N1. 0.5 mol gas in 2 L at 300 K. Pressure? P = nRT/V = (0.5 × 0.0821 × 300)/2 = 12.315/2 = 6.16 atm

N2. A gas occupies 8 L at 1 atm, 300 K. New volume at 2 atm, 600 K? $V_{2}$ = 8 × (1/2) × (600/300) = 8 × 0.5 × 2 = 8 L

N3. Molar mass of gas with density 2 g/L at 1 atm, 300 K? M = dRT/P = (2 × 0.0821 × 300)/1 = 49.26 g/mol

N4. r($H_{2}$)/r($CO_{2}$)? (M($CO_{2}$) = 44, M($H_{2}$) = 2) r($H_{2}$)/r($CO_{2}$) = √(44/2) = √22 ≈ 4.69

N5. v_rms of $O_{2}$ (M = 32 g/mol = 0.032 kg/mol) at 300 K? v_rms = √(3 × 8.314 × 300/0.032) = √(7482.6/0.032) = √233831 ≈ 483.6 m/s

N6. Boyle temperature for gas with a = 1 $L^{2}$·atm/$mol^{2}$, b = 0.02 L/mol? T_B = a/(Rb) = 1/(0.0821 × 0.02) = 1/0.001642 ≈ 609 K

N7. 4 g He (M=4) + 32 g $O_{2}$ (M=32) in 10 L at 300 K. Total pressure? n(He) = 1 mol, n($O_{2}$) = 1 mol; n_total = 2 mol P = (2 × 0.0821 × 300)/10 = 4.926 atm

N8. Gas A takes 10 min to effuse; gas B takes 20 min. M_A/M_B = ? t ∝ √M; (t_A/t_B)^{2} = M_A/M_B = (10/20)^{2} = 0.25. So M_A = 0.25 × M_B (gas A is lighter)

N9. v_rms at $T_{2}$ = $9T_{1}$ compared to v_{1}? v_{2} = v_{1} × √($T_{2}$/$T_{1}$) = v_{1} × √9 = 3v_{1}

N10. Partial pressure of $N_{2}$ if 2 mol $N_{2}$ + 3 mol $O_{2}$ in 5 L at 300 K? P_total = (5 × 0.0821 × 300)/5 = 24.63 atm; x($N_{2}$) = 2/5; p($N_{2}$) = 0.4 × 24.63 = 9.852 atm