Determine the molar concentration of ethanol (C2H6O) in a wine that is 14% ethanol by mass. The density of this wine is 0.93 g/cm^3.
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To determine the molar concentration of ethanol in the wine, we need to follow these steps:
Step 1: Calculate the mass of ethanol in the wine.
Step 2: Convert the mass of ethanol to moles using the molar mass.
Step 3: Calculate the volume of the wine.
Step 4: Convert the volume to liters.
Step 5: Calculate the molar concentration (Molarity) using the formula: Molarity (M) = Moles of solute / Volume of solution (in liters).
Let's go through each step:
Step 1: Calculate the mass of ethanol in the wine.
Given: Mass % of ethanol = 14%
Density of wine = 0.93 g/cm^3
To calculate the mass of ethanol, we need to know the total mass of the wine. Let's assume we have 100 g of wine (this is an arbitrary assumption, as we only need the ratio).
So, the mass of ethanol in the wine is (14/100) * 100 g = 14 g.
Step 2: Convert the mass of ethanol to moles using the molar mass of ethanol.
The molar mass of ethanol (C2H6O) can be calculated by adding the atomic masses of carbon (C), hydrogen (H), and oxygen (O).
C: 12.01 g/mol
H: 1.01 g/mol
O: 16.00 g/mol
Molar mass of ethanol = (2 * C) + (6 * H) + O
= (2 * 12.01) + (6 * 1.01) + 16.00
= 46.07 g/mol
Using the molar mass, we can calculate the number of moles of ethanol:
Moles of ethanol = mass of ethanol / molar mass
= 14 g / 46.07 g/mol
≈ 0.303 moles
Step 3: Calculate the volume of the wine.
We need to know the density of the wine to calculate its volume. Given: Density of wine = 0.93 g/cm^3
Since the density is given in grams per cubic centimeter, we can use the following equation to find the volume:
Volume = mass / density
= 100 g / 0.93 g/cm^3
≈ 107.53 cm^3
Step 4: Convert the volume to liters.
To convert the volume from cm^3 to liters, we divide by 1000 (since 1 liter = 1000 cm^3).
Volume in liters = Volume in cm^3 / 1000
= 107.53 cm^3 / 1000
≈ 0.1075 L
Step 5: Calculate the molar concentration (Molarity).
Molarity (M) = Moles of solute / Volume of solution (in liters)
= 0.303 moles / 0.1075 L
≈ 2.82 M
Therefore, the molar concentration of ethanol in the wine is approximately 2.82 M.
To determine the molar concentration of ethanol in the wine, you first need to convert the mass percent of ethanol to grams of ethanol. Then, you can use the molar mass of ethanol and the density of the wine to calculate the molar concentration.
Here's how you can do it step-by-step:
Step 1: Convert the mass percent of ethanol to grams of ethanol:
Assuming you have 100 grams of wine, 14% ethanol by mass means that you have 14 grams of ethanol.
Step 2: Calculate the volume of the wine:
To calculate the volume of the wine, divide the mass of the wine by its density. Given that the density is 0.93 g/cm^3, if you have 100 grams of wine, the volume would be 100 g / 0.93 g/cm^3 = 107.53 cm^3.
Step 3: Convert the volume of the wine to liters:
Since the molar concentration is usually expressed in moles per liter, you need to convert the volume from cm^3 to liters. 1 cm^3 is equal to 1 mL, so the volume in liters is 107.53 cm^3 / 1000 = 0.10753 L.
Step 4: Calculate the molar concentration:
Finally, you can calculate the molar concentration of ethanol by dividing the moles of ethanol by the volume of the wine in liters.
To find the moles of ethanol, divide the grams of ethanol by its molar mass. The molar mass of ethanol (C2H6O) is calculated as follows:
- 2 carbon atoms (12.01 g/mol) = 24.02 g/mol
- 6 hydrogen atoms (1.01 g/mol each) = 6.06 g/mol
- 1 oxygen atom (16.00 g/mol) = 16.00 g/mol
Therefore, the molar mass of ethanol is 24.02 g/mol + 6.06 g/mol + 16.00 g/mol = 46.08 g/mol.
Now, calculate the moles of ethanol: 14 g / 46.08 g/mol = 0.303 mol.
Finally, divide the moles of ethanol by the volume of the wine in liters:
Molar concentration = 0.303 mol / 0.10753 L = 2.82 M.
Therefore, the molar concentration of ethanol in the wine is 2.82 M.
a liter of the wine has a mass of 930 g
14% is ethanol ... .14 * 930 = ?
calculate the ethanol mass
divide by the molar mass to find the moles in the liter of wine (molar concentration)