The Molar Mass of a Gas

Through another simple rearrangement of the ideal gas law, we can determine the molar mass of an unknown gas or volatile liquid (one that is easily vaporized)  

Notice that this equation is just a rearrangement of Equation 5.9. 

SAMPLE PROBLEM 5.8 Finding the Molar Mass of a Volatile Liquid 

Problem An organic chemist isolates a colorless liquid from a petroleum sample. She places the liquid in a flask and puts the flask in a boiling water bath, which vaporizes the liquid and fills the flask with gas. She closes the flask, reweighs it, and obtains the following data  

Volume (V) of flask = 213 mL T= 100.0°C P = 754 torr Mass of flask + gas = 78.416 g Mass of empty flask = 77.834 g Calculate the molar mass of the liquid. 

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The ideal gas law offers a simple approach to the experimental determination of the molar mass of a gas. Indeed, this approach can be applied to volatile liquids like acetone (Example 5.4). All you need to know is the mass of a sample confined to a container of fixed volume at a particular temperature and pressure. 

We see that, for a given pressure and temperature, the greater the molar mass of the gas, the greater its density. Equation 10 also shows that, at constant temperature, the density of a gas increases with pressure. When a gas is compressed, its density increases because the same number of molecules are confined in a smaller volume. Similarly, heating a gas that is free to expand at constant pressure increases the volume occupied by the gas and therefore reduces its density. The effect of temperature on density is the principle behind hot-air balloons the hot air inside the envelope of the balloon has a lower density than that of the surrounding cool air. Equation 10 is also the basis for using density measurements to determine the molar mass of a gas or vapor. 

EXAMPLE 4.6 Sample exercise Calculating the molar mass of a gas from its density... 

From the graph obtained, what relationship exists between the molar mass of a gas and its boiling point ... 

The molar mass of a gas refers to the mass (in g) of one mole of the gas. You can calculate molar mass by adding the masses of atoms in the periodic table. You can also calculate molar mass by dividing the mass of a sample by the number of moles that are present. Molar mass is always expressed in the units g/mol. Table 12.2 summarizes molar volume, density, and molar mass. 

The molar mass of a gas may be calculated if the mass of a sample and the number of moles of the sample are both known. The ideal gas law may be used to determine the number of moles, from which the molar mass may be calculated. As introduced in Section 7.4, the molar mass, along with the empirical formula, may then be used to determine the molecular formula (Section 12.7). 

What is the molar mass of a gas if it diffuses 0.907 times the speed of... 

Estimate the molar mass of a gas that effuses at 1.60 times the effusion rate of carbon dioxide. 

Compare diffusion and effusion. Explain the relationship between the rates of these processes and the molar mass of a gas. (13.1)... 

To find the molar mass of a gas sample, the mass, temperature, pressure, and volume of the gas must be known. Remember from Chapter 12 that the number of moles of a gas (n) is equal to the mass (m) divided by the molar mass (M). Therefore, the n in the equation can be replaced by m/M. 

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. 

Arts. The molar mass of a gas is calculated from the rearranged ideal gas law ... 

Okulate the molar mass of a gas which has a density of 1.798gdm ac298Kandl01kNm- . 

Eq. (4.23) states that the molar mass of a gas is directly proportional to its densities in the case of same pressure and temperature. Based on standard values (normally 0 °C and 1 bar), the density for different pressures and temperature can be calculated according to ... 

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