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Thread: Mixtures

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    Within my grasp! ibelieveican's Avatar
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    Mixtures

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    A substance is 99% water. Some water evaporates, leaving a substance
    that is 98% water. How much of the water evaporated?

  2. #2
    Within my grasp! ibelieveican's Avatar
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    My approach

    let there be 1% alcohol
    Let the volume be 100x

    99x water 1x alcholol
    let the new volume be 100y

    98y water and 2y alchol

    now we know that water evaporated so this gives the volume of alchohol remains the same.
    so 1x= 2y
    x = 2y

    water evaporated is 99x-98y = 49x

    But the answer is
    SPOILER: 50.5%
    Last edited by ibelieveican; 10-05-2008 at 06:13 PM.

  3. #3
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    Good post? Yes | No
    water evaporated is 99x-98y = 50x not 49x
    50% of x

    but still we are not appropriate.

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    Within my grasp! ibelieveican's Avatar
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    Quote Originally Posted by Shooter View Post
    water evaporated is 99x-98y = 50x not 49x
    50% of x

    but still we are not appropriate.
    Thanks shooter..
    yeah it should be 50x

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    Let the two substances be w (water) and a

    now acc to ques: case 1) w1/a1 = 99/1
    ==> a1 = w1/99

    where w1 is water initially.
    case 2) w2/a2 = 98/2
    ==> a2 = w2/49...(where w2 is water in second case)
    now a1 = a2

    w1/99 = w2/49
    ==> w2 = 0.495w1

    hence water remaining in second case id 0.495 times that of W1
    wayer evaporated = w1 - w2 = w1 - 0.495w1 = 0.505 w1
    50.5%, hence is the amount of water that evaporated.

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    Within my grasp! ibelieveican's Avatar
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    Thanks buddy...
    I got your point but i think I am missing a concept somewhere.. could you tell me what went wrong with my approach

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    my mistake.. i got it..
    the % evaporated is 50/99 which is 50.5%

    silly percent pbl

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    Let us assume the water is 99 parts and substance is 1

    The water evaporates and the 1% substance becomes 2%, i.e 1 becomes 2% of the mixture.

    Let us assume the new mixture volume is x, which can be expressed as
    (1/x)*100 = 2
    2x=100
    x=50
    The new mixture is 50 parts with 49parts water and 1 part substance.

    The evaporated water percent = (99-49)/99 = 50/99 = 50.5%

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    tricky question,
    percent of water evaporated to be calculated of the intial water content and not the whole substance. so ans 50.5%

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    Let there be a total of 100 Litres of the solution. which contains 1 part as substance and 99 parts water.
    Let a parts of water is evaporated, then the resulting solution has (100-a) litres of water.

    Now (99% of 100) - a =98% (100-a)
    --> 99 - a = 98 - 98a
    --> 1 = 2a -->a=50
    i-e 50 parts of the initial total amount(100) is evaporated or 50 parts of initial water content(99)=50.5 is evaporated.
    Last edited by vijay1311; 09-12-2010 at 11:12 AM.

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