Pattern 1: PV = nRT Numericals (Most Common) NEET provides values of P, T, mass (or n) and asks for V (or another variable). The most common trap: forgetting to convert °C to K, or using grams instead of moles.

Sample approach:

• Step 1: Convert all units (T to K, mass to mol, mL to L)
• Step 2: Identify which variables are given and which to find
• Step 3: Apply PV = nRT; rearrange algebraically before substituting numbers

Pattern 2: Graham's Law (Very Common) Format: "Gas X effuses twice as fast as gas Y. If M_Y = 32, find M_X." Method: (r_X/r_Y)^{2} = M_Y/M_X → M_X = M_Y/(r_X/r_Y)^{2} = 32/4 = 8.

Trap: Inverting — students write r_{1}/r_{2} = √($M_{1}$/$M_{2}$) (wrong) instead of √($M_{2}$/$M_{1}$) (correct).

Pattern 3: Molecular Speed Comparison Format: "Which gas has the highest v_rms at the same T?" Answer: Always the gas with lowest M. v_rms = √(3RT/M) → lowest M → highest speed.

Or: "What is v_rms of gas at temperature $T_{2}$ if it was v_{1} at $T_{1}$?" v_{2} = v_{1} × √($T_{2}$/$T_{1}$).

Pattern 4: Z Factor Interpretation Format: "A gas has Z = 1.2 at high pressure. What does this indicate?" Answer: Z > 1 → repulsive forces dominate → gas less compressible than ideal → actual V > ideal V.

Or Z < 1 → attraction dominates → gas more compressible than ideal.

Pattern 5: Dalton's Law with Mole Fraction Format: "A mixture of gases in a container. Find total pressure or partial pressure." Method: n_total = n_{1} + n_{2}, use P = n_total RT/V for total, x_i = n_i/n_total for mole fractions, p_i = x_i × P_total.

Most-tested numerical pairs (NEET history):

• PV = nRT with mass conversion
• Graham's Law with rate ratios given
• v_rms at two temperatures (ratio method)
• Partial pressure from mole fraction