Using the Ideal Gas Law

The ideal gas law is a powerful tool that the chemist—and now you—can use to determine the molar mass of an unknown gas. By measuring the temperature, pressure, volume, and mass of a gas sample, you can calculate the molar mass of the gas. 

How can the equation for the ideal gas law be used to calculate the molar mass of a gas  

Prepare all written materials that you will take into the laboratory. Be sure to include safety precau-hons, procedure notes, and a data table. 

Because you will collect the aerosol gas over water, the beaker contains both the aerosol gas and water vapor. Form a hypothesis about how the presence of water vapor will affect the calculated value of the molar mass of the gas. Explain. 

The following gases are or have been used in aerosol cans, some as propellants. Use the gases molecular formulas to calculate their molar masses. 

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The mass flow rate w is related to the throughput using the ideal gas law. 

Density The measure of the amount of mass in a unit volume. The density of a gas is a function of its pressure and temperature, It can be determined by using the ideal gas laws. 

As pointed out in Chapter 3, a balanced equation can be used to relate moles or grams of substances taking part in a reaction. Where gases are involved, these relations can be ex tended to include volumes. To do this, we use the ideal gas law and the conversion factor approach described in Chapter 3. 

Use the ideal gas law to convert the smaller number of moles of C02 to volume. SOLUTION... 

In this case, Ptot is the measured pressure. The partial pressure of water vapor, Ph2o, is equal to the vapor pressure of liquid water. It has a fixed value at a given temperature (see Appendix 1). The partial pressure of hydrogen, PH2, can be calculated by subtraction. The number of moles of hydrogen in the wet gas, h2, can then be determined using the ideal gas law. 

Again, use the ideal gas law to find the mass of water that must be vaporized to reach the calculated pressure (7.9 mm Hg). Subtract the mass of vaporized water from the mass of water in the vaporizer, and use density to calculate the volume of water in the vaporizer. 

Strategy First calculate the partial pressures of N204 and N02, using the ideal gas law as applied to mixtures P, = tiiRT/V. Then calculate Q. Finally, compare Q and K to predict the direction of reaction. 

Strategy First (1), write a balanced equation for the reaction, which is very similar to that for ZnS, except that Zn2+ is replaced by Bi3+. (2) Using the balanced equation, calculate the number of moles of S02. Finally (3), use the ideal gas law to calculate the volume of S02. 

Only one way of working gas-law problems, using the ideal gas law in all cases (Chapter 5). 

Table 4.3 gives values of the molar volume of an ideal gas under a variety of common conditions. To obtain the volume of a known amount of gas at a specified temperature and pressure, we simply multiply the molar volume at that temperature and pressure by the amount in moles. Alternatively, we can use the ideal gas law to calculate the volume. 

STRATEGY We convert from the given volume of gas into moles of molecules (by using the molar volume), then into moles of reactant molecules or formula units (by using a mole ratio), and then into the mass of reactant (by using its molar mass). If the molar volume at the stated conditions is not available, then use the ideal gas law to calculate the amount of gas molecules. 

To extend our model, we should note that, at low pressures at least, all gases respond in the same way to changes in pressure, volume, and temperature. Therefore, for calculations of the type that we are doing in this chapter, it does not matter whether all the molecules in a sample are the same. A mixture of gases that do not react with one another behaves like a single pure gas. For instance, we can treat air as a single gas when we want to use the ideal gas law to predict its properties. 

We can now do something remarkable we can use the ideal gas law to calculate the root mean square speed of the molecules of a gas. We know that PV = nRT for an ideal gas therefore, we can set the right-hand side of Eq. 19 equal to nRT and rearrange the resulting expression ( nMv2ms = nRT) into... 

For reactions in which no gas is generated or consumed, little expansion work is done as the reaction proceeds and the difference between AH and AU is negligible so we can set AH = AU. However, if a gas is formed in the reaction, so much expansion work is done to make room for the gaseous products that the difference can be significant. We can use the ideal gas law to relate the values of AH and AU for gases that behave ideally. 

STRATEGY We expect a positive entropy change because the thermal disorder in a system increases as the temperature is raised. We use Eq. 2, with the heat capacity at constant volume, Cv = nCV m. Find the amount (in moles) of gas molecules by using the ideal gas law, PV = nRT, and the initial conditions remember to express temperature in kelvins. Because the data are liters and kilopascals, use R expressed in those units. As always, avoid rounding errors by delaying the numerical calculation to the last possible stage. 

The entropy change accompanying the isothermal compression or expansion of an ideal gas can be expressed in terms of its initial and final pressures. To do so, we use the ideal gas law—specifically, Boyle s law—to express the ratio of volumes in Eq. 3 in terms of the ratio of the initial and final pressures. Because pressure is inversely proportional to volume (Boyle s law), we know that at constant temperature V2/Vj = E /E2 where l is the initial pressure and P2 is the final pressure. Therefore,... 

Using the ideal gas law and the relationship (n — 1) oc p between refractive index n and density p leads us to the refractive index structure function. 

Note that this step uses the ideal gas law. Other equations of state could be substituted. 

Solution The obvious way to solve this problem is to choose a pressure, calculate Oq using the ideal gas law, and then conduct a batch reaction at constant T and P. Equation (7.38) gives the reaction rate. Any reasonable values for n and kfCm. be used. Since there is a change in the number of moles upon reaction, a variable-volume reactor is needed. A straightforward but messy approach uses the methodology of Section 2.6 and solves component balances in terms of the number of moles, Na, Nb, and Nc-... 

Here the rates are converted from mol/s to m /s using the ideal gas law. The component balances in terms of concentrations are as follows ... 

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