When the temperature drops from \(20^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C}\), the pressure of a cylinder of compressed \(\mathrm{N}_{2}\) drops by \(3.4 \%\). The same temperature change decreases the pressure of a propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) cylinder by \(42 \%\). Explain the difference in behavior.

Short Answer

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Question: Explain the difference in the pressure drop of a nitrogen gas cylinder and a propane gas cylinder when both experience a temperature change from 20°C to 10°C. Answer: The difference in the pressure drop between nitrogen and propane gas cylinders under the same temperature change is due to their molecular characteristics and intermolecular forces. Nitrogen, which behaves like an ideal gas, has a smaller and more linear pressure change according to the Ideal Gas Law. Propane, with more complex molecular interactions and larger molecular volumes, requires the Van der Waals equation to describe its behavior, leading to a more significant pressure decrease due to stronger intermolecular forces and larger molecular volume. As a result, propane experiences a larger pressure decrease compared to nitrogen in response to the same temperature change.

Step by step solution

01

Recall the Ideal Gas Law and Van der Waals equation

Recall the Ideal Gas Law, which states: PV = nRT Where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature (in Kelvin). For real gases, we can use the Van der Waals equation to account for the interactions between gas molecules and the volume occupied by these molecules: (P + a(n/V)^2)(V - nb) = nRT Here, a and b are empirical constants for a particular gas.
02

Convert temperatures to Kelvin

Given temperature values are in Celsius, we need to convert them to Kelvin. T1_Celsius = 20°C, T2_Celsius = 10°C T1_Kelvin = T1_Celsius + 273 = 293 K T2_Kelvin = T2_Celsius + 273 = 283 K
03

Analyze the behavior of Nitrogen gas cylinder

As Nitrogen gas (N2) is considered an ideal gas, we can use the Ideal Gas Law for it. When the temperature drops from 293 K to 283 K, we expect the pressure to decrease. The given decrease in pressure is 3.4%, which is relatively small compared to the 42% decrease observed in the propane gas cylinder.
04

Analyze the behavior of the Propane gas cylinder

Unlike Nitrogen, Propane (C3H8) is not an ideal gas because it has more complex molecular interactions. Propane molecules are larger and have stronger intermolecular forces. Therefore, we must use the Van der Waals equation to analyze the change in pressure. The Van der Waals equation accounts for these intermolecular forces (represented by the a constant) and molecular volumes (represented by the b constant). These additional parameters play a significant role when temperature drops, as they impact gas behavior compared to an ideal gas. As the temperature decreases, the propane molecules are moving more slowly, which increases the attractive intermolecular forces between them. These forces are more significant in the case of propane, which explains the higher pressure decrease (42%).
05

Explain the difference in behavior

The difference in behavior between nitrogen and propane gas cylinders under the same temperature change lies in their molecular characteristics and intermolecular forces. Nitrogen behaves like an ideal gas, which means its pressure changes according to the Ideal Gas Law. In contrast, propane has more complex interactions and molecular volumes; therefore, it requires the Van der Waals equation to describe its behavior. While Nitrogen's pressure change is smaller and relatively linear with the temperature change, propane exhibits a more significant pressure change due to stronger intermolecular forces and larger molecular volume. These factors contribute to a larger pressure decrease for propane compared to nitrogen when both gases experience the same drop in temperature.

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Most popular questions from this chapter

19\. Argon gas has its triple point at \(-189.3^{\circ} \mathrm{C}\) and \(516 \mathrm{~mm} \mathrm{Hg}\). It has a critical point at \(-122^{\circ} \mathrm{C}\) and \(48 \mathrm{~atm}\). The density of the solid is \(1.65 \mathrm{~g} / \mathrm{cm}^{3}\) whereas that of the liquid is \(1.40 \mathrm{~g} / \mathrm{cm}^{3}\). Sketch the phase diagram for argon and use it to fill in the blanks below with the words "boils" "melts" "sublimes," or "condenses." (a) Solid argon at \(500 \mathrm{~mm} \mathrm{Hg} \) when the temperature is increased. (b) Solid argon at 2 atm increased. (c) Argon gas at \(-150^{\circ} \mathrm{C}\) when the pressure is increased. (d) Argon gas at \(-165^{\circ} \mathrm{C} \) when the pressure is increased.

Classify each of the following solids as metallic, network covalent, ionic, or molecular. (a) It is insoluble in water, melts above \(500^{\circ} \mathrm{C}\), and does not conduct electricity either as a solid, dissolved in water, or molten. (b) It dissolves in water but does not conduct electricity as an aqueous solution, as a solid, or when molten. (c) It dissolves in water, melts above \(100^{\circ} \mathrm{C}\), and conducts electricity when present in an aqueous solution.

Consider a sealed flask with a movable piston that contains \(5.25 \mathrm{~L}\) of \(\mathrm{O}_{2}\) saturated with water vapor at \(25^{\circ} \mathrm{C}\). The piston is depressed at constant temperature so that the gas is compressed to a volume of \(2.00 \mathrm{~L}\). (Use the table in Appendix 1 for the vapor pressure of water at various temperatures.) (a) What is the vapor pressure of water in the compressed gas mixture? (b) How many grams of water condense when the gas mixture is compressed?

Explain in terms of forces between structural units why (a) HI has a higher boiling point than \(\mathrm{HBr}\). (b) \(\mathrm{GeH}_{4}\) has a higher boiling point than \(\mathrm{SiH}_{4}\). (c) \(\mathrm{H}_{2} \mathrm{O}_{2}\) has a higher melting point than \(\mathrm{C}_{3} \mathrm{H}_{8}\). (d) \(\mathrm{NaCl}\) has a higher boiling point than \(\mathrm{CH}_{3} \mathrm{OH}\).

Classify each of the following species as molecular, network covalent, ionic, or metallic. (a) Na (b) \(\mathrm{Na}_{2} \mathrm{SO}_{4}\) (c) \(\mathrm{C}_{6} \mathrm{H}_{6}\) (d) \(\mathrm{C}_{60}\) (e) \(\mathrm{HCl}(a q)\)

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