Answer
$10^{53}kg$.
Work Step by Step
The radius of the universe is estimated as the speed of light multiplied by the age of the universe.
$$r=(3.00\times10^8m/s)(13.8\times10^9y)(\frac{3.156\times10^7s}{y})=1.23\times10^{26}m$$
Use this to estimate the volume of the universe.
$$V=\frac{4}{3}\pi r^3=7.81\times10^{78}m^3$$
Take the product of the critical density and the volume to estimate the mass of the universe.
$$M=\rho V=(10^{-26}\frac{kg}{m^3})(7.81\times10^{78}m^3)\approx10^{53}kg$$
