A fixed number of moles of gas at a certain temperature and pressure occupies a certain volume. If the pressure and temperature of this fixed number of moles of gas are changed, then the new volume can be easily calculated. Equation (3.5) can be written as follows:
Since n is constant in this case, applying Eq. (3.14) to the two sets of conditions yields
(3.15)
or
Equation (3.16) can be applied to a static system or to a flow system as long as the number of moles under consideration remains constant.
EXAMPLE 3.11
A sample stream of dry gas is being withdrawn from a stack. The stack gases are at 200 °C and 730 mmHg. The stream flows through a heated filter, a set of cooled impingers, a small air pump, and then through a flow meter. The rate of flow is determined to be 30.0 l/min at 20 °C and 790 mmHg. (a) Calculate the actual volumetric flow rate through the filter (at T = 200 °C and P = 730 mm Hg). (b) If 1.42 mg of solid particles are collected on the filter in 30 minutes, calculate the concentration of particles in the stack gas (in μg/m3).
SOLUTION
- Qfilter = (30.0)
= 52.4 l/min - Total volume of gas sampled (at stack conditions):
In the preceding example problem, if a concentration of, say, 500 ppm of NO2 were measured in the gases exiting the flow meter, then we could state that the concentration in the stack was also 500 ppm. The reason for this is that ppm is a measure of relative concentration and as the total volume of the gas sample changes, so does the volume of NO2. The relative volume of NO2 (relative to the total) does not change. However, if some moles of a material that is gaseous in the stack are removed from the gas sample stream (such as water that is condensed in the impingers), we must account for the change in relative gas concentrations at the two places (upstream versus downstream of the impingers). This is shown in the following example problem.
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