Ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\), is responsible for the effects of intoxication felt after drinking alcoholic beverages. When ethanol burns in oxygen, carbon dioxide, and water are produced. (a) Write a balanced equation for the reaction. (b) How many liters of ethanol \(\left(d=0.789 \mathrm{~g} / \mathrm{cm}^{3}\right)\) will produce \(1.25 \mathrm{~L}\) of water \(\left(d=1.00 \mathrm{~g} / \mathrm{cm}^{3}\right) ?\) (c) A wine cooler contains \(4.5 \%\) ethanol by mass. Assuming that only the alcohol burns in oxygen, how many grams of wine cooler need to be burned to produce \(3.12 \mathrm{~L}\) of \(\mathrm{CO}_{2}\left(d=1.80 \mathrm{~g} / \mathrm{L}\right.\) at \(25^{\circ} \mathrm{C}, 1\) atm pressure) at the conditions given for the density?

To write the balanced equation for the reaction of ethanol and oxygen, we first need to identify the products formed, which are given as carbon dioxide (CO2) and water (H2O). The unbalanced equation is: $$C_2H_5OH + O_2 \rightarrow CO_2 + H_2O$$ Now, we need to balance the equation by adjusting the coefficients: $$C_2H_5OH + 3O_2 \rightarrow 2CO_2 + 3H_2O$$

First, we need to find the number of moles of water formed, and then use the stoichiometry of the balanced equation to determine the number of moles of ethanol required. Finally, we will find the volume of ethanol. 1. Calculate the mass of water produced: \(1.25~L * 1~g/cm^3 * 1000~cm^3/L = 1250~g\) 2. Determine the number of moles of water produced: \(1250~g / 18.02~g/mol ≈ 69.37~mol\) 3. Use the stoichiometry from the balanced equation to find the number of moles of ethanol: \(69.37~mol_{H_2O} * (1~mol_{C_2H_5OH} / 3~mol_{H_2O}) ≈ 23.12~mol_{C_2H_5OH}\) 4. Determine the mass of ethanol: \(23.12~mol * 46.07~g/mol ≈ 1064.7~g\) 5. Calculate the volume of ethanol: \(1064.7~g / 0.789~g/cm^3 ≈ 1349.9~cm^3\) Therefore, approximately 1349.9 cm³ of ethanol are needed to produce 1.25 L of water.

To determine the mass of wine cooler needed to produce the desired amount of CO2, we will first find the number of moles of CO2 produced, then use stoichiometry to obtain the number of moles of ethanol needed, and finally determine the mass of wine cooler containing the required amount of ethanol. 1. Calculate the mass of CO2 produced: \(3.12~L * 1.80~g/L = 5.616~g\) 2. Determine the number of moles of CO2 produced: \(5.616~g / 44.01~g/mol ≈ 0.127~mol\) 3. Use the stoichiometry from the balanced equation to find the number of moles of ethanol: \(0.127~mol_{CO_2} * (1~mol_{C_2H_5OH} / 2~mol_{CO_2}) = 0.0635~mol_{C_2H_5OH}\) 4. Determine the mass of ethanol: \(0.0635~mol * 46.07~g/mol ≈ 2.92~g\) 5. Calculate the mass of wine cooler needed: \(2.92~g / 0.045 ≈ 64.9~g\) Therefore, approximately 64.9 g of wine cooler need to be burned to produce 3.12 L of CO2 under the given conditions.