Two solution of `H_(2)SO_(4)` of molarities x and y are mixed in the ratio of `V_(1) mL : V_(2) mL` to form a solution of molarity `M_(1)`. If they are mixed in the ratio of `V_(2) mL : V_(1) mL`, they form a solution of molarity `M_(2)`. Given `V_(1)//V_(2) = (x)/(y) gt 1 and (M_(1))/(M_(2)) = (5)/(4)`, then `x : y` is

Options

A. `2 : 1`
B. `4 : 1`
C. `1 : 2`
D. `3 : 1`

Answer

A

Explanation

Molarity of the mixture can be calculated as:
`M_(1) V_(1) + M_(2) V_(2) = M_(R) (V_(1) + V_(2))`
Where, `M_(R) =` resultant solution
`V_(1) xx x + V_(2) xx y = M_(1) (V_(1) + V_(2))` .....(i)
`V_(2) xx x + V_(1) xx y = M_(2) (V_(1) + V_(2))` .....(ii)
Dividing e.q. (i) by eq (ii), we get
`(V_(1)x + V_(2)y)/(V_(2) x + V_(1) y) = (M_(1))/(M_(2))`
Substituting `(M_(1))/(M_(2)) = (5)/(4) " and " (V_(1))/(V_(2)) = (x)/(y)` we can calculate `x : y`