Understanding the Calculation of TDS (Total Dissolved Solids)

Total Dissolved Solids (TDS) quantifies all inorganic and organic substances dissolved in water. Calculating TDS is essential for water quality assessment and treatment processes.

This article explores detailed formulas, common values, and real-world applications of TDS calculation. It provides expert-level insights for professionals in water analysis and environmental engineering.

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Calculate TDS from electrical conductivity for a groundwater sample.
Determine TDS in mg/L using gravimetric analysis data.
Estimate TDS based on ion concentration measurements in wastewater.
Convert TDS values between ppm and mg/L for drinking water standards.

Comprehensive Table of Common TDS Values in Various Water Sources

Water Source	TDS Range (mg/L)	Typical TDS Value (mg/L)	Water Quality Implication
Drinking Water (WHO Standard)	0 – 500	300	Acceptable for human consumption
Groundwater (Fresh)	100 – 1000	450	Generally safe, may require treatment
Surface Water (Rivers, Lakes)	50 – 1500	700	Variable quality, depends on pollution
Seawater	30,000 – 45,000	35,000	High salinity, not potable
Wastewater (Municipal)	500 – 3000	1500	Requires treatment before discharge
Industrial Effluent	Variable (1000 – 10,000+)	4000	Highly variable, often toxic
Rainwater	0 – 50	20	Very low dissolved solids
Brackish Water	1,000 – 10,000	5,000	Intermediate salinity, treatment needed

Fundamental Formulas for Calculating Total Dissolved Solids

Calculating TDS involves several methods depending on the available data and required accuracy. The most common approaches include gravimetric analysis, electrical conductivity correlation, and summation of ion concentrations.

1. Gravimetric Method

This is the direct and most accurate method, involving evaporation and weighing of dissolved solids.

TDS (mg/L) = (Weight of residue in mg) / (Volume of sample in mL) × 1000

Weight of residue: Mass of solids remaining after evaporation (mg).
Volume of sample: Volume of water sample evaporated (mL).

Common values: Residue weights typically range from a few mg to several hundred mg depending on sample concentration.

2. Electrical Conductivity (EC) Correlation Method

Since dissolved ions conduct electricity, TDS can be estimated from EC measurements using empirical conversion factors.

TDS (mg/L) = k × EC (μS/cm)

k: Conversion factor (dimensionless), typically between 0.5 and 0.9 depending on water type.
EC: Electrical conductivity of the water sample in microsiemens per centimeter (μS/cm).

Typical values of k:

Freshwater: 0.65 – 0.75
Groundwater: 0.55 – 0.75
Wastewater: 0.7 – 0.9

3. Summation of Ion Concentrations

When ion concentrations are known, TDS can be calculated by summing the mass concentrations of all dissolved ions.

TDS (mg/L) = Σ (Concentration of each ion in mg/L)

Includes major cations: Na⁺, K⁺, Ca²⁺, Mg²⁺
Includes major anions: Cl^–, SO₄^2-, HCO₃^–, NO₃^–

This method requires comprehensive ion chromatography or titration data.

4. Conversion Between Units

TDS is often expressed in mg/L or ppm (parts per million), which are numerically equivalent for water due to its density.

1 mg/L = 1 ppm (for water at 25°C)

Note: For solutions with densities significantly different from water, corrections may be necessary.

Detailed Explanation of Variables and Their Typical Ranges

Weight of residue (mg): Obtained after evaporating a known volume of water; typical values range from 1 mg (very pure water) to several hundred mg (polluted water).
Volume of sample (mL): Usually 100 mL or 500 mL in laboratory tests; must be accurately measured for precise TDS calculation.
Electrical Conductivity (EC, μS/cm): Measured using a conductivity meter; freshwater typically ranges from 50 to 1500 μS/cm, seawater around 50,000 μS/cm.
Conversion factor (k): Empirical, depends on ionic composition; must be calibrated for each water type.
Ion concentrations (mg/L): Determined by chemical analysis; sum of all dissolved ions gives total dissolved solids.

Real-World Applications and Case Studies

Case Study 1: Groundwater TDS Estimation Using Electrical Conductivity

A water quality engineer is tasked with estimating the TDS of a groundwater sample from a rural well. The measured electrical conductivity is 850 μS/cm. Based on regional water characteristics, the conversion factor k is 0.65.

Using the formula:

TDS = 0.65 × 850 = 552.5 mg/L

This TDS value indicates moderately mineralized water, suitable for most agricultural and domestic uses but may require treatment for sensitive industrial applications.

Case Study 2: Gravimetric Determination of TDS in Industrial Wastewater

An environmental laboratory receives a 250 mL sample of industrial wastewater. After evaporation and drying, the residue weight is 1.2 grams (1200 mg). Calculate the TDS in mg/L.

Applying the gravimetric formula:

TDS = (1200 mg / 250 mL) × 1000 = 4800 mg/L

This high TDS value reflects significant dissolved solids, indicating the wastewater requires advanced treatment before discharge to comply with environmental regulations.

Additional Considerations in TDS Calculation

Temperature Effects: Electrical conductivity varies with temperature; measurements should be standardized at 25°C or corrected accordingly.
Calibration of Instruments: Conductivity meters must be calibrated with standard solutions to ensure accuracy.
Interferences: Non-ionic dissolved solids (e.g., organic compounds) do not contribute to conductivity, potentially causing underestimation of TDS via EC method.
Regulatory Standards: Different countries and agencies set maximum allowable TDS levels for drinking water, irrigation, and industrial use. For example, the US EPA recommends a secondary maximum contaminant level of 500 mg/L for TDS in drinking water.

Advanced Techniques and Emerging Trends

Recent advances in sensor technology enable real-time TDS monitoring using inline conductivity probes combined with machine learning algorithms to improve conversion accuracy. Additionally, spectroscopic methods are being explored to detect specific dissolved solids contributing to TDS.

Integration of Geographic Information Systems (GIS) with TDS data supports large-scale water resource management and pollution tracking.