θ = KP / (1 + KP)
The Langmuir isotherm (1918, Nobel Prize 1932) describes the adsorption of molecules onto a solid surface forming a monolayer. Key assumptions: (1) uniform surface with equivalent adsorption sites, (2) one molecule per site (monolayer), (3) no interaction between adsorbed molecules. The equation θ = KP/(1+KP) gives the fractional surface coverage, where K is the Langmuir constant (ratio of adsorption/desorption rate constants) and P is pressure (or concentration for solutions: q = qₘKC/(1+KC)). At low P: θ ≈ KP (linear, Henry's law). At high P: θ → 1 (saturation). The linearized form 1/q = 1/qₘ + 1/(qₘKC) allows determination of K and qₘ from experimental data. Applications include catalysis, gas masks, chromatography, and environmental remediation.