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6 February, 01:00

a 125 g chunk of aluminum at 182 degrees Celsius was added to a bucket filled with 365 g of water at 22.0 degrees Celsius. Ignoring the specific heat of the bucket, calculate the final temperature of the two compounds once thermal equilibrium is reached

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  1. 6 February, 01:02
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    32.98°C

    Explanation:

    We are given the following;

    Mass of Aluminium as 125 g

    Initial temperature of Aluminium as 182°C

    Mass of water as 265 g

    Initial temperature of water as 22°C

    We are required to calculate the final temperature of the two compounds;

    First, we need to know the specific heat capacity of each;

    Specific heat capacity of Aluminium is 0.9 J/g°C

    Specific heat capacity of water is 4.184 J/g°C

    Step 1: Calculate the Quantity of heat gained by water.

    Assuming the final temperature is X°C

    we know, Q = mcΔT

    Change in temperature, ΔT = (X-22) °C

    therefore;

    Q = 365 g * 4.184 J/g°C * (X-22) °C

    = (1527.16X-33,597.52) Joules

    Step 2: Calculate the quantity of heat released by Aluminium

    Using the final temperature, X°C

    Change in temperature, ΔT = - (X° - 182°) C (negative because heat was lost)

    Therefore;

    Q = 125 g * 0.90 J/g°C * (182°-X°) C

    = (20,475 - 112.5X) Joules

    Step 3: Calculating the final temperature

    We need to know that the heat released by aluminium is equal to heat absorbed by water.

    Therefore;

    (20,475 - 112.5X) Joules = (1527.16X-33,597.52) Joules

    Combining the like terms;

    1639.66X = 54072.52

    X = 32.978°C

    = 32.98°C

    Therefore, the final temperature of the two compounds will be 32.98°C
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