You are given a `2.18g` sample containing a mixture of XO and `X_2O_3`. It takes 0.015 " mol of "`K_2Cr_2O_7` to oxdise the sample completely to form `XO_4^(ɵ)` and `Cr^(3+)`. If 0.0187 " mol of "`XO_4^(ɵ)` is formed, what is the atomic mass of X?

Explanation

Let a " mol of "XO and b " mol of "`X_2O_3` react.
`6XO+5Cr_2O_7^(2-)+34H^(o+)to6XO_4^(ɵ)+10Cr^(3+)+17H_2O`
6 mnol of `XO=5 " mol of "Cr_2O_7^(2-)=6 " mol of "XO_4^(ɵ)`
a " mol of "`XO=(5)/(6)a " mol of "Cr_2O_7^(2-)`
`=a " mol of "XO_4^(ɵ)`
`3X_2O_3+4Cr_2O_7^(2-)+26H^(o+)to6XO_4^(ɵ)+8Cr^(3+)+13H_2O`
`3 " mol of "X_2O_3=4" mol of "Cr_2O_7^(2-)=6 " mol of "XO_4^(ɵ)`
b " mol of "`X_2O_3=(4)/(3)b " mol of "Cr_2O_7^(2-)`
`therefore(5a)/(6)+(4b)/(3)=0.015`
`a+2b=0.0187`
`thereforea=0.0152,b=0.00175`
Let the atomic weight of X be `=m`
Molecular weight of `XO=m+16`
Molecular weight of `X_2O_3=2m+48`
Weight of `XO=0.0152(m+16)`
Weight of `X_2O_3=0.00175(2m+48)`
Total weight`=2.18`
`therefore0.0152(m+16)+0.00175(2m+48)=2.18`
`thereforem=99.08`
`therefore` Atomic weight `=99.08`