Laws passed in some states define a drunk driver as one who...

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?

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?

Key Concepts

Redox Titration

Redox titration is an analytical technique used to determine the concentration of an analyte by means of an oxidation-reduction reaction. In this method, a reagent with a known concentration (titrant) is gradually added to a solution until the reaction reaches its end point, which is often indicated by a color change or other detectable signal. This approach is widely used to quantify substances that undergo redox reactions, such as alcohols being oxidized by dichromate ions.

Reaction Stoichiometry

Reaction stoichiometry involves using a balanced chemical equation to relate the amounts (in moles) of reactants and products. It allows for the calculation of the quantity of an analyte based on the known amount of titrant that reacts with it. Balancing the chemical reaction is a critical step to ensure that the mole ratios between the oxidizing agent (dichromate) and the reducing agent (ethanol) are correctly applied in subsequent calculations.

Molarity and Volume Calculations

Molarity, defined as the number of moles of solute per liter of solution, is a fundamental concept in quantitative chemical analysis. By multiplying the molarity of the titrant by its volume, one can determine the number of moles of titrant used in the titration. This value, when combined with stoichiometric relationships from the balanced equation, allows for the determination of the moles of the analyte present in the sample.

Percent by Mass Calculation

Percent by mass is a method to express the concentration of a component in a mixture by comparing its mass to the total mass of the mixture, multiplied by 100. In the context of the problem, after calculating the moles (and then the mass) of ethanol in the blood sample, this mass is used to compute the percentage of alcohol by mass. This calculation is critical to determine compliance with legal limits, such as the 0.10% threshold.

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