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A 500 mL bottle at room temperature (25˚C) of water is poured over 120 g of ice that is (-8˚C). What will be the final temperature of the water be when all the ice has melted? You can ignore loss of heat to the room.

  • Chemistry -

    q1 = heat to raise T of solid ice from -8 to zero C.
    q1 = mass ice x specific ice x (Tf - Ti) where Tf is 0 C and Ti is -8 C.

    q2 = heat to melt ice at zero C to liquid H2O at zero C.
    q2 = mass ice x heat fusion

    q3 = heat to raise water from zero C to final T.
    q3 = mass H2O x specific heat H2O x (Tf - Ti). Ti is zero.

    q4 = heat lost by the 500 mL H2O at 25 C.
    q4 = mass H2O x specific heat H2O x (Tf - Ti). Ti = 25 C.

    q1 + q2 + q3 + q4 = 0

    Plug all of that into q1 through q4 and solve for T. Tf is close to 18 C.

  • Chemistry -

    Dr. Bob,

    When I use the values that I have for latent heat of fusion and vaporization, I do not get the right answer.

    I have that latent heat of vaporization is 597.3 - 0.564T, and latent heat of fusion is 79.7 cal/gH2O.

  • Chemistry -

    Heat fusion is about 80 cal/g so your 79.7 cal/g (probably a better number than my memory) should be ok. However, I remember the heat vaporization as about 540 cal/g. But hold on ! You don't have heat vap anywhere in the equation.
    You need specific heat ice
    You need heat fusion water/ice.
    You need specific heat liquid water.
    Nowhere do you need heat vaporization for water. Somewhere you are substituting incorrectly. Allow me to use round numbers.
    q1 = [120 x 0.500 x (8)] [Note: I think I remember specific heat ice = about 0.5 cal/g but check that out.]
    q2 = [120 x 80]
    q3 = [120 x 1 x (Tf-0)]
    q4 = [500 x 1 x (Tf - 25)]
    I think the answer is in the neighborhood of 15-20 C.

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