Volume expansivity of an ideal solution

[gfd43tg]

Hello,

I'm not sure if I'm approaching this the right way, but essentially I used the definition of volume expansivity and a result for the molar volume of an ideal solution to get my expression, so my result is that the claim is wrong. Am I going about this one correctly?

 

[gfd43tg]

Attempt

 

[Chestermiller]

It doesn't look like you did the math correctly.

V=n_1\overline{V_1}+n_2\overline{V_2}

\frac{dV}{dT}=n_1\frac{d\overline{V_1}}{dT}+n_2\frac{\overline{dV_2}}{dT}
\frac{1}{V}\frac{dV}{dT}=\frac{(n_1\frac{d\overline{V_1}}{dT}+n_2\frac{\overline{dV_2}}{dT})}{n_1\overline{V_1}+n_2\overline{V_2}}

β=\frac{(n_1\overline{V_1}β_1+n_2\overline{V_2}β_2)}{n_1\overline{V_1}+n_2\overline{V_2}}