Calculating the mass percent from a given volume % and density

In summary, the conversation was about solving a problem involving the density of wine and water. The speaker initially struggled with finding the solution, but then realized that the density of wine/water is 1g/ml. However, the density of wine is different due to the presence of other substances, making calculations difficult. The speaker suggests using approximate calculations, but notes that they are not completely accurate.
  • #1
CynicusRex
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Homework Statement
A bottle of wine contains 12.5 % ethanol (volume%). The density of ethanol (C2H5OH) is 0.789 g/cm^3. Calculate the concentration of alcohol in wine in: a. mass percent, b. molarity.
Relevant Equations
mass solute a / solution * 100 = mass percent a
p = m/v
[I've solved b, but can't figure out a for the life of me. I have a couple of attempts, but it's just nonsense, it's like I've short circuited.]
 
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  • #2
Okay, never mind. I didn't know the density of wine/water was 1g/ml.
 
  • #3
CynicusRex said:
Okay, never mind. I didn't know the density of wine/water was 1g/ml.
It wasn't :wink:

1 g/mL is a rather exact number for water and often a reasonably good approximation for not too concentrated water based solutions, but for better answer you need the density to be measured. 12.5% ethanol solution has a density of 0.9795 g/mL - that can be easily checked in tables. The density of wine is different, as it also contains many other substances, including substantial amount of sugars (which makes the density higher).

Plus, especially in the case of ethanol, calculations are quite difficult, as volumes are not additive - if you mix 50 mL of water with 50 mL of ethanol, you get 96.4 mL of solution.

You are probably expected to do only approximate calculations, but bear in mind they are a bit wrong by definition.
 
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1. How do you calculate mass percent from a given volume percent and density?

To calculate mass percent, you first need to convert the given volume percent to a decimal by dividing it by 100. Then, you can multiply this decimal by the density to get the mass per unit volume. Finally, you can convert this value to a percentage by multiplying it by 100.

2. What is the formula for calculating mass percent?

The formula for calculating mass percent is: (volume % / 100) x density x 100.

3. Can you provide an example of calculating mass percent from a given volume percent and density?

Sure, let's say we have a solution with a volume percent of 20% and a density of 1.5 g/mL. First, we convert 20% to a decimal by dividing it by 100, giving us 0.2. Then, we multiply 0.2 by 1.5 g/mL, giving us 0.3 g/mL. Finally, we multiply 0.3 by 100 to get a mass percent of 30%.

4. How is mass percent different from volume percent?

Mass percent is a measure of the mass of a substance in a solution, while volume percent is a measure of the volume of a substance in a solution. Mass percent takes into account the density of the solution, while volume percent does not.

5. What units are used for mass percent and density?

Mass percent is typically expressed as a percentage (%), while density is usually measured in grams per milliliter (g/mL). However, other units such as kilograms per liter (kg/L) or pounds per gallon (lb/gal) may also be used.

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