A certain elixir is 92 proof. A proof is twice the volume percentage of alcohol in a blend. Ethanol's structural formula is CH3CH2OH with a molar mass of 46 grams/mole. The density is .79 g/ml. How many liters of elixir must one have in order to have 50 moles of carbon?

To determine the number of liters of elixir needed to have a certain number of moles of carbon, we need to calculate the amount of carbon in the elixir.

First, let's find the volume percentage of alcohol in the elixir. Since the proof is twice the volume percentage of alcohol, we can divide the proof by 2 to get the alcohol volume percentage.

Alcohol volume percentage = 92 proof / 2 = 46%

Next, we need to convert the alcohol volume percentage to grams of alcohol per liter of elixir.

To do this, we need to know the density of the elixir. Given that the density is 0.79 g/ml, we can multiply the density by the volume in milliliters (ml) to get the mass in grams (g).

Mass of alcohol per liter = Alcohol volume percentage * Density * Volume

The volume of alcohol in the elixir will be the same as the volume of the elixir since the alcohol is mixed uniformly.

Now, we can convert the mass of alcohol to moles of alcohol using the molar mass of ethanol.

Moles of alcohol = Mass of alcohol / Molar mass of ethanol

Since ethanol has a molar mass of 46 g/mole, we can substitute this value into the equation.

Finally, we can equate the number of moles of alcohol to the number of moles of carbon in the elixir, given that the molecular formula of ethanol is C2H6O.

Moles of carbon = 2 * Moles of alcohol

Now we can solve the equation to find the volume of the elixir.

Let X be the volume of the elixir in liters.

Moles of carbon = 2 * (Moles of alcohol) = 2 * (Mass of alcohol / Molar mass of ethanol)

50 moles = 2 * ((Alcohol volume percentage * Density * X) / Molar mass of ethanol)

Rearranging the equation, we get:

X = (50 moles * Molar mass of ethanol) / (2 * Alcohol volume percentage * Density)

Plugging in the given values:

X = (50 moles * 46 g/mol) / (2 * 46% * 0.79 g/ml)

Now you can solve for X using a calculator.