TCLP regulatory limit for arsenic $= 2.5$ mg/L; TCLP liquid-to-solid ratio (EPA Method 1311) $= 20$ L extraction fluid per kg dry solid.
Find. (a) mixed waste density; (b) dry-basis arsenic concentration of the mixture; (c) whether the mixture is a leachate-toxic waste for arsenic.
Approach. Work on a 100 kg basis of the total wet mixture. Split into wet masses of A and B by weight fraction, convert each to a volume (via its own density) to get the mixed density; separately convert each to dry solids mass (via $1-\text{MC}$) and combine the arsenic mass (from the wet-basis concentration) to get the dry-basis concentration; then estimate the TCLP leachate concentration from the standard 20:1 liquid-to-solid extraction ratio and compare to the regulatory limit.
Wet mass of each waste (100 kg total basis).
$$m_A = 100\times0.75 = 75\ \text{kg}, \qquad m_B = 100\times0.25 = 25\ \text{kg}$$
Volume of each waste, from its own density.
$$V_A = \frac{75}{300} = 0.250\ \text{m}^3, \qquad V_B = \frac{25}{210} = 0.1190\ \text{m}^3$$
Mixed waste density. Total mass over total volume:
$$\rho_{mix} = \frac{m_A+m_B}{V_A+V_B} = \frac{100}{0.250+0.1190} = \frac{100}{0.3690} = \boxed{271\ \text{kg/m}^3}$$
Dry solids mass of each waste.
$$m_{A,dry} = 75\times(1-0.20) = 60\ \text{kg}, \qquad m_{B,dry} = 25\times(1-0.40) = 15\ \text{kg}$$
$$m_{dry,total} = 60+15 = 75\ \text{kg}$$
Total arsenic mass. The arsenic concentrations are given per kg of WET waste, so apply them to the wet masses:
$$M_{As} = (75\times110) + (25\times55) = 8250+1375 = 9625\ \text{mg}$$
Dry-basis arsenic concentration. Divide the total arsenic mass by the total DRY solids mass:
$$C_{As,dry} = \frac{9625\ \text{mg}}{75\ \text{kg}} = \boxed{128.3\ \text{mg/kg-dry}}$$
TCLP leachate arsenic concentration. Assuming all the arsenic present is available to leach into the standard 20:1 (L extraction fluid : kg dry solid) TCLP extraction:
$$C_{leachate} = \frac{M_{As}}{20\times m_{dry,total}} = \frac{9625}{20\times75} = \frac{9625}{1500} = \boxed{6.42\ \text{mg/L}}$$
Compare to the regulatory limit.
$$6.42\ \text{mg/L} > 2.5\ \text{mg/L}\ \Rightarrow\ \boxed{\text{the mixture IS a leachate-toxic waste for arsenic}}$$
Final results
Quantity
Value
(a) Mixed waste density
271 kg/m3
(b) Dry-basis arsenic concentration
128.3 mg/kg-dry
Estimated TCLP leachate concentration
6.42 mg/L
(c) Leachate-toxic (TCLP) classification
Yes — 6.42 mg/L > 2.5 mg/L limit
Check: assumes 100% of the measured arsenic mass is available to the TCLP extraction fluid at the standard 20:1 liquid:solid ratio (a conservative, standard estimating approach) — the actual regulatory determination requires running the physical TCLP procedure rather than this mass-balance estimate, but the large margin above the 2.5 mg/L limit (more than 2.5×) makes the qualitative classification robust to that simplification.
