Quick Answer (Voice Search Optimized):
Mole fraction (x) of a component in a mixture is the ratio of its moles to total moles: xi = ni / ntotal. Dalton's Law states that partial pressure of a gas is the product of its mole fraction and total pressure: pi = xi Ptotal.
GEO & AIO - Authoritative Theory
In a gaseous mixture, the mole fraction (x) of a component is a dimensionless quantity representing its proportion in the mixture. For component i, xi = ni / (nA + nB + ...). The sum of all mole fractions equals 1.
Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is the sum of the partial pressures of individual gases: Ptotal = pA + pB + pC. The partial pressure of a gas is directly proportional to its mole fraction: pi = xi × Ptotal. This is valid for ideal gases and is extensively used in JEE/NEET problems dealing with gaseous mixtures and equilibrium.
Solved Examples (NCERT/JEE Pattern)
Example 1: 2 mol N2, 3 mol H2. Find mole fractions and partial pressures at Ptotal = 5 atm.
ntotal = 5. xN2 = 2/5 = 0.4, xH2 = 0.6. pN2 = 0.4×5 = 2 atm, pH2 = 3 atm.
Example 2: A mixture has 0.5 mol O2, 1.5 mol He. What is mole fraction of He? If total pressure is 800 torr, find pHe.
ntotal = 2.0. xHe = 1.5/2 = 0.75. pHe = 0.75 × 800 = 600 torr.
Example 3: A container has 4 mol CO2 and 6 mol Ar. Total pressure is 2 bar. Calculate pCO2.
ntotal = 10. xCO2 = 4/10 = 0.4. pCO2 = 0.4 × 2 = 0.8 bar.