The lightest element that is a solid at room temperature, lithium, absorbs hydrogen to form $\mathrm { LiH }$. Compare the energy density of LiH (i.e., energy per $\mathrm { kg }$ ) to the energy density of gasoline.

Question

Quizplus · Accepted Answer

The Answer is

ext { The atomic mass of } \mathrm { Li } ext { is } 7 \mathrm { u } ext {, so } \mathrm { LiH } ext { has a hydrogen content of }

100 imes ( 1 \mathrm { u } ) / ( 7 \mathrm { u } + 1 \mathrm { u } ) = 12.5 \%

Therefore

1 \mathrm {~kg}

of

\mathrm { LiH }

contains

( 1 \mathrm {~kg} ) imes ( 0.125 ) = 0.125 \mathrm {~kg} ext { hydrogen }

The energy content of hydrogen is

142 \mathrm { MJ } / \mathrm { kg }

so the energy density of

\mathrm { LiH }

is

( 0.125 \mathrm {~kg} / \mathrm { kg } ) imes ( 142 \mathrm { MJ } / \mathrm { kg } ) = 17.75 \mathrm { MJ } / \mathrm { kg }

The energy content of gasoline is

34.8 \mathrm { MJ } / \mathrm { L }

and its density is about

0.72 \mathrm {~kg} / \mathrm { L }

so the energy density is

( 34.8 \mathrm { MJ } / \mathrm { L } / ( 0.72 \mathrm {~kg} / \mathrm { L } ) = 48.3 \mathrm { MJ } / \mathrm { kg }

The relative energy density of

\mathrm { LiH }

compared to gasoline is

100 imes ( 17.75 \mathrm { MJ } / \mathrm { kg } ) / ( 48.3 \mathrm { MJ } / \mathrm { kg } ) = 37 \%

The Lightest Element That Is a Solid at Room Temperature LiH\mathrm { LiH }LiH

The Lightest Element That Is a Solid at Room Temperature $\mathrm { LiH }$