Question

Alcohol levels in blood can be determined by a redox reaction with potassium dichromate according to the balanced equation \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{Cr}_{2} \mathrm{O}_{7}^{2-}(a q)+16 \mathrm{H}^{+}(a q)\) $$ 2 \mathrm{CO}_{2}(g)+4 \mathrm{Cr}^{3+}(a q)+11 \mathrm{H}_{2} \mathrm{O}(l) $$ What is the blood alcohol level in mass percent if \(8.76 \mathrm{~mL}\) of \(0.04988 \mathrm{M} \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) is required for complete reaction with a \(10.002 \mathrm{~g}\) sample of blood?

Short answer

The blood alcohol level is 0.1005% mass percent.

Step-by-step solution

Determine moles of Potassium Dichromate

To find the number of moles of potassium dichromate \(\text{K}_2\text{Cr}_2\text{O}_7\), use the formula: \[ \text{moles} = \text{volume (L) } \times \text{ molarity (M)} \].Given a volume of 8.76 mL, convert it to liters by dividing by 1000: \[ \text{Volume in liters} = \frac{8.76}{1000} = 0.00876 \text{ L} \].The molarity is 0.04988 M. Thus, the moles of \(\text{K}_2\text{Cr}_2\text{O}_7\) are: \[ 0.00876 \text{ L} \times 0.04988 \text{ M} = 0.000436 \text{ moles} \].

Determine moles of Ethanol

From the balanced equation, 2 moles of dichromate react with 1 mole of ethanol (C_2H_5OH). Calculate moles of ethanol: \[ \text{moles of ethanol} = \frac{0.000436}{2} = 0.000218 \text{ moles} \].

Calculate mass of Ethanol

Find the molar mass of ethanol, \( \text{C}_2\text{H}_5\text{OH} \):- Carbon (C): 2 x 12.01 g/mol- Hydrogen (H): 6 x 1.01 g/mol- Oxygen (O): 1 x 16.00 g/molTotal molar mass = 46.08 g/mol.Calculate the mass of ethanol: \[ 0.000218 \text{ moles} \times 46.08 \text{ g/mol} = 0.0100486 \text{ g} \].

Calculate Mass Percent of Ethanol in Blood

Use the mass percent formula: \[ \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \].Substitute the known quantities: \[ \frac{0.0100486}{10.002} \times 100 = 0.1005\% \].

Key concepts

Blood Alcohol Level

Blood alcohol level refers to the concentration of alcohol in a person's bloodstream. It's typically measured as a percentage, representing the ratio of ethanol, the active ingredient in alcoholic beverages, to a specific volume of blood. Understanding how blood alcohol levels work is crucial in fields like medicine and law enforcement, as it helps in assessing intoxication levels.

• It can affect bodily functions, impair judgment, and reduce coordination.
• Legal limits for driving vary by country but are commonly around 0.08%.

Determining blood alcohol levels often involves chemical reactions, such as redox reactions, which can precisely determine ethanol concentrations.

Potassium Dichromate

Potassium dichromate ( ext{K}_2 ext{Cr}_2 ext{O}_7) is a chemical compound used as an oxidizing agent in various scientific applications. In the context of measuring blood alcohol levels, it serves a critical role in the redox reaction process.

• This compound is highly effective in oxidizing ethanol.
• In the reaction, it gets reduced from dichromate ions ( ext{Cr}_2 ext{O}_7^{2-}) to chromium ions ( ext{Cr}^{3+}).

The reduction of potassium dichromate as it oxidizes ethanol is the key mechanism that allows the concentration of alcohol to be quantified accurately. Care should be taken with this chemical as it is toxic and a known carcinogen.

Mass Percent Calculation

Mass percent is a way to express the concentration of a component in a mixture. In processes like determining the blood alcohol level, it is crucial. It provides a standardized way of expressing the amount of solute (ethanol, in this case) in a given mass of the solution (blood).

• The formula for mass percent is: \( \text{Mass percent} = \left( \frac{\text{mass of solute}}{\text{total mass of solution}} \right) \times 100 \).
• It gives a comparative measure of solute in relation to the entire solution's mass.

In our example, by finding the mass of ethanol in the blood sample and applying the formula, we derived the final value of 0.1005% ethanol by mass. This shows the percentage of the blood sample that is ethanol, crucial for determining blood alcohol concentration.