Intelligent reflecting surface (IRS) is envisioned as a key technology for the next-generation wireless communication systems that enhances coverage and performance by reconfiguring the wireless propagation environment. In this letter, the performance of an IRS-aided wireless-powered internet-of-things (IoT) network over Rayleigh fading channels is investigated that consists a power station, an IRS, an access point, and IoT devices. In particular, the impact of transceiver hardware impairments (HIs) is considered. An IoT node selection strategy is adopted that maximizes the harvested energy and improves the system performance. The closed-form expressions of outage probability (OP), ergodic capacity, and symbol error rate are derived by using the Gaussian Chebyshev Quadrature method. Further, the closed-form expressions of the asymptotic OP and asymptotic ergodic capacity are derived and the diversity order of the considered network is obtained. The impact of HIs, overall system ceiling effect, IoT devices, reflecting elements, and various system parameters on the considered network are highlighted. Finally, the Monte-Carlo simulations are performed to verify the derived closed-form expressions.