The average adult male has a total blood volume of 5.0 L. After drinking a few beers, he has a BAC of 0.10 (see Exercise 4.65). What mass of alcohol is circulating in his blood?

Verified step by step guidance

Step 1: Understand that BAC (Blood Alcohol Concentration) is expressed as a percentage, which represents the mass of alcohol per volume of blood. A BAC of 0.10 means there are 0.10 grams of alcohol per 100 mL of blood.

Step 2: Convert the total blood volume from liters to milliliters. Since 1 liter is equal to 1000 milliliters, multiply the blood volume in liters by 1000 to get the volume in milliliters.

Step 3: Calculate the total mass of alcohol in the blood by using the BAC value. Multiply the BAC (in grams per 100 mL) by the total blood volume in milliliters, and then divide by 100 to account for the BAC being per 100 mL.

Step 4: Set up the equation for the mass of alcohol: \( \text{Mass of alcohol} = \left( \frac{\text{BAC}}{100} \right) \times \text{Total blood volume in mL} \).

Step 5: Solve the equation to find the mass of alcohol circulating in the blood.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Blood Alcohol Concentration (BAC)

Blood Alcohol Concentration (BAC) is a measure of the amount of alcohol present in a person's bloodstream, expressed as a percentage. A BAC of 0.10 means that there are 0.10 grams of alcohol per 100 milliliters of blood. Understanding BAC is crucial for determining the effects of alcohol on the body and for calculating the total mass of alcohol in the blood based on total blood volume.

Total Blood Volume

Total blood volume refers to the total amount of blood circulating in the body, which varies by individual but averages around 5.0 liters for adult males. This volume is essential for calculating the total mass of substances, such as alcohol, in the bloodstream. Knowing the total blood volume allows for the conversion of BAC into a mass of alcohol present in the body.

Mass Calculation

Mass calculation involves determining the total mass of a substance based on its concentration and the volume of the solution. In this context, to find the mass of alcohol in the blood, one can use the formula: mass = BAC × total blood volume. This calculation is fundamental in quantifying the amount of alcohol circulating in the bloodstream after consumption.

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