The concentration of alcohol 1CH3CH2OH2 in blood, called the 'blood alcohol concentration' or BAC, is given in units of grams of alcohol per 100 mL of blood. The legal definition of intoxication, in many states of the United States, is that the BAC is 0.08 or higher. What is the concentration of alcohol, in terms of molarity, in blood if the BAC is 0.08?

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Identify the given BAC as 0.08 grams of alcohol per 100 mL of blood.

Convert the BAC from grams per 100 mL to grams per liter by multiplying by 10, since 1 L = 1000 mL.

Determine the molar mass of ethanol (CH3CH2OH) by adding the atomic masses of its constituent atoms: C, H, and O.

Convert the mass of ethanol in grams to moles using the formula: \( \text{moles} = \frac{\text{mass in grams}}{\text{molar mass}} \).

Calculate the molarity by dividing the number of moles of ethanol by the volume of the solution in liters.

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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 in grams of alcohol per 100 mL of blood. A BAC of 0.08 means there are 0.08 grams of alcohol in every 100 mL of blood, which is a common legal threshold for intoxication in many jurisdictions.

Molarity

Molarity is a way to express the concentration of a solution, defined as the number of moles of solute per liter of solution. It is commonly used in chemistry to quantify the concentration of substances in a solution, allowing for easy calculations in chemical reactions and analyses.

Conversion from grams to moles

To convert grams of a substance to moles, one must use the molar mass of the substance, which is the mass of one mole of that substance in grams. For ethanol (C2H5OH), the molar mass is approximately 46.07 g/mol. This conversion is essential for calculating molarity from a given mass concentration.

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Mass and Moles Conversion

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Textbook Question

(a) How many grams of ethanol, CH3CH2OH, should you dissolve in water to make 1.00 L of vodka (which is an aqueous solution that is 6.86 M ethanol)? (b) Using the density of ethanol (0.789 g/mL), calculate the volume of ethanol you need to make 1.00 L of vodka.

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Textbook Question

A person suffering from hyponatremia has a sodium ion concentration in the blood of 0.118 M and a total blood volume of 4.6 L. What mass of sodium chloride would need to be added to the blood to bring the sodium ion concentration up to 0.138 M, assuming no change in blood volume?