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Chapter 11: Problem 72

Consider two samples of water vapor, one at \(101^{\circ} \mathrm{C}\) and the other at \(200^{\circ} \mathrm{C}\). Which behaves more ideally and why?

Short Answer

Expert verified
The second sample of water vapor at \( 200^{\circ} \mathrm{C} \) (473.15 K) behaves more ideally as compared to the first sample at \( 101^{\circ} \mathrm{C} \) (374.15 K), due to the weaker inter-molecular interactions and larger average distance between the molecules at a higher temperature.

Step by step solution

01

Understand Ideal Gas Behavior

According to the ideal gas law, an ideal gas obeys the equation PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature (measured in Kelvin). A gas behaves ideally when the interactions between its molecules are negligible and the size of the molecules is much smaller than the volume it occupies. As the temperature increases, gases generally become more ideal due to the larger average distance between the molecules, resulting in weaker inter-molecular interactions.
02

Convert given temperatures to Kelvin

To compare the behavior of the two water vapor samples, we need to convert the given temperatures in Celsius to Kelvin. The formula to convert Celsius to Kelvin is: Kelvin = Celsius + 273.15. For the first sample (101°C), the temperature in Kelvin would be: \( 101+273.15 = 374.15 K\). For the second sample (200°C), the temperature in Kelvin would be: \( 200+273.15 = 473.15 K\).
03

Compare the Two Samples

Now that we have the temperatures of both samples in Kelvin, we can analyze their behavior. Since an increase in temperature generally results in more ideal gas behavior, the sample with the higher temperature should behave more ideally. In this case, the second sample of water vapor (at 200°C or 473.15 K) has a higher temperature than the first sample (at 101°C or 374.15 K). Therefore, the second sample of water vapor at 200°C behaves more ideally.
04

Conclusion

The second sample of water vapor at 200°C (473.15 K) behaves more ideally as compared to the first sample at 101°C (374.15 K), due to the weaker inter-molecular interactions and larger average distance between the molecules at a higher temperature.

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Most popular questions from this chapter

A sample of gas at \(25^{\circ} \mathrm{C}\) and \(759.0 \mathrm{~mm} \mathrm{Hg}\) has a volume of \(1.58 \mathrm{~L}\). If the temperature is raised to \(35^{\circ} \mathrm{C}\) but the pressure is held constant at \(759.0 \mathrm{~mm} \mathrm{Hg}\), will the volume increase or decrease? Explain your answer.

A tank of acetylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\) contains \(48.5 \mathrm{lb}\) of the gas and is at a pressure of \(600.2 \mathrm{lb} / \mathrm{in} .^{2}\) Express the pressure of the gas in atmospheres and the amount of gas in moles. \([760.0 \mathrm{~mm} \mathrm{Hg}=\) \(\left.14.696 \mathrm{lb} / \mathrm{in} .^{2}, 453.6 \mathrm{~g}=1 \mathrm{lb}\right]\)

In the ideal gas law, pressure must be expressed in units of _______ volume must be expressed in units of _______ temperature must be expressed in _______ and \(n\) represents the number of _______

Explain why gases always occupy the entire container they are in, but solids and liquids do not.

You are on the balcony of the upper floor of a high-rise building in Chicago. Way down below on the street, your friend is engaged in conversation with someone and is drinking a particularly flavorful mixed drink. You decide to take a sip from his glass without his knowing, so you collect together every drinking straw in the apartment and start taping them together to create a very long drinking straw. If the atmospheric pressure is currently \(760 \mathrm{~mm} \mathrm{Hg}\), what is the longest straw you can use to get a sip of your friend's drink? (Assume the density of the drink is the same as pure water, \(1.0 \mathrm{~g} / \mathrm{mL}\).)
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