  We compute the scalar curvature of 7-dimensional ${G}_2$-manifolds admitting
a connection with totally skew-symmetric torsion. We prove the formula for the
general solution of the Killing spinor equation and express the Riemannian
scalar curvature of the solution in terms of the dilation function and the NS
3-form field. In dimension n=7 the dilation function involved in the second
fermionic string equation has an interpretation as a conformal change of the
underlying integrable ${G}_2$-structure into a cocalibrated one of pure type
$W_3$.
