Molar mass of gas

Click Coached Problems for a self-study module on determiniug the molar mass of gases. 

Graham s law tells us qualitatively that light molecules effuse more rapidly than heavier ones (Figure 5.8, p. 119). In quantitative form, it allows us to determine molar masses of gases (Example 5.11). 

The Berthelot equation has been found to be more accurate than the van der Waals equation for determining molar masses of gases. 

DETERMINATION OF MOLAR MASSES OF GASES AND VOLATILE SUBSTANCES... 

The fact that the behavior of a real gas approaches that of the ideal gas as the pressure is lowered is used as a basis for the precise determination of the molar masses of gases. According to Eq. (2.20), the ratio of density to pressure should be independent of pressure p/p = M/RT. This is correct for an ideal gas, but if the density of a real gas is measured at one temperature and at several different pressures, the ratio of density to pressure is found to depend slightly on the pressure. At sufficiently low pressures, p/p is a linear function of... 

It provided a method for determining the molar masses of gases and for comparing the densities of gases of known molar mass (see Sections 12.11 and 12.12). 

B The two rates of effusion are related as the square root of the ratio of the molar masses of the two gases. The lighter gas, H2, effuses faster, and thus requires a shorter time for the same amount of gas to effuse. 

As the molar masses of oxygen, nitrogen and argon are so similar, we can approximate the mole fractions of the gases to their percentage compositions. 

B—Lighter gases effuse faster. The only gas among the choices that is lighter than methane is helium. To calculate the molar mass, you would begin with the molar mass of methane and divide by the rate difference squared ... 

Carbon dioxide gas (C02) has a molar mass of 44 g/mol. The two major components of air, which are oxygen and nitrogen, have molar masses of 32 g/mol and 28 g/mol, respectively. Calculate the room-temperature densities in g/L of nitrogen (N2), oxygen (02), and carbon dioxide (C02) gases. 

Drawing a Conclusion How does your experimental molar mass compare with the molar masses of methane, ethane, and propane Suggest which of these gases are in the burner gas in your laboratory. 

A chemist monitoring air pollution collects gaseous wastes in an initially empty 22.1-L steel tank until the pressure reaches 0.84 atm at 26°C. Assuming that the gases have an average molar mass of... 

Ultrasonic Mainly gases of low molar mass Hj, N2. COj, He. Ar. A quartz crystal transducer transmits a sound wave through a sample of gas with a similar crystal used as the receiver. The velocity of the sound wave is proportional to the square root of the molar mass of the sample. The phase shift of the sound signal is measured by comparison with a reference signal. Precise temperature control is required. 1-10 Gas chromatography... 

Using a periodic table, record the molar mass of each of the gases listed in the table. 

By combining these ideas, Avogadro related the volume of a gas to the amount that is present (calculated from the mass). Avogadro divided Dalton s mass ratios by the molar masses of the elements to obtain the mole ratios. He realized that these mole ratios were the same as the volume ratios that Gay-Lussac had obtained. For example, 1 L of hydrogen gas reacts with 1 L of chlorine gas. Avogadro decided that there must be the same number of molecules in each litre of gas. Thus, Avogadro s hypothesis was formulated Equal volumes of all ideal gases at the same temperature and pressure contain the same number of molecules. 

To identify the gas, compare the molar masses of the four gases mentioned. 

The answer is probably correct, since it is so close to the molar mass of one of the given gases. 

Gases with greater masses will have greater densities. Cl2 gas has the greatest molar mass of these choices. You could also calculate the density of the gases by using the equation Dgas = molar mass / 22.4 liters. 

Ethane has molar mass of 30, the lowest molar mass of any of these gases. Ethane will have the fastest rate of effusion and, because of its low molar mass, the lowest density. 

Section 12.1 introduces the concept of pressure and describes a simple way of measuring gas pressures, as well as the customary units used for pressure. Section 12.2 discusses Boyle s law, which describes the effect of the pressure of a gas on its volume. Section 12.3 examines the effect of temperature on volume and introduces a new temperature scale that makes the effect easy to understand. Section 12.4 covers the combined gas law, which describes the effect of changes in both temperature and pressure on the volume of a gas. The ideal gas law, introduced in Section 12.5, describes how to calculate the number of moles in a sample of gas from its temperature, volume, and pressure. Dalton s law, presented in Section 12.6, enables the calculation of the pressure of an individual gas—for example, water vapor— in a mixture of gases. The number of moles present in any gas can be used in related calculations—for example, to obtain the molar mass of the gas (Section 12.7). Section 12.8 extends the concept of the number of moles of a gas to the stoichiometry of reactions in which at least one gas is involved. Section 12.9 enables us to calculate the volume of any gas in a chemical reaction from the volume of any other separate gas (not in a mixture of gases) in the reaction if their temperatures as well as their pressures are the same. Section 12.10 presents the kinetic molecular theory of gases, the accepted explanation of why gases behave as they do, which is based on the behavior of their individual molecules. 

Since the molar mass of O2 is 32, and the molar mass of the He is 4 the masses of oxygen and helium gases are ... 

Discrepancies in the experimental values of the molar mass of nitrogen provided some of the first evidence for the existence of the noble gases. If pure nitrogen is collected from the decomposition of ammonium nitrite,... 

One method of estimation the temperature of the center of the sun is based on the assumption that the center consists of gases that have an average molar mass of 2.00 g/mol. If the density of the center of the sun is 1.40 g/cm at a pressure of 1.30 x 10 atm, calculate the temperature in degrees Celsius. 

You would expect the molar mass of a gas to fall somewhere between that of one of the lightest gases under normal conditions, such as 2 g/mol for H2, and that of a relatively heavy gas, such as 222 g/mol for Rn. The answer seems reasonable. The unit is g/mol, which is the molar mass unit. 

When you analyze data, you may be asked to compare measured quantities. Or, you may be asked to determine the relative amounts of elements in a compound. Suppose, for example, you are asked to compare the molar masses of the diatomic gases, hydrogen (H2) and oxygen (O2). The molar mass of hydrogen gas equals 2.00 g/mol the molar mass of oxygen equals 32.00 g/mol. The relationship between molar masses can be expressed in three ways a ratio, a fraction, or a percent. 

The molecular formula is some whole-number multiple of the empirical formula. To determine the molecular formula, you must know the approximate molar mass of the compound under study. From Avogadro s hypothesis, the ratio of molar masses of two gaseous compounds is the same as the ratio of their densities, provided that those densities are measured at the same temperature and pressure. (This is true because a given volume contains the same number of molecules of the two gases.) The density of the welding gas from Example 2.4 is 1.06 g at 25°C... 

Baseball reporters say that long fly balls that would have carried for home runs in July die in the cool air of October and are caught. The idea behind this observation is that a baseball carries better when the air is less dense. Dry air is a mixture of gases with an effective molar mass of 29.0 g mol . ... 

In order to calculate the time of effusion, we need to know only the molar mass of the gases. 

We used Eq. 2.22 to calculate some D p values, which are related to the conditions and results of the experiments with the halides of heavy elements. The results are displayed in Fig. 2.1. In such studies the molar mass of the tracer is usually much larger than that of the carrier gas. Then the term 1 / M in the parentheses in Eq. 2.22 becomes negligible, and the diffusion coefficients could be plotted in Fig. 2.1 as a function of only the molar volume. The l) p values are given for 500K the figures for 273 K are less by a factor of 0.77, those for 700 K are obtained by multiplying with 1.18. We see that the combinations of common carrier gases with heavy voluminous molecules are characterized by >12 of the order of 0.01-0.1 cm2 s 1 at atmospheric pressure. 

When 1.00 g of a certain fuel gas is burned in a calorimeter, the temperature of the surrounding 1.000 kg of water increases from 20.00°C to 28.05°C. All products and reactants in the process are gases. Calculate the heat given off in this reaction. How much heat would 1.00 mol of the fuel give off, assuming a molar mass of 65.8 g/mol ... 

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