`A_(m)^(@)H_(2)O` is equal to:

Options

A. `Lambda_(m(HCl))^(@)+Lambda_(m(NaOH))^(@)-Lambda_(m(NaCl))^(@)`
B. `Lambda_(m(HNO_(3))^(@)+Lambda_(m(NaNO_(3)))^(@))-Lambda_(m(NaOH))^(@)`
C. `Lambda_(m(HNO_(3)))^(@)+Lambda_(m(NaOH))^(@)-Lambda_(m(NaNO_(3)))^(@)`
D. `Lambda_(m(NH_(4)OH))^(@)+Lambda_(m(HCl))^(@)-Lambda_(m(NH_(4)Cl))^(@)`

Explanation

(a) `Lambda_(m(HCl))^(@)=Lambda_(m(H^(+)))^(@)+Lambda_(m(Cl^(-)))^(@)`
`Lambda_(m(NaOH))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(CH^(-)))^(@)`
`Lambda_(m(NaCl))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(Cl^(-)))^(@)`
`Lambda_(m(NaCl))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(NaCl))^(@)=Lambda_(m(H^(+)))^(@)+Lambda_(m(HO^(-)))^(@)`
`=Lambda_(m(H_(2)O))^(@)`
(d) `Lambda_(m(NH_(4)OH))^(@)=Lambda_(m(NH_(4)^(+)))^(@)+Lambda_(m(OH^(-)))^(@)`
`Lambda_(m(HCl))^(@)=Lambda_(m(H^(+)))^(@)+Lambda_(m(Cl^(-)))^(@)`
`Lambda_(m(NH_(4)Cl))^(@)=Lambda_(m(NH_(4)^(+)))^(@)+Lambda_(m(Cl^(-)))^(@)`
- - -
`Lambda_(m(NH_(4)CH))^(@)+Lambda_(m(HCl))^(@)-Lambda_(m(NH_(4)Cl))^(@)`
`Lambda_(m(H^(+)))^(@)+Lambda_(m(OH(-)))^(@)=Lambda_(m(H_(2)O))^(@)`
This type of decompostion is not possible due to weak basic strength of `NH_(4)OH`. this line will be placed above.
(b) `Lambda_(m(HNO_(3)))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(NO_(3)^(-)))^(@)`
`Lambda_(m(NaOH))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(OH^(-)))^(@)`
`Lambda_(m(NaOH))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(OH^(-)))^(@)`
- - -
`Lambda_(m(HNO_(3)))^(@)+Lambda_(m(NaNO_(3)))^(@)-Lambda_(m(NaOH))^(@)`
`=Lambda_(m(H^(+)))^(@)+2Lambda_(m(NO_(3)^(-))) -Lambda_(m(CH^(-)))^(@)`
(b) is correct
(c) `Lambda_(m(HNO_(3)))^(@)=Lambda_(m(H^(+)))^(@)+Lambda_(m(NO_(3)^(-)))^(@)`
`Lambda_(m(NaOH))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(OH^(-)))^(@)`
`Lambda_(m(NaNO_(3)))^(@)=Lambda_(m(Na^(+)))^(@)+Lambda_(m(NO_(3)^(-)))^(@)`
- - -
`Lambda_(m(HNO_(3)))^(@)+Lambda_(m(NaOH))^(@)-Lambda_(m(NaNO_(3)))^(@)`
`=Lambda_(m(H^(+)))^(@)+Lambda_(m(OH^(-)))^(@)=Lambda_(m(H_(2)O))^(@)`
Hence, Option a and c are the correct choices.