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5 October, 09:12

A piece of iron metal is heated to 155 degrees C and placed into a calorimeter that contains 50.0 mL of water at 18.7 degrees C. The temperature of the water rises to 26.4 degrees C. The specific heat of iron of iron is 0.444 J/g degrees C. Assuming no loss of heat to the surroundings, what is the mass of the iron?

A-26.2 g

B-28.3 g

C-29.2 g

D-28.2 g

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  1. 5 October, 10:22
    0
    D = 28.2g

    Explanation:

    Initial temperature of metal (T1) = 155°C

    Initial Temperature of calorimeter (T2) = 18.7°C

    Final temperature of solution (T3) = 26.4°C

    Specific heat capacity of water (C2) = 4.184J/g°C

    Specific heat capacity of metal (C1) = 0.444J/g°C

    Volume of water = 50.0mL

    Assuming no heat loss

    Heat energy lost by metal = heat energy gain by water + calorimeter

    Heat energy (Q) = MC∇T

    M = mass

    C = specific heat capacity

    ∇T = change in temperature

    Mass of metal = M1

    Mass of water = M2

    Density = mass / volume

    Mass = density * volume

    Density of water = 1g/mL

    Mass (M2) = 1 * 50

    Mass = 50g

    Heat loss by the metal = heat gain by water + calorimeter

    M1C1 (T1 - T3) = M2C2 (T3 - T2)

    M1 * 0.444 * (155 - 26.4) = 50 * 4.184 * (26.4 - 18.7)

    0.444M1 * 128.6 = 209.2 * 7.7

    57.0984M1 = 1610.84

    M1 = 1610.84 / 57.0984

    M1 = 28.21g

    The mass of the metal is 28.21g
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