In a lithium-ion cell the anode on discharge is lithiated graphite, LiC6, which releases Li+ and one electron per formula unit: LiC6 -> 6C + Li+ + e-. The theoretical specific capacity of the anode, in mAh per gram of LiC6, is closest to (Li = 7, C = 12, F = 96500 C mol^-1, 1 mAh = 3.6 C)

JEE Advanced levelSingle correct optionDifficulty 3 of 3ec157

In a lithium-ion cell the anode on discharge is lithiated graphite, $LiC X_{6}$ , which releases $Li X^{+}$ and one electron per formula unit: $LiC X_{6} 6 C + Li X^{+} + e X^{-}$ . The theoretical specific capacity of the anode, in $mAh$ per gram of $LiC X_{6}$ , is closest to (Li = 7, C = 12, $F = 96500 C mo l^{- 1}$ , $1 mAh = 3.6 C$ )

Molar mass of

LiC X_{6} = 7 + 72 = 79 g mo l^{- 1}

and one mole gives one Faraday. Charge per gram

= 96500/79 = 1221.5 C g^{- 1}

. Dividing by

3.6 C mA h^{- 1}

gives

339 mAh g^{- 1}

. Option (C) is the value per gram of carbon (

72 g

) only, and (D) wrongly assumes two electrons.