  We use Voiculescu's concept of free probability to construct a completely
isomorphic embedding of the operator space OH in the predual of a von Neumann
algebra. We analyze the properties of this embedding and determine the operator
space projection constant of OH_n: It is of the order (n/1+ln n)^{1/2} The
lower estimate is a recent result of Pisier and Shlyakhtenko that improves an
estimate of order 1/(1+ln n) of the author. The additional factor 1/(1+ln
n)^{1/2} indicates that the operator space OH_n behaves differently than its
classical counterpart l_2^n. We give an application of this formula to positive
sesquilinear forms on B(H). This leads to logarithmic characterization of
C*-algebras with the weak expectation property introduced by Lance.
