Using Specific Gravity to Determine the Concentration of a Solution
100% ethanol has a specific gravity of .785 which is lighter than water with a specific gravity of 1.0
A 50/50 mixture of water and ethanol (100 proof / 50%) will have the following specific gravity.
(.5L x 1.0) + (.5 L x 0.785) = 0.8925
A 75/25 mixture of water and ethanol (50 proof / 25%) will have the following specific gravity
(.75 L x 1.0) + (.25 L x 0.785) = 0.9463
As you can see the specific gravity of the mixture is inversely proportional to the alcohol concentration. As the alcohol concentration decreases the specific gravity increases and the hydrometer floats higher in the solution.
The alcohol hydrometer is calibrated in two scales % alcohol and proof.(1% alcohol = 2 proof ) The manufacturer used the specific gravity of alcohol at various concentrations to calibrate the instrument.
To determine the concentration of a 1 liter solution of alcohol and water using specific gravity.
1) Measure the specific gravity of the solution
Let X = unknown volume of water
Let (1-X) = unknown volume of alcohol
Then X + (1-X) = 1 Liter
Specific Gravity of water = 1.0
Specific Gravity of ethanol = 0.785
(X)(1.0) + (1-X)(0.785) = Sp. G of solution
Solve for X
Example: Assume the measured specific gravity is 0.9463
X (1.0) + (1-X)(0.785) = 0.9463
X + (0.785 - 0.785X) = 0.9463
0.215X + 0.785 = 0.9463
0.215X = 0.1613
(X)(100%) = the concentration of water
(0.75)(100%) = 75% water
(1-X)(100%) = the concentration of alcohol
(0.25)(100%) = 25% alcohol