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

Explanation

Given: The data are
`C ("graphite") + (1)/(2) O _(2)(g) to CO (g) " "","Delta 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 fraction of CO in the mixture, then the amount of `O _(2)` consumed 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`