Answer
$10.9g\space CH_4N_2O$
Work Step by Step
We can find the required mass as follows:
$n_{solv}=n_{sol}-n_{solute}$
$n_{solv}=1.0000mol-0.0770mol=0.9230mol$
We calculate the mass of the solute and solvent
$m_{solute}=\frac{0.0770mol\space CH_4N_2O(60.0551g\space CH_4N_2O)}{1mol\space CH_4N_2O}=4.6242g\space CH_4N_2O$
and $m_{solv}=\frac{(0.9230mol\space H_2O)(18.0152g\space H_2O)}{1mol\space H_2O}=16.628g\space H_2O$
$m_{soln}=4.6242g+16.628g=21.2522g$
Now the mass of urea is
$\frac{(50.0g\space soln)(4.6242g\space CH_4N_2O)}{21.2522g\space soln}=10.9g\space CH_4N_2O$
