[en] Microwave emission lines from eight linear molecules have reported in the direction of the carbon star, IRC+10216. We propose that the observed excitation of the rotational energy levels of these molecules is a result of absorption of infrared radiation into excited vibrational states and the subsequent decay back to the rotational levels of vibrational state. A model of the source is constructed in which the molecules are contained in a spherically symmetric envelope (having an r^-2 density dependence) around the central infrared source whose spectra and structure are known. The abundances of CS, SiS, SiO, and HC₃N are derived by fitting their observed lines to the prediction of the model. The molecular abundances yield an estimate for the total mass of the envelope of (2-35) times10^-3 M/sub sun/. Conditions which determine the shapes of emission lines from expanding clouds are discussed, including the geometrical effect of excitation by the anisotropic infrared radiation field, the effect of finite optical depth, and the effect of partial resolution of the cloud. Comparison of the extended molecular cloud with the smaller CO shell observed by Geballe et al. suggests that IRC + 10216 might have recently undergone more violent events than in previous eras