The chemical effect of the muon transfer process from muonic hydrogen atom was examined for benzene and cyclohexane under low pressure gaseous conditions. The muon transfer rates were investigated by measuring the resulting muonic X-rays resulting from muon irradiation of hydrogen and neon gas mixtures. The muon transfer rates to benzene and cyclohexane carbon atoms were very similar in the gaseous state. The results differed from previous results obtained for muon and pion transfer rates to benzene and cyclohexane under high density liquid conditions. It was concluded that the difference originated from the atomic muon state of the muonic hydrogen atoms with a large radius.