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

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Multiple Choice

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

Explanation:
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.

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