Universal gas constant (R_u): Is the value of the universal gas constant the same for all gases?

Introduction / Context:In the ideal-gas equation pV = nR_uT, the constant R_u is universal because it is based on Avogadro’s number and Boltzmann’s constant. Distinguishing between the universal constant and the specific gas constant prevents common mistakes when switching between per-mole and per-mass formulations.

Given Data / Assumptions:

• Ideal-gas behavior for equation-of-state context.
• R_u is defined per mole of substance.
• Specific gas constant R is defined per unit mass, R = R_u/M.

Concept / Approach:The universal gas constant has the same numerical value for all gases (e.g., 8.314 kJ/(kmol·K) or 8.314 J/(mol·K)), because a mole always contains the same number of molecules (Avogadro’s number). In contrast, the mass-based specific gas constant R varies with molecular mass M for each gas (R = R_u / M).

Step-by-Step Solution:

Verification / Alternative check:Using SI units, R_u ≈ 8.314462618 J/(mol·K). Converting to per-kilomole gives 8.314 kJ/(kmol·K), a constant in property tables for all gases.

Why Other Options Are Wrong:

• No/Only at low pressure/Only for monatomic: These confuse universality with ideality. While ideal behavior is approximate, R_u’s value as a constant of nature does not change across gases.

Common Pitfalls:Mixing up R_u and the gas-specific R; forgetting unit consistency when switching between molar and mass bases.

Final Answer:Yes