For an ideal gas equation PV= nRT, the dimensions of Real Gas Constant R are:
Correct answer: A. [M1 L2 T-2 K-1]
- A. [M1 L2 T-2 K-1]
- B. [M1 L-3 T-1 K-1]
- C. [M1 L-2 T-1 K-1]
- D. [M1 L-3 T-2 K-1]
Explanation
The ideal gas equation is:PV=nRTWhere:P is pressure with dimensions [ML−1T−2]V is volume with dimensions [L³][n is the number of moles (dimensionless),R is the gas constant (which we are solving for),T is temperature with dimensions [K]We rearrange the ideal gas equation to solve for R:R=PV/nTR Now, substituting the dimensions:P has dimensions of [ML⁻¹T⁻²]V has dimensions of [L³]T has dimensions of [K].So the dimensions of r are:RR=[ML−1T−2]⋅[L³] /K]=[M L2T−2K−1] Thus, the correct answer is [M1 L2 T-2 K-1], which corresponds to Option A.
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