considers the kinetic energy and motion of gas particles, can explain the relationship between the volume of a gas and its temperature, as observed in Charles's law. In contrast, Newton's model, which assumes static and uniformly distributed gas particles without accounting for their kinetic energy, cannot adequately explain this relationship.

Step by step solution

01

Understanding Charles's Law

Charles's law states that the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant. Mathematically, it can be represented as: \[V \propto T\] where V is the volume of the gas and T is its temperature in Kelvin.
02

Understanding the Kinetic-Molecular Theory

The kinetic-molecular theory is a model that helps explain the behavior of gases. It is based on the following main assumptions: 1. Gas particles are in constant, random motion. 2. Gas particles are very small compared to the distances between them, so the volume occupied by the particles themselves is negligible. 3. Gas particles interact only through elastic collisions, and there are no other forces acting on them. 4. The average kinetic energy of gas particles is directly proportional to the temperature of the gas.
03

Understanding Newton's Model

In Newton's model of gases, he assumed that all gas molecules repel one another and the walls of their container. Consequently, the molecules of a gas are statically and uniformly distributed, trying to get as far apart as possible from one another and the vessel walls. This repulsion gives rise to pressure but does not consider the kinetic energy or motion of gas particles.
04

Comparing Charles's Law with the Kinetic-Molecular Theory

According to Charles's law, the volume of a gas is directly proportional to its temperature when pressure and the amount of gas are held constant. This is consistent with the kinetic-molecular theory, as the average kinetic energy of gas particles is directly proportional to the temperature of the gas. As the temperature increases, the average kinetic energy of the particles also increases, which results in the expansion of gas and an increase in volume.
05

Comparing Charles's Law with Newton's Model

On the other hand, Newton's model does not explain the relationship between the volume of a gas and its temperature. Since it assumes that gas particles are static and uniformly distributed, it does not account for the effects of temperature on the kinetic energy of the gas molecules. As a result, this model does not adequately explain the phenomena observed in Charles's law.
06

Conclusion

In conclusion, Charles's law supports the kinetic-molecular theory and goes against Newton's model since the kinetic-molecular theory explains the observed relationship between the volume of a gas and its temperature, considering the kinetic energy of gas particles. In contrast, Newton's model cannot adequately explain this relationship, as it assumes the gas particles to be static and uniformly distributed without accounting for their kinetic energy or motion.

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Most popular questions from this chapter

Does the effect of intermolecular attraction on the properties of a gas become more significant or less significant if (a) the gas is compressed to a smaller volume at constant temperature; (b) the temperature of the gas is increased at constant volume?

Consider the following gases, all at STP. Ne, \(\mathrm{SF}_{6}, \mathrm{~N}_{2}, \mathrm{CH}_{4}\). (a) Which gas is most likely to depart from the assumption of the kinetic- molecular theory that says there are no attractive or repulsive forces between molecules? (b) Which one is closest to an ideal gas in its behavior? (c) Which one has the highest root-mean-square molecular speed at a given temperature? (d) Which one has the highest total molecular volume relative to the space occupied by the gas? (e) Which has the highest average kinetic-molecular energy? (f) Which one would effuse more rapidly than \(\mathrm{N}_{2}\) ? (g) Which one would have the largest van der Waals \(b\) parameter?

Calcium hydride, \(\mathrm{CaH}_{2}\), reacts with water to form hydrogen gas: $$ \mathrm{CaH}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+2 \mathrm{H}_{2}(g) $$ This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating \(\mathrm{H}_{2}\) is desired. How many grams of \(\mathrm{CaH}_{2}\) are needed to generate \(145 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas if the pressure of \(\mathrm{H}_{2}\) is 825 torr at \(21^{\circ} \mathrm{C}\) ?

A sample of \(5.00 \mathrm{~mL}\) of diethylether \(\left(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{OC}_{2} \mathrm{H}_{5}\right.\) ? density \(=0.7134 \mathrm{~g} / \mathrm{mL}\) ) is introduced into a \(6.00-\mathrm{L}\) vessel that already contains a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\), whose partial pressures are \(P_{\mathrm{N}_{2}}=0.751 \mathrm{~atm}\) and \(P_{\mathrm{O}_{1}}=0.208 \mathrm{~atm}\). The temperature is held at \(35.0^{\circ} \mathrm{C}\), and the diethylether totally evaporates. (a) Calculate the partial pressure of the diethylether. (b) Calculate the total pressure in the container.

A 4.00-g sample of a mixture of \(\mathrm{CaO}\) and \(\mathrm{BaO}\) is placed in a \(1.00-\mathrm{L}\) vessel containing \(\mathrm{CO}_{2}\) gas at a pressure of 730 torr and a temperature of \(25^{\circ} \mathrm{C}\). The \(\mathrm{CO}_{2}\) reacts with the \(\mathrm{CaO}\) and \(\mathrm{BaO}\), forming \(\mathrm{CaCO}_{3}\) and \(\mathrm{BaCO}_{3}\). When the reaction is complete, the pressure of the remaining \(\mathrm{CO}_{2}\) is 150 torr. (a) Calculate the number of moles of \(\mathrm{CO}_{2}\) that have reacted. (b) Calculate the mass percentage of \(\mathrm{CaO}\) in the mixture.
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