Using v_rms = sqrt(3 R T / M), calculate v_rms for T = 298 K and M = 0.028 kg/mol (approximate for nitrogen).

Using v_rms = sqrt(3 R T / M), calculate v_rms for T = 298 K and M = 0.028 kg/mol (approximate for nitrogen).

• A. 600 m/s
• B. 450 m/s
• C. 515 m/s
• D. 400 m/s

Answer: (C)

Root-mean-square speed of gas molecules is given by v_rms = sqrt(3RT/M). Here R is 8.314 J/(mol·K), T is 298 K, and M is 0.028 kg/mol for nitrogen. Compute inside the square root: 3RT/M = (3 × 8.314 × 298) / 0.028 ≈ 2.65 × 10^5 (m^2/s^2). Taking the square root gives v_rms ≈ sqrt(2.65 × 10^5) ≈ 5.15 × 10^2 m/s, about 515 m/s. So the best match is approximately 515 m/s.

Root-mean-square speed of gas molecules is given by v_rms = sqrt(3RT/M). Here R is 8.314 J/(mol·K), T is 298 K, and M is 0.028 kg/mol for nitrogen. Compute inside the square root: 3RT/M = (3 × 8.314 × 298) / 0.028 ≈ 2.65 × 10^5 (m^2/s^2). Taking the square root gives v_rms ≈ sqrt(2.65 × 10^5) ≈ 5.15 × 10^2 m/s, about 515 m/s. So the best match is approximately 515 m/s.