Final answer:
For a 10 kg canine, a small rebreathing bag of 0.5 liter (500 ml) should be selected, as it fits the general rule of 10 ml/kg for the patient's body weight.
Step-by-step explanation:
To determine the correct size rebreathing bag for a 10 kg canine, it is essential to use a size that corresponds to the patient's tidal volume. The general rule of thumb for selecting a rebreathing bag is to use approximately 10 ml/kg of the patient's body weight. For a 10 kg canine, you would need a 100 ml bag. However, traditional rebreathing bag sizes are 0.5 liter (500 ml), 1 liter (1000 ml), 2 liters (2000 ml), and 3 liters (3000 ml). Therefore, the closest size available for a 10 kg dog would be the small size, which is 0.5 liter (500 ml). This allows enough volume for the dog to comfortably breathe without having an excessively large bag that could hamper the effectiveness of the anesthesia machine.