SCIENCE · INVESTIGATE AND EXPLAIN

Compare molecular speed without confusing it with bulk transport

Use temperature and molar mass to distinguish characteristic speed, energy and a conditional effusion ratio .

Learning outcome: Compare masses20 and 40 at300 K, then raise temperature while holding mass fixed. Retain SI mass conversion, energy and speed separately.

Starting recap

Review amount dimensions, chemical formulas and charge, signed differences, ratio bounds and the distinction between a theoretical constraint and measured conversion.

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Try

At equal temperature, a 40 g/mol gas has 1/√2 the rms speed and effusion rate of a 20 g/mol reference under the stipulated molecular-flow conditions.

Open the experiment

Predict

Do gases at equal temperature have equal rms speeds or equal mean translational energy per mole?

Your prediction and reason

Experiment

Compare masses20 and 40 at300 K, then raise temperature while holding mass fixed. Retain SI mass conversion, energy and speed separately.

Separate characteristic molecular speed from effusion rate

Worked teaching model · synthetic values · Ideal thermal gas with rms speed sqrt(3RT/M), R=8.314 J/(mol K) and M in kg/mol. Compare effusion to a20 g/mol reference at the same selected temperature and equal pressure through identical sufficiently small apertures in the molecular-flow limit. No gas release experiment.

Temperature: 300 K Molar mass: 30 g/mol

Reset keeps your prediction, captures and practice history.

Axes rescale. Connected samples show a declared parameter relationship, not elapsed reaction time. Dashed comparison, when present, is the unbiased gas pressure or ideal-gas Z=1 reference described in the model.

Numerical diagram coordinates

temperature (K)	rms speed (m/s)
250	455.9057
275	478.1579
300	499.4197
325	519.8125
350	539.4349
375	558.3682
400	576.6802
425	594.4283
450	611.6617

Calculated evidence under the stated assumptions
Quantity	Value	Unit
Rms speed	499.4197	m/s
Mean translational energy per mole	3741.3	J/mol
Effusion rate relative to20 g/mol gas	0.8164966	ratio
Molar mass in SI units	0.03	kg/mol

Equal temperature gives equal mean translational energy per mole, not equal speed across molar masses.

Rms is a characteristic of a distribution, not the speed of every particle. Graham-type effusion ratios require the same temperature and comparable pressures/apertures in the molecular-flow limit. Bulk diffusion and a macroscopic gas jet need not obey this simple rate comparison.

Retain the reaction/measurement boundary with every number. This mathematical packet is not a chemical procedure or evidence of actual laboratory technique.

Equal temperature gives equal mean translational energy per mole, not equal speed across molar masses.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

A distribution is not one particle speed

A thermal gas contains particles with a range of speeds. Root-mean-square speed is a characteristic derived from squared speeds, not the velocity of every molecule. Mean velocity can be zero in a gas with no bulk flow while particles still move rapidly in random directions. Keep a directional average separate from a speed statistic.

Convert molar mass for the supplied relation

Use urms=√(3RT/M), with R=8.314 J/(mol K) and M in kg/mol. A 30 g/mol gas requires M=.030 kg/mol. At 300 K, urms≈499.42 m/s. Substituting30 without converting grams to kilograms gives a dimensional and numerical error, not a different physical prediction.

Compare equal-temperature gases

Mean translational energy per mole is 3RT/2, independent of molar mass in this ideal model. At the same temperature, heavier particles therefore have a lower characteristic speed. Doubling molar mass divides urms by√2. Increasing temperature by a factor of four doubles urms, not quadruples it.

Bound an effusion inference

For equal-temperature gases compared at equal pressure through equivalent sufficiently small apertures in the molecular-flow regime, the elementary rate ratio scales as the inverse square root of molar mass . A 40 g/mol gas has rate1/√2 relative to a 20 g/mol reference. The aperture and surrounding conditions are part of the assumption, not optional details.

Do not confuse macroscopic processes

A large gas jet, pressure-driven pipe flow or diffusion through another dense gas can depend on additional collision and transport mechanisms. They need not follow the simple effusion ratio . A mass inferred from such a ratio is conditional on its regime and calibration. This lesson provides only mathematical comparisons and authorizes no gas release or aperture experiment. Retain the specified temperature, pressure comparison and model boundary with every ratio .

Sources and evidence boundary

Conceptual sources checked 30 October 2026: Effusion and diffusion, Kinetic-molecular theory. All prose, cases, code and diagrams are original. The supplied models are not measured structures, a performed laboratory investigation or certification of independent mastery. No chemical handling, heating, pressure vessel or cryogenic experiment is requested. Retain predictions, contrasting evidence and a changed-case explanation.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why cannot this effusion relation be applied automatically to an open pipe or every diffusion process?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

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Previous: Keep wet totals separate from dry-gas composition Next: Interpret nonideal gas evidence without a single-cause shortcut

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