The freezing point of pure nitrobenzene is 278.8 K. When 2.5 g of unknown substance is dissolved in 100 g of nitrobenzene, the freezing point of solution is found to be 276.8 K, If the freezing point depression constant of nitrobenzene is 8.0 K kg/mol, what is the molar mass of unknown substance?

Options

A. `200 g mol^(-1)`
B. `100 g mol^(-1)`
C. `55 g mol^(-1)`
D. `129 g mol^(-1)`

Answer

B

Explanation

`T_f^@ = 278.8 K, T_f = 276.8 K`
`DeltaT_f=278.8 - 276. 8=2 K,K_f=8 K kg mol^(-1)`
`m = ("Mole")/(M_A)xx1000 implies m=(w_B/m_B)/M_A xx1000 = (2.5/m_B)/100 xx 1000 = 25/m_B`
`DeltaT_f = K_fxxm`
`2=8xx 25/m_B implies m_B = (8xx25)/2 =100 g mol^(-1)`