Given. The data table above (density is not needed for a mass-basis mixing calculation and is a decoy for this sub-question). TCLP cadmium limit $= 5\ \text{mg/L}$.
Find. (a) Cadmium concentration of the mixed waste on a wet-mass and dry-mass basis; (b) whether the mixed waste is hazardous under TCLP.
Approach. Compute each stream's total cadmium mass and dry mass, combine by simple mass balance to get the mixed concentrations, then screen the mixed waste against the TCLP limit using the standard 20:1 extraction liquid-to-solid ratio applied to the total cadmium mass over the total dry solids mass (a worst-case, 100%-mass-transfer screening estimate).
Part (a) — dry mass of each stream. Dry mass $=$ wet mass $\times(1-\text{MC})$: $$m_{A,\text{dry}} = 40(1-0.40) = 24\ \text{kg}, \qquad m_{B,\text{dry}} = 50(1-0.50) = 25\ \text{kg}$$
Cadmium mass in each stream. The stated concentration is already on a wet basis, so the cadmium mass follows directly from the wet mass: $$m_{Cd,A} = 40\ \text{kg}\times370\ \tfrac{\text{mg}}{\text{kg}} = 14{,}800\ \text{mg}, \qquad m_{Cd,B} = 50\ \text{kg}\times190\ \tfrac{\text{mg}}{\text{kg}} = 9{,}500\ \text{mg}$$
Mix and compute the wet and dry concentrations. Total cadmium mass, total wet mass and total dry mass all add directly: $$m_{Cd,\text{tot}} = 14{,}800+9{,}500 = 24{,}300\ \text{mg}, \qquad m_{\text{wet,tot}} = 90\ \text{kg}, \qquad m_{\text{dry,tot}} = 49\ \text{kg}$$ giving $$C_{Cd,\text{wet}} = \frac{24{,}300}{90} = \boxed{270\ \text{mg/kg-wet}}, \qquad C_{Cd,\text{dry}} = \frac{24{,}300}{49} = \boxed{495.9\ \text{mg/kg-dry}}$$
Part (b) — screen against the TCLP limit. Treating the worst case — all of the cadmium mass-transfers into the leachate — the TCLP extraction fluid is applied at its standard 20:1 (L extraction fluid per kg dry solid) ratio, so the estimated leachate concentration is the total cadmium mass diluted into 20 times the total DRY mass: $$C_{Cd,\text{leachate}} = \frac{m_{Cd,\text{tot}}}{20\times m_{\text{dry,tot}}} = \frac{24{,}300\ \text{mg}}{20\times49\ \text{kg}} = \boxed{24.8\ \text{mg/L}}$$ Since $24.8\ \text{mg/L} \gg 5\ \text{mg/L}$, the mixed waste is classified as a hazardous waste by the toxicity (TCLP) characteristic for cadmium.
Final results
Quantity
Value
Mixed cadmium concentration, wet basis
270 mg/kg-wet
Mixed cadmium concentration, dry basis
495.9 mg/kg-dry
Estimated TCLP leachate concentration
24.8 mg/L
Hazardous under TCLP (limit 5 mg/L)?
Yes
Check: the TCLP screening estimate assumes 100% of the cadmium mass-transfers from the solid into the leachate at the standard 20:1 liquid:solid extraction ratio — a conservative worst-case screen, not a leach-test result. The actual laboratory TCLP extract concentration depends on cadmium's chemical speciation and leachability in this specific waste matrix and could be lower; regardless, the wide margin above the 5 mg/L limit (nearly 5×) makes the hazardous classification robust to that uncertainty.
