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A substance with a mass of 9 g absorbs 439.2 J of heat, and its temperature increases by 20 °C. Calculate its specific heat capacity and select the correct option.

Chemistry

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Answer

2.44 J/g⋅°C\text{2.44 J/g} \cdot \text{°C}

Step-by-step solution

4 steps
  1. Identify the given values.

    The heat gained (QQ) is 439.2 J439.2 \text{ J}.
    The mass of the substance (mm) is 9 g9 \text{ g}.
    The change in temperature (ΔT\Delta T) is 20 °C20 \text{ °C}.

  2. Use the formula for specific heat capacity.

    The formula relating heat, mass, specific heat capacity, and temperature change is:

    Q=mcΔTQ = mc\Delta T

    Where cc is the specific heat capacity. To find cc, we rearrange the formula:

    c=QmΔTc = \frac{Q}{m\Delta T}
  3. Substitute the values and calculate.

    c=439.2 J(9 g)(20 °C)c = \frac{439.2 \text{ J}}{(9 \text{ g})(20 \text{ °C})} c=439.2 J180 g⋅°Cc = \frac{439.2 \text{ J}}{180 \text{ g} \cdot \text{°C}} c=2.44 J/g⋅°Cc = 2.44 \text{ J/g} \cdot \text{°C}
  4. Compare the result with the given options.

    The calculated specific heat capacity is 2.44 J/g⋅°C2.44 \text{ J/g} \cdot \text{°C}.
    The options provided are:
    1: 2.44
    2: 4.18
    3: 2.06
    4: 0.449

    The calculated value matches option 1.

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