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Chapter 5: Problem 21

The volume of a gas is \(5.80 \mathrm{~L}\), measured at 1.00 atm. What is the pressure of the gas in \(\mathrm{mmHg}\) if the volume is changed to \(9.65 \mathrm{~L} ?\) (The temperature remains constant.)

Short Answer

Expert verified
The pressure of the gas, when the volume is changed to \(9.65 L\), is approximately \(455.17 mmHg\).

Step by step solution

01

Identify known and unknown quantities

Given values are: \n- Initial volume, \(V1 = 5.80 L\) \n- Initial pressure, \(P1 = 1.00 atm\) \n- Final Volume, \(V2 = 9.65 L\) \n\nWe need to find the final pressure \(P2\) in 'mmHg'). It's also important to note there are conversion factors that link 'atm' and 'mmHg': \(1 atm = 760 mmHg\).
02

Apply Boyle's law

Apply Boyle's Law, which is \(P1 \cdot V1 = P2 \cdot V2\) and rearrange to find \(P2\): \n\[P2 = \frac{P1 \cdot V1}{ V2}\] \n\nSubstitute given values into the formula: \n\n\[P2 = \frac{1.00 atm \cdot 5.80 L}{ 9.65 L}\]
03

Convert units and solve

Solve the equation to get the final pressure in atm, then convert the pressure from atm to mmHg using the conversion factor (\(1 atm = 760 mmHg\)):\n\n\[P2 = \frac{1.00 atm \cdot 5.80 L}{9.65 L}\] in atm, then \n\n\[P2 = P2_{atm} \cdot 760 \frac{mmHg}{atm}\] in mmHg.

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Most popular questions from this chapter

A certain amount of gas at \(25^{\circ} \mathrm{C}\) and at a pressure of 0.800 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.00 atm. How high can you raise the temperature of the gas without bursting the vessel?

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures \(15.2 \mathrm{~m}\) long, \(6.6 \mathrm{~m}\) wide, and \(2.4 \mathrm{~m}\) high. (a) Calculate the mass of mercury vapor (in grams) in the room at \(20^{\circ} \mathrm{C}\). The vapor pressure of mercury at \(20^{\circ} \mathrm{C}\) is \(1.7 \times 10^{-6} \mathrm{~atm} .\) (b) Does the concentration of mercury vapor exceed the air quality regulation of \(0.050 \mathrm{mg} \mathrm{Hg} / \mathrm{m}^{3}\) of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, \(\mathrm{N}_{2}\), or \(\mathrm{CH}_{4}\) ? Explain.

A gas at \(772 \mathrm{mmHg}\) and \(35.0^{\circ} \mathrm{C}\) occupies a volume of \(6.85 \mathrm{~L}\). Calculate its volume at STP.
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