Question

The value of the gas constant $R$ in $\text{J K}^{-1}\text{ mol}^{-1}$ is

• A. 8.314
• B. 0.0821
• C. 1.987
• D. 83.14

Hint:

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.

Answer 1

The Correct Option is A

Step 1: Know the gas constant.
The gas constant $R$ appears in the ideal gas law $PV = nRT$. Its number changes with the units we pick, so we must match the right value to the right units.
Step 2: Read the units asked.
The question wants $R$ in joule per kelvin per mole, that is $\text{J K}^{-1}\text{ mol}^{-1}$. These are SI units.
Step 3: Recall the SI value.
In SI units the value of the gas constant is\[ R = 8.314\ \text{J K}^{-1}\text{ mol}^{-1} \]This is the standard number used in most chemistry work.
Step 4: Match the other values.
The value 0.0821 belongs to litre atmosphere per kelvin per mole. The value 1.987 belongs to calories per kelvin per mole. These use different units.
Step 5: Rule out 83.14.
The value 83.14 belongs to units like litre kilopascal or millilitre bar, again not joules. So it does not fit.
Step 6: Final choice.
For joule units the correct value is 8.314.\[ \boxed{8.314\ \text{J K}^{-1}\text{ mol}^{-1}} \]