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8 November, 22:22

A chemist is adding pure (100%) acid to a 12 liter solution that is 15% acid in order to increase it to 49% acid. How much pure acid must she add?

How many ounces of 35% ethanol must be added to a 23 ounce mixture that contains 26% ethanol in order to obtain a mixture of 30.86% ethanol?

How many liters of 30% acid must be added to 10 liters of 53.66% acid in order to obtain a mixture that is 43% acid?

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  1. 8 November, 22:32
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    1) 8 liters of pure acid

    2) 27 liters of 35% ethanol

    3) 8.2 liters of 30% acid

    Step-by-step explanation:

    The inicial amount of acid is 15% of 12 L, and the inicial volume is 12L.

    Adding 'x' L of 100% acid, we have the amount of acid equal to 12 * 0.15 + x * 1, and the volume of 12 + x. The concentration is the amount of acid over the volume, so we have that:

    (12*0.15 + x) / (12 + x) = 49/100

    (1.8 + x) * 100 = (12 + x) * 49

    180 + 100x = 588 + 49x

    51x = 408

    x = 8 liters of pure acid

    Similar to the solution above, for the second question we have:

    (23*0.26 + 0.35*x) / (23 + x) = 30.86/100

    (5.98 + 0.35*x) * 100 = (23 + x) * 30.86

    598 + 35x = 709.78 + 30.86x

    4.14x = 111.78

    x = 27 liters of 35% ethanol

    For the third question, we have:

    (10*0.5366 + 0.3*x) / (10 + x) = 43/100

    (5.366 + 0.3x) * 100 = (10 + x) * 43

    536.6 + 30x = 430 + 43x

    13x = 106.6

    x = 8.2 liters of 30% acid
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