Final answer:
It takes about 4 to 5 half-lives to achieve a steady-state plasma concentration with a first-order elimination rate constant of a drug. Without half-life data, we cannot determine the exact time to reach a steady state, but generally, it's between 3 to 7 half-lives.
Step-by-step explanation:
The time it takes to achieve a steady-state plasma drug concentration with a first-order elimination rate constant, which is 0.23 L/hour, is typically around 4 to 5 half-lives of the drug. In general, the steady-state concentration is reached after approximately 5 half-lives, so if the elimination rate constant is 0.23 L/hour, it would take 5 times longer than the half-life period to reach a steady-state concentration. Since the half-life information is not provided, a precise time cannot be accurately determined based on the rate constant alone. However, a general estimation for first-order kinetics would suggest that steady-state would likely be reached somewhere between 3 to 7 times the half-life, depending on the particular drug's pharmacokinetic properties.