Exposure, Dose, Hazard Quotient & Cancer Risk

Quick Answer: Compute ADD for each pathway, divide by RfD for HQ, sum for HI, multiply by slope factor for cancer risk. Children and groundwater ingestion often dominate residential scenarios. Quantitative risk (~6% exam weight) rewards systematic setup. Write variables before calculating — unit errors mimic wrong conceptual answers.

Average Daily Dose — Ingestion Drinking water / groundwater: $ADD_{ing} = \frac{C_w \times IR_w \times EF \times ED}{BW \times AT}$ Worked example: Benzene in groundwater $C_w = 0.010$ mg/L; $IR_w = 2$ L/day; (EF = 350) days/yr; (ED = 30) yr; (BW = 70) kg; chronic $AT = 70 \times 365$ days. $ADD = \frac{0.010 \times 2 \times 350 \times 30}{70 \times 70 \times 365} = \frac{210}{1{,}794{,}500} \approx 1.17 \times 10^{-4} \text{ mg/kg-day}$

Soil Ingestion — Child Resident Children have higher soil ingestion rates (~200 mg/day order of magnitude — use problem values). $ADD_{soil} = \frac{C_s \times IR_s \times EF \times ED}{BW \times AT}$ Exam tip: If multiple pathways exist, calculate each ADD separately before summing HQs.

Inhalation Exposure $ADD_{inh} = \frac{C_{air} \times IR_{air} \times EF \times ED}{BW \times AT}$ Air concentration may come from dispersion modeling or indoor volatilization from groundwater (Johnson-Ettinger models — conceptual; exam gives $C_{air}$). Unit watch: IR in m³/day; concentrations in mg/m³ or µg/m³ — convert consistently.

Hazard Quotient and Hazard Index $HQ_i = \frac{ADD_i}{RfD_i}$ $HI = \sum HQ_i$ | Result | Interpretation (screening) | |--------|--------------------------| | HI ≤ 1 | Below reference level for non-cancer (screening) | | HI > 1 | Potential non-cancer concern; refine data | Multiple chemicals with similar target organs — sum HQs (additive assumption unless data say otherwise). Worked example: ADD = 0.002 mg/kg-day; RfD = 0.001 mg/kg-day → HQ = 2 → potential concern.

Cancer Risk Calculations Oral: $\text{Risk} = ADD \times SF$ Inhalation: $\text{Risk} = C \times UR$ Worked example: ADD = 1×10⁻⁴ mg/kg-day; SF = 1.5×10⁻¹ (mg/kg-day)⁻¹ → Risk = 1.5×10⁻⁵ (15 per million). Sum cancer risks across pathways for same carcinogen (also generally additive in screening).

Risk-Based Cleanup Goals Solve for C given target HQ = 1 or target risk = 1×10⁻⁶: $C_{goal} = \frac{RfD \times BW \times AT}{IR \times EF \times ED}$ Engineers compare soil or groundwater to goal for remediation endpoints under state or federal programs.

EPC and Statistics Soil 95% upper confidence limit (95% UCL) of the mean is a conservative exposure point concentration for risk — higher than sample mean when variance exists. Detection limits: Replace nondetects per agency guidance (half DL common in screening).

Dermal Pathway (When Given) $ADD_{derm} = \frac{C \times SA \times AF \times ABS \times EF \times ED}{BW \times AT}$ SA = skin surface area contacted; AF = adherence factor; ABS = absorption fraction — exam provides if needed.

Comparative Receptor Analysis | Receptor | Often critical pathway | |----------|------------------------| | Child resident | Soil ingestion | | Adult worker | Inhalation dust | | Tap water user | Groundwater ingestion |

FE Calculation Checklist 1. List all pathways in the scenario. 2. Copy IR, EF, ED, BW, AT from the stem (do not invent). 3. Compute ADD per pathway with units. 4. Apply RfD or SF per chemical. 5. Sum for HI or total cancer risk. 6. Compare to stated threshold. > Exam trap: Using mg/day as ADD without dividing by body weight — ADD is per kg body weight per day. > Exam trap: Multiplying HQ by SF — HQ is non-cancer; cancer uses slope factor, not RfD. Practice one full residential soil + groundwater problem in under four minutes. Quantitative risk items are among the most formula-transparent on the Environmental FE if you stay organized.

Worked Multi-Pathway Example Site: Residential yard with lead in soil and indoor dust from track-in. | Pathway | C (mg/kg) | IR | Notes | |---------|-----------|-----|-------| | Soil ingestion (child) | 450 | 200 mg/day | Use stem BW = 15 kg | | Inhalation dust | 0.8 µg/m³ | 20 m³/day | Outdoor play | Compute each ADD, compare to lead RfD (order 0.003 mg/kg-day — use stem), sum HQs. If HI > 1, screening indicates potential non-cancer concern.

Cancer vs. Non-Cancer Decision Use RfD and HQ for non-carcinogens (lead chronic, manganese). Use slope factor for carcinogens (benzene, trichloroethylene). Some metals have both — evaluate each endpoint separately.

Groundwater Ingestion Sensitivity $ADD = \frac{C_w \times 2.0 \text{ L/day} \times 350 \times 30}{70 \times 25550}$ Small changes in C_w linearly change ADD — remediation goals often back-calculate allowable C_w at risk target 1×10⁻⁶.

Common FE Errors (Expanded) - Using ppm in air as mg/kg-day without conversion - Forgetting averaging time AT in denominator (chronic vs. subchronic) - Summing cancer risks with HQ as if interchangeable Practice writing ADD with units: (mg/L × L/day × days) / (kg × days) = mg/kg-day.

Worked Multi-Pathway Example Site: Residential yard with lead in soil and indoor dust from track-in. | Pathway | C (mg/kg) | IR | Notes | |---------|-----------|-----|-------| | Soil ingestion (child) | 450 | 200 mg/day | Use stem BW = 15 kg | | Inhalation dust | 0.8 µg/m³ | 20 m³/day | Outdoor play | Compute each ADD, compare to lead RfD (order 0.003 mg/kg-day — use stem), sum HQs. If HI > 1, screening indicates potential non-cancer concern.

Cancer vs. Non-Cancer Decision Use RfD and HQ for non-carcinogens (lead chronic, manganese). Use slope factor for carcinogens (benzene, trichloroethylene). Some metals have both — evaluate each endpoint separately.

Groundwater Ingestion Sensitivity $ADD = \frac{C_w \times 2.0 \text{ L/day} \times 350 \times 30}{70 \times 25550}$ Small changes in C_w linearly change ADD — remediation goals often back-calculate allowable C_w at risk target 1×10⁻⁶.

Common FE Errors (Expanded) - Using ppm in

Study Structure

• Skim the Quick Answer, then the table above
• Close with one practice quiz item before moving on