Question

the accepted value of r is 8.314 j mol⁻¹ k⁻¹. which of the following units are exactly equivalent to this numerical value (magnitude) of r when its expressed in those units? select as many answers as appropriate however marks will be deducted for incorrect guesses. select one or more: kpa m³ mol⁻¹ k⁻¹ × kpa l mol⁻¹ k⁻¹ pa l mol⁻¹ k⁻¹ × pa m³ mol⁻¹ k⁻¹ bar l mol⁻¹ k⁻¹

Explanation:

Step1: Recall the relationship between joules and pressure - volume

$1\ J = 1\ Pa\cdot m^{3}$ and $1\ kPa= 1000\ Pa$, $1\ m^{3}=1000\ L$, $1\ bar = 100\ kPa$.

Step2: Analyze each option

• For $kPa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}$: Since $1\ kPa = 1000\ Pa$ and $1\ m^{3}=1000\ L$, $kPa\cdot m^{3}=1000\ Pa\times1000\ L = 10^{6}\ Pa\cdot L$. And $8.314\ J\cdot mol^{-1}\cdot K^{-1}=8.314\ Pa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}=8.314\ kPa\cdot L\cdot mol^{-1}\cdot K^{-1}$, so $kPa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}$ is not equivalent.
• For $kPa\cdot L\cdot mol^{-1}\cdot K^{-1}$: We know that $8.314\ J\cdot mol^{-1}\cdot K^{-1}=8.314\ Pa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}$, and since $1\ kPa = 1000\ Pa$ and $1\ m^{3}=1000\ L$, $8.314\ Pa\cdot m^{3}=8.314\ kPa\cdot L$, so $8.314\ J\cdot mol^{-1}\cdot K^{-1}=8.314\ kPa\cdot L\cdot mol^{-1}\cdot K^{-1}$, this option is correct.
• For $Pa\cdot L\cdot mol^{-1}\cdot K^{-1}$: Since $1\ m^{3}=1000\ L$, $8.314\ Pa\cdot m^{3}=8314\ Pa\cdot L$, so $Pa\cdot L\cdot mol^{-1}\cdot K^{-1}$ is not equivalent.
• For $Pa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}$: Since $1\ J = 1\ Pa\cdot m^{3}$, $8.314\ J\cdot mol^{-1}\cdot K^{-1}=8.314\ Pa\cdot m^{3}\cdot mol^{-1}\cdot K^{-1}$, this option is correct.
• For $bar\cdot L\cdot mol^{-1}\cdot K^{-1}$: Since $1\ bar = 100\ kPa$, $8.314\ kPa\cdot L\cdot mol^{-1}\cdot K^{-1}=0.08314\ bar\cdot L\cdot mol^{-1}\cdot K^{-1}$, so this option is not correct.

Answer:

kPa L mol⁻¹ K⁻¹, Pa m³ mol⁻¹ K⁻¹