Thank you for your question! If the new replacement motor has 2 capacitor wires and you are using a dual capacitor, you will only be using one of the wires. The two capacitor wires should be brown in color and one of them will have a white stripe on it - You will need to connect the solid brown wire to the capacitor and cap the brown wire with the white stripe.
Click the link below to see a short YouTube clip on this topic :
https://www.youtube.com/watch?v=Py28TXEz55g Let us know if you have any other questions!