Final answer:
Kathy's blood alcohol content (BAC) can be calculated by considering the amount of alcohol consumed, the concentration of alcohol in the drinks, and the rate at which alcohol is metabolized by the body. Convert the volume of the drinks from deciliters to liters and calculate the amount of alcohol consumed. Convert the amount of alcohol consumed from liters to millimoles and calculate the BAC using the formula BAC = (amount of alcohol / body water) - (metabolism rate x time). Kathy's BAC is approximately 0.05 mmol/L, which is below the legal limit.
Step-by-step explanation:
To calculate Kathy's blood alcohol content (BAC), we need to consider the amount of alcohol consumed, the concentration of alcohol in the drinks, and the rate at which alcohol is metabolized by the body. First, we need to convert the volume of the drinks from deciliters (dl) to liters (L), so 7 dl = 0.7 L. Then, we can calculate the amount of alcohol consumed by multiplying the volume of each drink by the alcohol concentration, so 0.7 L x 0.10 = 0.07 L of alcohol per drink.
Next, we need to determine the total amount of alcohol consumed, so 0.07 L/drink x 5 drinks = 0.35 L of alcohol consumed. To calculate the BAC, we need to consider the rate at which alcohol is metabolized. The average rate of alcohol metabolism is 3.3 mmol/L (15 mg/dL) per hour. Since concentration is given in mmol/L, we need to convert the amount of alcohol consumed from liters to mmol, so 0.35 L x 1000 mL/L x 1 g/1000 mL x 1 mol/46.07 g = 7.61 mmol.
Finally, we can calculate the BAC using the formula BAC = (amount of alcohol / body water) - (metabolism rate x time). Since Kathy is a female, we need to consider that women metabolize alcohol a little more slowly than men. Assuming a body water percentage of 60% for Kathy, the BAC can be calculated as (7.61 mmol / (0.6 x 70 kg)) - (3.3 mmol/L/hr x (4 hr + 4 hr)). The final BAC for Kathy is approximately 0.05 mmol/L, which is below the legal limit of 5.4-17.4 mmol/L.