Molar mass of a gas

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... 

It can be assumed that the gas mixture follows ideal gas behavior and that the kilogram molar mass of a gas occupies 22.4 m3 at standard conditions of 0°C and 1 atm (1.013 bar)... 

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. 

The ideal gas law can be rearranged to calculate the density and molar mass of a gas. In a mixture of gases, each component contributes its own partial pressure to the total pressure (Dalton s law of partial pressures). The mole fraction of each component is the ratio of its partial pressure to the total pressure. When a gas is in contact with water, the total pressure is the sum of the gas pressure and the vapor pressure of water at the given temperature. 

---