Question:
The value of the gas constant $R$ in $\text{J K}^{-1}\text{ mol}^{-1}$ is}
The value of the gas constant $R$ in $\text{J K}^{-1}\text{ mol}^{-1}$ is}
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Remember to always check the units when dealing with physical constants like the gas constant \( R \). Different systems of units can lead to different numerical values for the same constant.
Updated On: May 31, 2026
- 8.314
- 0.0821
- 1.987
- 83.14
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The Correct Option is A
Solution and Explanation
Step 1: Concept
The gas constant \( R \) is a fundamental physical constant used in the ideal gas law, which relates pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and amount of substance (in moles, \( n \)) of an ideal gas. The equation for the ideal gas law is given by: \[PV = nRT\] The value of \( R \) in different units can vary depending on the chosen system of units.
Step 2: Meaning
In this context, we are asked to identify the correct value of the gas constant \( R \) when expressed in joules per kelvin per mole (J K\(^{-1}\) mol\(^{-1}\)).
Step 3: Analysis
To prove that option A is the correct answer, let's consider the units involved: Joule (J) is the unit of energy. Kelvin (K) is the unit of temperature. Mole (mol) is the unit of amount of substance. The gas constant \( R \) in these units should have dimensions that make sense for the equation \( PV = nRT \). The pressure \( P \) has units of Pascal (Pa), which can be expressed as J m\(^{-3}\). Since volume \( V \) is in cubic meters (m\(^3\)), and amount of substance \( n \) is in moles (mol), the equation balances if \( R \) is in J K\(^{-1}\) mol\(^{-1}\). The value 8.314 J K\(^{-1}\) mol\(^{-1}\) is a well-known and accepted standard value for the gas constant, used extensively in thermodynamics and chemistry. Option B (0.0821 L atm K\(^{-1}\) mol\(^{-1}\)) corresponds to another common unit of \( R \), where 1 liter-atmosphere (L atm) is approximately equal to 101.325 J. Option C (1.987 cal K\(^{-1}\) mol\(^{-1}\)) is in calories, and 1 calorie is approximately 4.184 joules. Option D (83.14 L atm K\(^{-1}\) mol\(^{-1}\)) again refers to the liter-atmosphere unit.
Step 4: Conclusion
Given that the correct units for \( R \) in this problem are J K\(^{-1}\) mol\(^{-1}\), and considering the standard value, option A is indeed the correct answer. Final Answer: (A)
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