Question 499339: what is the mass of a 1 cup of a 12% alcohol-water solution?
10% solution is 0.98569
15% is 0.98024
Answer by chessace(471)   (Show Source):
You can put this solution on YOUR website! Let DA = density (mass/vol) of Alcohol; DW = density of water
Mass (density * volume): 0.1*DA + 0.9*DW = 0.98569
0.15*DA + 0.85*DW = 0.98024
0.12*DA + 0.88*DW = x
3*DA + 27*DW = 30*0.98569
3*DA + 17*DW = 20*0.98024
10DW = 29.5707 - 19.6048 = 9.9659
DW = 0.99659
DA = 10 * (0.98569 - (0.9 * 0.99659))
DA = 10 * (0.98569 - 0.896931)
DA = 0.88759
x = 0.12 * 0.88759 + 0.88 * 0.99659
x = 0.1065108 + 0.8769992
x = 0.98351
Note that this is between the stronger and weaker solutions, and proportional so, thus the simpler approach would be weighted average:
x = (3 * 0.98569 + 2 * 0.98024) / 5
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