Ideal gas equations for

To use the ideal gas equation for quantitative calculations, we must express each quantity in appropriate units. The ideal gas equation holds only when temperature is expressed using an absolute scale. We will always use the Kelvin scale, applying the conversion introduced in Chapter E 7 (K) = T(° C) + 273.15. Typical laboratory pressures are expressed in atmospheres, and typical laboratory volumes are expressed in liters. For this choice of... 

However, suppose that you have forgotten the convenient formula for the density of an ideal gas You can still solve a problem such as this one. The density of 1.00 g/L indicates a mass of 1.00 g of gas in a 1.00-L volume. Of course, the mass of a gas, given its identity (oxygen in this case) enables us to determine the amount in moles of the gas (n in the ideal gas equation). Then, we can solve the ideal gas equation for the desired property, such as temperature, as follows ... 

Now you can rearrange the ideal gas equation for the unknown quantity, the volume. 

Step 2 Solve the ideal gas equation for n. Put the known values into the equation to find the number of moles present (n). 

FIGURE 11.1 Description of (a) van der Waals and (b) ideal gas equation for water. For low energy (low pressure, high volume) the equations are similar, for high energy though the difference is apparent. 

We list the variables with the proper units. Then we solve the ideal gas equation for P and... 

A.6.6 There is a clear trend that the coefficient a and the boiling point are positively correlated. The internal energy required before a substance will change state from the more highly associated liquid state into the vapor phase is determined by the force of attraction between the molecules. Thus the observed relationship is consistent with fact that a corrects the ideal gas equation for the force of attraction between gas particles, this force is ignored in the ideal gas law but accounted for in the van der Waals treatment. Consistent with this interpretation, gases with very small values of a, such as H2 and He, are cooled to almost absolute zero before they condense to form a liquid. 

Defining the partial pressure of component i as p, = (n/n)P, and combining this definition with the ideal gas equation to eliminate P, the ideal gas equation for component i may be written as... 

We convert from moles to volume by solving the ideal gas equation for Vand plugging in the given values for n, T, and P ... 

SOLUTION Since there are four variables, we can calculate the value of one of them if the values of the other three are given. We solve the ideal gas equation for V by symbolically dividing both sides of the equation by P, obtaining... 

An ideal gas is one that exactly follows the ideal gas equation. Rearranging the ideal gas equation for n, we obtain ,... 

In this chapter we have considered several properties of gases and have seen how the relationships among these properties can be expressed by various laws written in the form of mathematical equations. The most useful of these is the ideal gas equation, which relates all the important gas properties. However, under certain conditions gases do not obey the ideal gas equation. For... 

Convert to consistent units. Make certain that quantities are converted to the proper units. In using the ideal-gas equation, for example, we usually use the value of R that has units of L-atm/mol-K. If you are given a pressure in torr, you will need to convert it to atmospheres before using this value of R in your calculations. 

The gas laws we discussed in Section 10.3 are special cases of the ideal-gas equation. For example, when n and T are held constant, the product nRT contains three constants and so must itself be a constant ... 

We solve the ideal-gas equation for V and calculate its derivative with respect to T p p ... 

The measured pressures of NO2 or NF2 gases are significantly smaller than the pressure predicted by the ideal gas equation for these systems at all pressures. Is the ideal gas equation invalid for these systems, or is there another explanation ... 

This relationship is called the ideal gas equation or the Ideal Gas Law. The numerical value of R, the universal gas constant, depends on the choices of the units for P, V, and T. One mole of an ideal gas occupies 22.414 liters at 1.0000 atmosphere and 273.15 K (STP). Solving the ideal gas equation for R gives... 

---