Chemistry Gases SZABMU 2024
PMDC Verified Question 6 of 65
The S.I unit of R in general gas equation is:
A
\( 8.3143 \text{ NmK}^{-1} \text{mol}^{-1} \)
B
\( 0.0821 \text{ dm}^3 \text{atom mol}^{-1} \text{K}^{-1} \)
C
\( 8.3143 \text{ J mol}^{-1} \text{ K}^{-1} \)
D
\( 0.0821 \text{ dm}^3 \text{ torr K}^{-1} \text{mol}^{-1} \)
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: \( 8.3143 \text{ NmK}^{-1} \text{mol}^{-1} \)
Concept:

The universal gas constant (R) changes its numerical value and units depending on the units used for pressure and volume in the ideal gas equation (\( PV = nRT \)).

Solution:

  • In the International System of Units (SI), Pressure is measured in Pascals (\( \text{N/m}^2 \)) and Volume in cubic meters (\( \text{m}^3 \)).


  • The product of \( P \times V \) yields \( \text{N/m}^2 \times \text{m}^3 = \text{N} \cdot \text{m} \) (Newton-meters).


  • A Newton-meter (\( \text{Nm} \)) is the strict fundamental definition of a Joule (J).


  • Therefore, the standard SI value of R is \( 8.3143 \text{ J K}^{-1} \text{mol}^{-1} \), which is identically equal to \( 8.3143 \text{ Nm K}^{-1} \text{mol}^{-1} \).


  • Note: While Option C is also functionally correct, Option A is explicitly highlighted in the source's answer key to emphasize the fundamental dimensional units of Work (Force × Distance).


Why other options are incorrect:

  • Options B & D: These use non-SI units for volume (\( \text{dm}^3 \)) and pressure (torr), which correspond to the 0.0821 numerical value but are definitively not SI units.

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