If `Delta _(f) H ^(@) (CO,g) =- 110.5 kJ mol ^(-1)` and `Delta _(f) H ^(@) (CO _(2), g) =- 393. 5 kJ mol ^(-1)` the mass ofoxygen consumed in the reaction C (graphite) `+ O _(2) (g) to` mixture of `CO (g) + CO _(2) (g) ` for which `Delta H =- 313.8 kJ mol ^(-1)` will be about

Options

A. `24.0g`
B. `25.5g `
C. `27.5g `
D. `29.0 g`

Answer

C

Explanation

Given, The data are
`{:(C ("graphite") + (1)/(2) O _(2) (g) to CO (g) , :Delta_(f) H ^(@) =- 110. 5 kJ mol ^(-1)), (C ("graphite")+O _(2) (g) to CO _(2) (g), , Delta _(f) H ^(@) =- 393.5 kJ mol ^(-1)), (C ("graphite") + O _(2) (g) to "a mixture of CO (g) and " CO _(2) (g), , Delta _(r) H ^(@) =- 313.8 kJ mol ^(-1)):}`
If x is the amount function of CO in the mixture, then the amount of `O _(2)` conumed will be
`(x)/(2) + (1-x) = 1 - (x)/(2),` where x may be calculated from the expression `x (-110 . 5 kJ mol ^(-1))`
`+ (1- x) ( - 393.5 kJ mol ^(-1)) =- 313. 8 kJ mol ^(-1) ` which gives `x = 0.282.` Mass of `O _(2)` consumed
`= { (1- (0.282)/(2)) mol } (32 g mol ^(-1)) = 27.5 g`