Stack flow rate $Q = 37{,}500$ dscfm; required DRE $= 99.99\%$; particulate standard $= 0.08$ grains/dscf ($7000$ grains $= 1$ lb); emissions already corrected to $7.0\%$ O2 in the flue gas.
Find. Whether the destruction/removal efficiency of each organic pollutant, and the particulate emission rate, both meet the stated standards.
Approach. Compute the DRE of each organic compound from its inlet/outlet mass flow rates and compare to the 99.99% requirement; separately convert the particulate mass emission rate to a stack concentration (grains/dscf) using the stack volumetric flow, and compare to the 0.08 gr/dscf standard.
Destruction/removal efficiency (DRE). For each organic compound, $\text{DRE} = \dfrac{W_{in}-W_{out}}{W_{in}}\times100\%$:
$$\text{DRE}_{Benzene} = \frac{1025-0.087}{1025}\times100\% = 99.9915\%$$
$$\text{DRE}_{Tetrachlorophenol} = \frac{760-0.056}{760}\times100\% = 99.9926\%$$
$$\text{DRE}_{Toluene} = \frac{756-0.024}{756}\times100\% = 99.9968\%$$
All three exceed the required $99.99\%$ DRE.
Particulate concentration in the stack gas. Convert the mass emission rate to grains per hour, then divide by the stack volumetric flow (converted to dscf/hr):
$$20.3\ \text{lb/hr}\times7000\ \text{grains/lb} = 142{,}100\ \text{grains/hr}$$
$$37{,}500\ \text{dscfm}\times60\ \text{min/hr} = 2{,}250{,}000\ \text{dscf/hr}$$
$$C_{PM} = \frac{142{,}100\ \text{grains/hr}}{2{,}250{,}000\ \text{dscf/hr}} = \boxed{0.0632\ \text{grains/dscf}}$$
Compare to the particulate standard. The computed concentration is below the $0.08$ gr/dscf standard:
$$0.0632 < 0.08\ \text{grains/dscf}\ \Rightarrow\ \text{particulate standard is MET}$$
Final results
Quantity
Value
Standard
Meets standard?
DRE, Benzene
99.9915%
≥ 99.99%
Yes
DRE, Tetrachlorophenol
99.9926%
≥ 99.99%
Yes
DRE, Toluene
99.9968%
≥ 99.99%
Yes
Particulate concentration
0.0632 grains/dscf
≤ 0.08 grains/dscf
Yes
Overall
All emission standards are MET
Check: since the problem states the emissions are already corrected to 7.0% O2, the reported particulate mass rate (20.3 lb/hr) and stack flow (37,500 dscfm) are used directly with no further oxygen-correction factor applied; no measured (uncorrected) O2% is supplied that would call for a separate $(20.9-7)/(20.9-\text{measured})$ correction step.