Answer
$V(CH_{3}CH_{2}OH) = 1.231l$
Work Step by Step
$N(ethanol) = N(water) = n(water) \times N_{A} = \frac{m(H_{2}O)}{M(H_{2}O)} \times N_{A} = \frac{\rho (H_{2}O)\times V(H_{2}O)}{M(H_{2}O)} \times N_{A}$
Additionally,
$N(ethanol) = \frac{\rho (CH_{3}CH_{2}OH)\times V(CH_{3}CH_{2}OH)}{M(CH_{3}CH_{2}OH)} \times N_{A}$
Hence,
$V(CH_{3}CH_{2}OH) = \frac{\rho (H_{2}O)\times V(H_{2}O)\times M(CH_{3}CH_{2}OH)}{\rho (CH_{3}CH_{2}OH)\times M(H_{2}O)}=\frac{1\frac{g}{ml}\times 380ml\times 46\frac{g}{mol}}{0.789\frac{g}{ml}\times 18\frac{g}{mol}}=1230.8ml\approx 1.231l$
