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Chapter 6: Problem 134

For a fixed amount of gas at a fixed pressure, changing the temperature from \(100.0^{\circ} \mathrm{C}\) to \(200 \mathrm{K}\) causes the gas volume to (a) double; (b) increase, but not to twice its original value; (c) decrease; (d) stay the same.

Short Answer

Expert verified
The answer is (c) decrease. The volume of the gas will decrease because, for a fixed amount of gas at a fixed pressure, the volume is directly proportional to the temperature (Gay-Lussac's Law). So if the temperature decreases, the volume will also decrease.

Step by step solution

01

Conversion of temperature from Celsius to Kelvin

First, we need to convert the initial temperature given in Celsius degrees to Kelvin, since Kelvin is the standard measurement for temperature in this context. The formula for changing Celsius to Kelvin is \( K = C + 273.15 \). So the starting temperature in Kelvin is \( 100.0^{\circ} \mathrm{C} + 273.15 = 373.15K \)
02

Compare the initial and final temperatures

We then compare the initial and final temperatures. As stated, the final temperature is 200K and the initial temperature is 373.15K. Notice that the final temperature is less than the initial temperature.
03

Apply Gay-Lussac’s Law

Next, we apply Gay-Lussac's law which states that the volume of a gas is directly proportional to its temperature, provided that the pressure remains the same. Since our pressure is constant, a decrease in temperature would cause a corresponding decrease in volume as per this law. This is true because as the temperature decreases, the gas particles slow down and occupy less space.

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Most popular questions from this chapter

Monochloroethylene is used to make polyvinylchloride (PVC). It has a density of \(2.56 \mathrm{g} / \mathrm{L}\) at \(22.8^{\circ} \mathrm{C}\) and 756 mmHg. What is the molar mass of monochloroethylene? What is the molar volume under these conditions?

A particular gaseous hydrocarbon that is \(82.7 \%\) C and \(17.3 \%\) H by mass has a density of \(2.33 \mathrm{g} / \mathrm{L}\) at \(23^{\circ} \mathrm{C}\) and \(746 \mathrm{mm} \mathrm{Hg} .\) What is the molecular formula of this hydrocarbon?

Explain the important distinctions between (a) barometer and manometer; (b) Celsius and Kelvin temperature; (c) ideal gas equation and general gas equation; (d) ideal gas and real gas.

Consider the statements (a) to (e) below. Assume that \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) behave ideally. State whether each of the following statements is true or false. For each false statement, explain how you would change it to make it a true statement. (a) Under the same conditions of temperature and pressure, the average kinetic energy of \(\mathrm{O}_{2}\) molecules is less than that of \(\mathrm{H}_{2}\) molecules. (b) Under the same conditions of temperature and pressure, \(\mathrm{H}_{2}\) molecules move faster, on average, than \(\mathrm{O}_{2}\) molecules. (c) The volume of \(1.00 \mathrm{mol}\) of \(\mathrm{H}_{2}(\mathrm{g})\) at \(25.0^{\circ} \mathrm{C}\) 1.00 atm is \(22.4 \mathrm{L}\) (d) The volume of \(2.0 \mathrm{g} \mathrm{H}_{2}(\mathrm{g})\) is equal to the volume of \(32.0 \mathrm{g} \mathrm{O}_{2}(\mathrm{g}),\) at the same temperature and pressure. (e) In a mixture of \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) gases, with partial pressures \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}^{\prime}}\) respectively, the total pressure is the larger of \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}}\).

A 2.00 L container is filled with \(\operatorname{Ar}(g)\) at 752 mm Hg and \(35^{\circ} \mathrm{C} .\) A \(0.728 \mathrm{g}\) sample of \(\mathrm{C}_{6} \mathrm{H}_{6}\) vapor is then added. (a) What is the total pressure in the container? (b) What is the partial pressure of \(\mathrm{Ar}\) and of \(\mathrm{C}_{6} \mathrm{H}_{6} ?\)
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