In the equation $P V = n R T$ which one cannot be numerically equal to $R$ .

8.31 \times 10^{7} e r g K^{- 1} {m o l}^{- 1}

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8.31 \times 10^{7} d y n e s C m K^{- 1} {m o l}^{- 1}

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8.31 J K^{- 1} {m o l}^{- 1}

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8.31 L a t m K^{- 1} {m o l}^{- 1}

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Solution

The correct option is D $8.31 L a t m K^{- 1} {m o l}^{- 1}$
Answer $D .$
In S.I unit, $R = 8.314 J / m o l / K e l v i n$
$1 J = 10^{7} e r g s$
$∴ R = 8.314 \times 10^{7} e r g s / m o l / k e l v i n$
And $R = 0.0821 L a t m / m o l / K$
$1 c a l = 4.18 J, R = 1.987 C a l / m o l / K . = 8.31 \times 10^{7} d y n e s c m / m o l / K$

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