The concentration of ethanol in the solution called 86-proof vodka is 6.5 M. If the density of the solution is $0.95\mathrm{g}{\mathrm{cm}}^{-3}$ , the amount fraction of ethanol in vodka is 

For 1 L of vodka, we have $n_2=6.5\mathrm{mol}$ and $V=1000{\mathrm{cm}}^3$

Mass of solution, $m=V\rho =\left(1000{\mathrm{cm}}^3\right)\left(0.95\mathrm{g}{\mathrm{cm}}^{-3}\right)=950\mathrm{g}$

Mass of ethanol, $m_2=n_2{M}_2=\left(6.5\mathrm{mol}\right)\left(46\mathrm{g}{\mathrm{mol}}^{-1}\right)=299\mathrm{g}$

Mass of water $m_1=m-m_2=950\mathrm{g}-299\mathrm{g}=651\mathrm{g}$

Amount of water, $n_1=\frac{m_1}{M_1}=\frac{651\mathrm{g}}{18\mathrm{g}{\mathrm{mol}}^{-1}}=36.167\mathrm{mol}$

Amount fraction of ethanol, $x_2=\frac{n_2}{n_1+n_2}=\frac{6.5}{(36.167+6.5)}=0.152$.