Chapter 11

A tank of \(\mathrm{O}_{2}\) gas is stored in a cool basement \(\left(T=10.0^{\circ} \mathrm{C}\right)\). Its pressure gauge reads \(50.5 \mathrm{lb} / \mathrm{in} .^{2} .\) Diver Dan then places the tank in his truck, where the sun warms it to \(20.0^{\circ} \mathrm{C}\). What does the pressure gauge read at this elevated temperature?

On an atomic basis, and given that the average kinetic energy of motion of molecules in the gas phase is given by \(\mathrm{KE}=3 R T / 2\), explain why the pressure of a gas doubles when its temperature in Kelvin is doubled. (Hint: Pressure is due to collisions of molecules on the container walls and the force of those collisions.)

A tank initially at a pressure of \(6.70\) atm contains \(20.0\) moles of oxygen gas at \(25.0^{\circ} \mathrm{C}\). Its temperature is then increased to \(45.0{ }^{\circ} \mathrm{C}\), and an additional \(10.0\) moles of gas are added. What is the final pressure in the tank?

The Kelvin temperature of a gas is doubled. At the same time, its volume is cut in half by compressing it with a piston. What happens to the pressure of the gas? (Hint: Set \(T_{f}=2 T_{i}\) and \(\left.V_{f}=0.5 V_{i}\right)\)

Consider the reaction \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\) If this reaction takes place at STP, what volume in liters of \(\mathrm{H}_{2}\) gas would be required to react completely with \(22.4 \mathrm{~L}\) of \(\mathrm{O}_{2}\) gas? What volume in liters of \(\mathrm{H}_{2} \mathrm{O}(g)\) would be produced? Explain how you arrived at your answers.

Consider the reaction \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) (a) What volume in liters of oxygen gas at STP is required to produce 2 moles of sulfur trioxide gas? (b) What volume in liters of oxygen gas at \(25.0^{\circ} \mathrm{C}\) and 1 atm pressure is required to produce 2 moles of sulfur trioxide gas?

To produce \(500.0 \mathrm{~g}\) of gaseous \(\mathrm{H}_{2} \mathrm{O}\), what volumes in liters of hydrogen gas and oxygen gas, both at STP, must combine via the reaction \(2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(g)\)

Zinc metal reacts with hydrochloric acid to form hydrogen gas via the reaction \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)\) How many grams of zinc would be required to produce enough hydrogen gas to fill a 50.0-L cylinder to a pressure of \(10.0 \mathrm{~atm}\) at \(25.0^{\circ} \mathrm{C}\) ?

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?

According to the ideal gas model, why does the chemical identity of a gas not matter when it comes to producing pressure?

A 5.00-L container is filled with \(0.8004\) g of helium gas at \(107.0^{\circ} \mathrm{C}\). What is the pressure of the gas in atmospheres and in millimeters of mercury?

A chemical reaction produces \(100.0\) mL of hydrogen gas at \(745.5 \mathrm{~mm} \mathrm{Hg}\) and \(24.0^{\circ} \mathrm{C}\). What is the amount of \(\mathrm{H}_{2}\) produced in moles and in grams?

What is the density in grams per liter of nitrogen gas at STP?

A gaseous compound of carbon and hydrogen contains \(80.0 \%\) by mass carbon. A \(2.00\) -L sample has a mass of \(2.678 \mathrm{~g}\) at \(\mathrm{STP}\). (a) Calculate the molar mass of the compound. (b) What is the empirical formula of the compound? (c) What is the molecular formula of the compound?

When it is heated, potassium chlorate decomposes to potassium chloride and oxygen: \(2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) A sample of solid \(\mathrm{KClO}_{3}\) decomposes to produce \(150.0 \mathrm{~mL}\) of oxygen at \(22.0^{\circ} \mathrm{C}\) and \(780.5 \mathrm{~mm} \mathrm{Hg}\). How many grams of \(\mathrm{KClO}_{3}\) decomposed?

To what temperature must a gas initially at \(20.0^{\circ} \mathrm{C}\) be heated to double the volume and triple the pressure?

A sample of argon at \(0.0^{\circ} \mathrm{C}\) and \(700.0 \mathrm{~mm} \mathrm{Hg}\) occupies \(15.0 \mathrm{~mL}\). What is its volume at STP?

A sample of gas at \(25.0^{\circ} \mathrm{C}\) and \(655 \mathrm{~mm} \mathrm{Hg}\) has a density of \(2.26 \times 10^{-3} \mathrm{~g} / \mathrm{mL}\). What is the molar mass of the compound?

In the Haber process, nitrogen reacts with hydrogen to produce ammonia: \(\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \rightarrow 2 \mathrm{NH}_{3}(g)\) (a) Suppose \(2.0 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at STP is combined with \(6.0 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas, with the two gases being at the same temperature and pressure. Is this reaction being run in a balanced fashion or in a limiting fashion? Explain how you can tell without doing any calculations. (b) If \(50.0 \mathrm{~L}\) of \(\mathrm{N}_{2}\) gas at \(200.0 \mathrm{lb} / \mathrm{in}^{2}\) and \(22.0^{\circ} \mathrm{C}\) is combined with \(100.0 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas at \(240.0 \mathrm{lb} / \mathrm{in}^{2}\) and \(22.0^{\circ} \mathrm{C}\), what mass in grams of ammonia is produced? \(\left[14.70 \mathrm{lb} / \mathrm{in}^{2}=760.0 \mathrm{~mm} \mathrm{Hg}\right]\)

How many atoms of nitrogen are there in a \(230.0-\mathrm{mL}\) sample of \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas that has a pressure of \(745.0 \mathrm{~mm} \mathrm{Hg}\) at \(34.0^{\circ} \mathrm{C}\) ?

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.

Consider two identical \(1-\mathrm{L}\) containers, both at room temperature \((300 \mathrm{~K})\). One of them contains 1 mole of helium gas, and the other contains 1 mole of hydrogen gas. Is the pressure higher in the helium container, higher in the hydrogen container, or the same in the two containers?

Consider two identical \(1-\mathrm{L}\) containers, both at room temperature \((300 \mathrm{~K})\). One of them contains 1.0 \(\mathrm{g}\) of helium gas, and the other contains \(1.0 \mathrm{~g}\) of hydrogen gas. Is the pressure higher in the helium container, higher in the hydrogen container, or the same in the two containers?

What volume in milliliters of \(\mathrm{N}_{2} \mathrm{O}_{4}\) gas at \(0.996 \mathrm{~atm}\) and \(25.0^{\circ} \mathrm{C}\) contains \(0.200 \mathrm{~g}\) of oxygen?

Carbon dioxide in a gas cylinder of unchangeable volume is at a pressure of \(25.0 \mathrm{~atm}\) at \(25^{\circ} \mathrm{C}\). When placed in the sunlight on a hot summer day, the temperature increases to \(40^{\circ} \mathrm{C}\). What is the new pressure of the \(\mathrm{CO}_{2}\) ?

When a balloon is placed in a freezer, the size of the balloon decreases. Explain why.

A sample of Ne gas in a 10.0-L container at \(25.0^{\circ} \mathrm{C}\) exerts a pressure of \(7.35 \mathrm{~atm}\). What is the number of moles of Ne in the container? What is the mass in grams of the Ne?

Of the values for \(P, V, n\), and \(T\), which ones remain constant during the following changes? (a) Air in a sealed glass bulb is heated from \(25^{\circ} \mathrm{C}\) to \(32^{\circ} \mathrm{C}\). (b) An He-filled balloon is cooled from \(23^{\circ} \mathrm{C}\) to \(10^{\circ} \mathrm{C} .\) (c) The amount of \(\mathrm{CO}_{2}\) in a sealed steel cylinder is increased by adding \(50.0 \mathrm{~g}\) of \(\mathrm{CO}_{2}\).

Under what two conditions are gas molecules unable to overcome the weak attractive forces that exist between them?

Arrange these gases, all at STP, in order of increasing density: \(\mathrm{CO}_{2}, \mathrm{H}_{2}, \mathrm{O}_{2}, \mathrm{CH}_{4}, \mathrm{He}\).

If a gas sample occupies \(1.80 \mathrm{~L}\) at \(250^{\circ} \mathrm{C}\) and \(792 \mathrm{~mm} \mathrm{Hg}\), what is the number of moles in the sample?

Which variable is not needed to describe the behavior of an ideal gas: volume, number of moles, temperature, molar mass, or pressure?

(a) How many liters of \(\mathrm{O}_{2}\) are there in \(5.38\) moles at STP? (b) How many moles of \(\mathrm{NH}_{3}\) are there in \(859 \mathrm{~mL}\) at STP? (c) How many moles of \(\mathrm{H}_{2}\) are there in \(0.518 \mathrm{~L}\) at STP?

Are gases denser or less dense than liquids and solids? Explain.

If a gas occupies \(2.40 \mathrm{~L}\) at \(1 \mathrm{~atm}\) and \(22^{\circ} \mathrm{C}\), at what Celsius temperature will it occupy \(7.20 \mathrm{~L}\) at \(1 \mathrm{~atm} ?\)

A chemistry student realizes she has forgotten the value of \(R\) and needs to determine it experimentally. She decides to measure the mass, volume, pressure, and temperature of a sample of carbon dioxide gas. She finds that \(4.505 \mathrm{~g}\) of the gas occupies \(2.50 \mathrm{~L}\) at \(23^{\circ} \mathrm{C}\) and \(0.9960 \mathrm{~atm}\). Calculate the value of \(R\) she determines from these data.

A gas at \(25.0{ }^{\circ} \mathrm{C}\) occupies a volume of \(5.00\) gallons and exerts a pressure of \(755 \mathrm{~mm} \mathrm{Hg}\). Express (a) the temperature of the gas in Kelvin, (b) the volume of the gas in liters, and (c) the pressure of the gas in atmospheres.

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 _______

A radial tire has an air pressure of \(2.20 \mathrm{~atm}\) at \(32^{\circ} \mathrm{F}\). After hours of high-speed driving, the temperature of the air in the tire reaches \(80{ }^{\circ} \mathrm{F}\). What is the pressure in the tire at this temperature? Assume that the volume of the tire does not change.

An 84.0-g sample of an unknown gas occupies \(60.8 \mathrm{~L}\) at \(23{ }^{\circ} \mathrm{C}\) and \(1.2 \mathrm{~atm}\). What is the molar mass of the gas?

In the laboratory preparation of oxygen gas, the following reaction is carried out: \(2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)\) (a) How many moles of oxygen gas can be produced from the decomposition of \(500.0 \mathrm{~g}\) of \(\mathrm{KClO}_{3} ?\) (b) What volume in liters would the oxygen gas produced in part (a) occupy at \(24.0{ }^{\circ} \mathrm{C}\) and \(750.0 \mathrm{~mm} \mathrm{Hg} ?\) (c) What volume in liters would this gas occupy at STP?

In an ideal gas, the molecules are considered to have no forces.

(a) If the temperature of a gas is doubled while the pressure is kept constant, the volume of the gas (b) If the pressure of a gas is halved while the temperature is kept constant, the volume of the gas

What is the Celsius temperature of a gas if \(3.200\) moles of it occupy \(12.00 \mathrm{~L}\) at \(8.500 \mathrm{~atm} ?\)

A \(1.25-g\) sample of a gas of unknown identity occupies \(2.50 \mathrm{~L}\). and exerts a pressure of \(0.400 \mathrm{~atm}\) at \(0^{\circ} \mathrm{C}\). (a) What is the molar mass of the gas? (b) Combustion analysis determines that the empirical formula of the gas is \(\mathrm{CH}_{2}\). What is its molecular formula?

If a quantity of gas occupies \(850 \mathrm{~mL}\) at \(300 \mathrm{~K}\) and \(750 \mathrm{~mm} \mathrm{Hg}\), what volume in milliliters will the gas occupy at \(200 \mathrm{~K}\) and \(1200 \mathrm{~mm} \mathrm{Hg}\) ?

Perform the following conversions: (a) \(30.2\) in. \(\mathrm{Hg}\) to millimeters of mercury (b) \(890.0 \mathrm{~mm} \mathrm{Hg}\) to atmospheres (c) \(300.0 \mathrm{lb} / \mathrm{in} .^{2}\) to atmospheres

If \(8.50\) moles of He gas occupy a volume of \(25.0 \mathrm{~L}\) at \(28^{\circ} \mathrm{C}\), what pressure in atmospheres does the gas exert?

If \(48.3 \mathrm{~g}\) of an unknown gas occupies \(10.0 \mathrm{~L}\) at \(40^{\circ} \mathrm{C}\) and \(3.10 \mathrm{~atm}\), what is the molar mass of the gas?

A gas tank contains \(\mathrm{CO}_{2}\) at a pressure of \(6.80 \mathrm{~atm}\). What would the \(\mathrm{CO}_{2}\) pressure be if the container were (a) twice as large and (b) one-fourth as large?