Physics · Kinetic Theory · NEET
Because at the same temperature every gas molecule has the same average kinetic energy, which is (3/2)k_B T. Kinetic energy is (1/2)m v squared. If the energy is fixed and the mass m is small, then v squared must be large to keep the energy the same. So a light molecule (small m) is forced to move fast, and a heavy molecule (large m) moves slow. This is why hydrogen molecules move much faster than oxygen molecules in the same warm room.
To the square root of M, not to M itself. The full relation is v_rms = square root of (3RT / M). Since only M is under the root, v_rms is proportional to 1 divided by square root of M. Example: oxygen (M = 32) versus hydrogen (M = 2). The molar mass ratio is 16, but the speed ratio is square root of 16 = 4. So hydrogen is 4 times faster, not 16 times faster. Students who forget the root get the wrong ratio.
Both work, but you must match R with M and k_B with m. Two correct forms: v_rms = square root of (3RT / M) where M is molar mass in kg per mole and R = 8.314 J per mol per K; OR v_rms = square root of (3 k_B T / m) where m is the mass of ONE molecule in kg and k_B = 1.38 x 10^-23 J per K. Never mix R with single-molecule mass or k_B with molar mass — that is the most common unit error.
No. RMS speed depends only on temperature and the TYPE of gas (its molar mass M), not on how much gas you have. 2 grams of oxygen and 200 grams of oxygen at the same temperature have exactly the same RMS speed. In problems that give you a mass ratio of two gases (like argon and chlorine in 2:1 ratio), that mass ratio is usually a distractor — ignore it and use only the molar masses.
No. At the same temperature all gases have the SAME average translational kinetic energy = (3/2)k_B T. The heavy gas balances its large mass with a low speed, and the light gas balances its small mass with a high speed, so the energy comes out equal. Speed differs with mass; average kinetic energy does not.
A flask contains argon and chlorine in the ratio of 2 : 1 by mass. The temperature of the mixture is 27 degrees C. The ratio of root mean square speeds of the molecules of the two gases (v_rms of Ar / v_rms of Cl) is: (Atomic mass of argon = 40.0 u and molecular mass of chlorine = 70.0 u)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
v_rms = square root of (3RT / M), where R is the gas constant, T is absolute temperature in kelvin, and M is molar mass in kg per mole. At fixed T, v_rms is proportional to 1 / square root of M.
The gas with the smallest molar mass. Hydrogen (M = 2) has the highest RMS speed of common gases, followed by helium (M = 4). Heavy gases like chlorine or carbon dioxide have the lowest RMS speed.
Molar masses are 2 and 32, a ratio of 16. RMS speed uses the square root, so hydrogen is square root of 16 = 4 times faster than oxygen at the same temperature.
No. RMS speed depends only on temperature and the molar mass of the gas type. Taking more moles or more grams does not change it.
Because v_rms is proportional to square root of absolute temperature. Celsius can be zero or negative, which would give zero or imaginary speeds. Always convert: T(K) = T(C) + 273.
