Chapter 5 - solve problem PDF

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Chapter 5: gases Matter: 1) solid 2) liquid

3) gases

- air  67% N2, 21%O2, 1% other gases - study gases under normal condition (1atm, 25 C'). - 11 element are gases under normal condition. 1) diatomic gases N2, O2, F2, Cl2. 2) mono atomic gases (element in grap 8A He, Ne, Ar, Xe, Rn) 3) O3 (ozone), other form of oxygen gases. Ex: O2: essential for our survival, HCN: deadly poison. CO, H2S, No2Q3, and So2  less toxic He, Ne (Ar) chemically inert Most gases are colorless. Exceptions are F2, Cl2, and The dark-brown color of NO2 is sometimes visible in polluted air.

Table 5.1 Some Substances Found as Gases at 1 Atm and 25°C Elements H2 (molecular hydrogen) N2 (molecular nitrogen) O2 (molecular oxygen) O3 (ozone) F2 (molecular fl uorine) Cl2 (molecular chlorine) He (helium) Ne (neon) Ar (argon) Kr (krypton) Xe (xenon) Rn (radon)

Compounds HF (hydrogen fl uoride) HCl (hydrogen chloride) HBr (hydrogen bromide) HI (hydrogen iodide) CO (carbon monoxide) CO 2 (carbon dioxide) NH 3 (ammonia) NO (nitric oxide) NO 2 (nitrogen dioxide) N 2O (nitrous oxide) SO 2 (sulfur dioxide) H 2S (hydrogen sulfi de) HCN (hydrogen cyanide)*

* The boiling point of HCN is 26°C, but it is close enough to qualify as a gas at ordinary atmospheric conditions.

All gases have the following physical characteristics: • Gases assume the volume and shape of their containers. • Gases are the most compressible of the states of matter. • Gases will mix evenly and completely when confined to the same container. • Gases have much lower densities than liquids and solids.

5.2 Pressure of a Gas Gases exert pressure on any surface with which they come in contact, because gas (molecule) molecules are constantly in motion.

SI Units of Pressure Pressure is one of the most readily measurable properties of a gas. pressure = force / area The SI unit of pressure is the pascal (Pa), defined as one newton per square meter: 1Pa = 1N/m2

Atmospheric Pressure The atoms and molecules of the gases in the atmosphere, like those of all other matter, are subject to Earth’s gravitational pull. Earth’s atmosphere ( Pressure): is equal to the weight of the column of air above it. Atmospheric pressure is the pressure exerted by Earth’s atmosphere.

NO2.

The actual value of atmospheric pressure depends on location, temperature, and weather conditions. How is atmospheric pressure measured? The barometer is probably the most familiar instrument for measuring atmospheric pressure. Standard atmospheric pressure(1 atm) = to the pressure that supports a column of mercury exactly 760 mm (or 76 cm) high at 0°C at sea level. 1 torr = 1 mmHg And 1 atm = 760 mmHg (exactly) = 760 torr 1 atm = 101,325 Pa = 1.01325*10 Pa. and because 1000 Pa = 1 kPa (kilopascal) 1 atm = 1.01325*10 kPa 5

2

EXAMPLE 5.1 The pressure outside a jet plane flying at high altitude falls considerably below standard atmospheric pressure. Therefore, the air inside the cabin must be pressurized to protect the passengers. What is the pressure in atmospheres in the cabin if the barometer reading is 672 mmHg?

There are two types of manometers (used): a) The closed-tube manometer is normally used to measure pressures below atmospheric pressure [Figure 5.3(a)]. (gas pressures less than atmospheric pressure). b) open-tube manometer is better suited for measuring pressures equal to or greater than atmospheric pressure (gas pressures greater than atmospheric pressure).

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Why Hg?? Hg toxic. High density 13.6 g/mlv use small manometers or barometers.

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The dots between L and atm and between K and mol remind us that both L and atm are in the numerator and both K and mol are in the denominator. For most calculations, we will round off the value of R to three significant figures (0.0821 L . atm/K . mol) and use 22.4 L for the molar volume of a gas at STP. EXAMPLE 5.2 Sulfur hexafluoride (SF6) is a colorless, odorless, very unreactive gas. Calculate the pressure (in atm) exerted by 1.39 moles of the gas in a steel vessel of volume 6.09 L at 55°C.

EXAMPLE 5.3 Calculate the volume (in liters) occupied by 5.58 g of NH3 at STP.

Practice Exercise What is the volume (in liters) occupied by 49.8 g of HCl at STP?

The ideal gas equation is useful for problems that do not involve changes in P, V, T, and n for a gas sample. At times, however, we need to deal with changes in pressure, volume, and temperature, or even in the amount of a gas. When conditions change, we must employ a modified form of the ideal gas equation that takes into account the initial and final conditions. We derive the modified equation as follows. From Equation (5.8),

EXAMPLE 5.4 A small bubble rises from the bottom of a lake, where the temperature and pressure are 8°C and 6.4 atm, to the water’s surface, where the temperature is 25°C and the pressure is 1.0 atm. Calculate the fi nal volume (in mL) of the bubble if its initial volume was 2.1 mL.

Density and Molar Mass of a Gaseous Substance The ideal gas equation can be applied to determine the density or molar mass of a gaseous substance. Rearranging Equation (5.8), we write

The number of moles of the gas, n, is given by

in which m is the mass of the gas in grams and m is its molar mass. Therefore,

Because density, d, is mass per unit volume, we can write

Equation (5.11) enables us to calculate the density of a gas (given in units of grams per liter). More often, the density of a gas can be measured, so this equation can be rearranged for us to calculate the molar mass of a gaseous substance:

EXAMPLE 5.5

A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 8.14 g/L at 47°C and 3.15 atm. Calculate the molar mass of the compound and determine its molecular formula.

and determine its molecular formula

Gas Stoichiometry In Chapter 3 we used relationships between amounts (in moles) and masses (in grams) of reactants and products to solve stoichiometry problems. When the reactants and/or products are gases, we can also use the relationships between amounts (moles, n) and volume (V) to solve such problems (Figure 5.12). Amount of reactant (grams or volume) Moles of reactant Moles of product Amount of product (grams or volume)

Figure 5.12 Stoichiometric calculations involving gases.

EXAMPLE 5.6 Sodium azide (NaN3) is used in some automobile air bags. The impact of a collision triggers the decomposition of NaN3 as follows: 2NaN3(s) ¡2Na(s) 1 3N2(g) The nitrogen gas produced quickly infl ates the bag between the driver and the windshield and dashboard. Calculate the volume of N 2 generated at 85°C and 812 mmHg by the decomposition of 50.0 g of NaN3.

5.5 Dalton’s Law of Partial Pressures Thus far we have concentrated on the behavior of pure gaseous substances, but experimental studies very often involve mixtures of gases. For example, for a study of air pollution, we may be interested in the pressure-volume temperature relationship of a sample of air, which contains several gases. In this case, and all cases involving mixtures of gases, the total gas pressure is related to partial pressures, that is, the pressures of individual gas components in the mixture. In 1801 Dalton formulated a law, now known as Dalton’s law of partial pressures, which states that the total pressure of a mixture of gases is just the sum of the pressures that each gas would exert if it were present alone. Figure 5.13 illustrates Dalton’s law. Consider a case in which two gases, A and B, are in a container of volume V. The pressure exerted by gas A, according to the ideal gas equation, is

EXAMPLE 5.7 A mixture of gases contains 3.85 moles of neon (Ne), 0.92 mole of argon (Ar), and 2.59 moles of xenon (Xe). Calculate the partial pressures of the gases if the total pressure is 2.50 atm at a certain temperature.

EXAMPLE 5.8

Oxygen gas generated by the decomposition of potassium chlorate is collected as shown in Figure 5.14. The volume of oxygen collected at 26°C and atmospheric pressure of 771 mmHg is 141 mL. Calculate the mass (in grams) of oxygen gas obtained. The pressure of the water vapor at 26°C is 25.2 mmHg.

Chapter 7: The Electronic Structure of Atoms 7.5 Quantum Mechanics The square of the wave function, c2, defines the distribution of electron density in three-dimensional space around the nucleus. SyFy Channel USA...