Laws passed in some states define a drunk driver as one who drives with a blood alcohol level of \(0.10 \%\) by mass or higher. The level of alcohol can be determined by titrating blood plasma with potassium dichromate according to the unbalanced equation $$ \mathrm{H}^{+}(a q)+\mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q) \longrightarrow \mathrm{Cr}^{3+}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O} $$ Assuming that the only substance that reacts with dichromate in blood plasma is alcohol, is a person legally drunk if \(38.94 \mathrm{~mL}\) of \(0.0723 \mathrm{M}\) potassium dichromate is required to titrate a \(50.0\) -g sample of blood plasma?

Chemical titration is a laboratory technique used to determine the concentration of a solute in a solution by reacting it with a standard solution (titrant). In the context of blood alcohol level determination, a specific volume of blood plasma is reacted with a measured amount of potassium dichromate solution. The endpoint of this reaction is typically signified by a color change, indicating that a stoichiometrically equal amount of reactant and titrant have combined.

When performing a titration, the key steps include the preparation of standard solutions, the careful measurement of volumes, and the precise detection of the endpoint. It is a fundamental process in analytical chemistry for quantitative analysis, serving a variety of purposes from blood alcohol testing to the determination of water hardness.

Essential Variables in Titrations:

• Standard Solution: A solution of known concentration, used to determine the unknown concentration of another solution.
• Equivalence Point: The point in the titration where the amount of titrant is stoichiometrically equivalent to the quantity of substance in the sample.
• Indicator: A substance that changes color at (or near) the equivalence point, visually indicating the completion of the reaction.

Blood plasma analysis involves studying the liquid component of blood, which remains after the removal of blood cells, to determine the presence and concentrations of various substances, like glucose, hormones, or, in this case, alcohol. In forensic science and medical diagnostics, testing blood plasma is crucial for assessing blood alcohol levels and drug usage.

For blood alcohol analysis, the ethanol in the plasma reacts with a chemical titrant. The measurement of the volume of titrant required to complete the reaction provides information about the amount of ethanol present in the blood. This method is preferred for its reliability and accuracy compared to other methods like breath analyzers, as it directly measures the substance of interest in the body.

Importance of Blood Plasma Analysis:

• Medical Diagnosis: Helps in the detection of various medical conditions or toxic substances in the bloodstream.
• Legal Implications: Determines whether a person's blood alcohol content exceeds legal limits for safe operation of vehicles.
• Research: Assists in clinical research and the study of metabolic processes.

Stoichiometry is the aspect of chemistry that relates to the quantitative relationships between the substances as they participate in chemical reactions. It relies on the balanced chemical equation and the mole concept, allowing chemists to predict how much product will be formed from a given amount of reactant or how much reactant is needed to produce a desired amount of product.

When applying stoichiometry to chemical titrations, like in the blood plasma alcohol determination, it is crucial to use a correctly balanced chemical equation. From the balanced equation, a stoichiometric conversion factor is derived which is essential to relate moles of different substances involved in the reaction. For example, in the exercise above, 3 moles of alcohol (ethanol) react with 2 moles of potassium dichromate, which is the stoichiometric basis for calculating the moles and consequently, the mass of ethanol in the blood plasma.

Key Concepts in Stoichiometry:

• Molar Ratios: The ratios of moles of each substance involved in a chemical reaction derived from a balanced equation.
• The Mole: A fundamental unit in chemistry for expressing amounts of a chemical substance, defined as the number of atoms found in exactly 12 grams of carbon-12.
• Conversion Factors: Ratios derived from the coefficients of a balanced chemical equation used to convert between amounts of reactants and products.