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Chapter 6: Problem 145

Under which conditions is \(\mathrm{Cl}_{2}\) most likely to behave like an ideal gas? Explain. (a) \(100^{\circ} \mathrm{C}\) and \(10.0 \mathrm{atm}\) (b) \(0^{\circ} \mathrm{C}\) and 0.50 atm; \((\mathrm{c}) 200^{\circ} \mathrm{C}\) and \(0.50 \mathrm{atm}\) (d) \(400^{\circ} \mathrm{C}\) and \(10.0 \mathrm{atm}\).

Short Answer

Expert verified
Among the given conditions, Cl2 is most likely to behave like an ideal gas in condition (c) 200°C and 0.50 atm as this condition is at a high temperature and a low pressure.

Step by step solution

01

Identify the behavior of ideal gases

As per the kinetic molecular theory, ideal gases behave best at high temperatures and low pressures. This is because at high temperatures, the kinetic energy of the gas molecules is high, meaning they move quickly and interact less with each other. At low pressures, there is more space between the molecules, reducing the chances of intermolecular collisions.
02

Apply the conditions on given scenarios

(a) In this scenario, the temperature is high, which is good for ideal gas behavior. However, the pressure is also high, which is not ideal. Therefore, Cl2 will not behave ideally under these conditions. (b) In this condition, the temperature is not high, but the pressure is low, which is ideal. However, the low temperature may cause Cl2 to not behave ideally. (c) Both the temperature is high and the pressure is low in this scenario, which are ideal conditions for an ideal gas. Thus, Cl2 is most likely to behave like an ideal gas under this condition. (d) Similar to scenario (a), the high temperature is ideal but the high pressure is not, hence Cl2 will likely not behave ideally under these conditions.
03

Choose the most ideal condition

From the above explanations, it is clear that a gas behaves ideally at high temperatures and low pressures. Therefore, among the given options, condition (c) 200°C and 0.50 atm is the condition under which Cl2 is most likely to behave like an ideal gas.

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Most popular questions from this chapter

If the Kelvin temperature of a sample of ideal gas doubles (e.g., from 200 K to 400 K), what happens to the root-mean-square speed, \(u_{\mathrm{rms}}\) ? (a) \(u_{\mathrm{rms}}\) increases by a factor of \(\sqrt{2} ;\) (b) \(u_{\mathrm{rms}}\) increases by a factor of \(2 ;(\mathrm{c}) u_{\mathrm{rms}}\) decreases by a factor of 2 (d) \(u_{\mathrm{rms}}\) increases by a factor of \(4 ;\) (e) \(u_{\mathrm{rms}}\) decreases by a factor of 4.

Which actions would you take to establish a pressure of 2.00 atm in a 2.24 L cylinder containing \(1.60 \mathrm{g} \mathrm{O}_{2}(\mathrm{g})\) at \(0^{\circ} \mathrm{C} ?\) (a) add \(1.60 \mathrm{g} \mathrm{O}_{2} ;\) (b) release \(0.80 \mathrm{g} \mathrm{O}_{2} ;\) (c) add \(2.00 \mathrm{g} \mathrm{He} ;\) (d) add \(0.60 \mathrm{g}\) He.

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(24^{\circ} \mathrm{C}\) The volume of gas is 1.16 L. In a subsequent experiment, it is determined that the mass of \(\mathrm{O}_{2}\) present is 1.46 g. What must have been the barometric pressure at the time the gas was collected? (Vapor pressure of water \(=22.4 \text { Torr. })\)

What is the volume, in milliliters, occupied by \(89.2 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g})\) at \(37^{\circ} \mathrm{C}\) and \(737 \mathrm{mmHg} ?\)

A 1.072 g sample of \(\mathrm{He}(\mathrm{g})\) is found to occupy a volume of 8.446 L when collected over hexane at \(25.0^{\circ} \mathrm{C}\) and \(738.6 \mathrm{mmHg}\) barometric pressure. Use these data to determine the vapor pressure of hexane at \(25^{\circ} \mathrm{C}\).
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