x = 70 ml of 100% ethanol should be mixed with 30 ml of pure water. However, this assumes that the volumes are additive, i.e. that 70 ml ethanol + 30 ml water = 100 mls. This is not likely to be the case, but in many introductory chemistry courses, they assume it is.
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Answer:
V1C1 = V2C2
V1 = volume 1 = x ml
C1 = concentration 1 = 100%
V2 = volume 2 = 100 ml
C2 = concentration 2 = 70%
(x ml)(100%) = (100 ml)(70%)
x = 70 ml of 100% ethanol should be mixed with 30 ml of pure water. However, this assumes that the volumes are additive, i.e. that 70 ml ethanol + 30 ml water = 100 mls. This is not likely to be the case, but in many introductory chemistry courses, they assume it is.