5.2: Specific Heat Capacity

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Exercise \(\PageIndex{1}\)

The specific heat capacity of water(liquid) is 4.18 J/g⋅°C. What is the molar specific heat capacity of this substance? The molar mass of water is 18.01 g/mol.

Answer

75.3 J/mol * °C

\(c_{m}=\frac{4.18 J}{\left ( \frac{1}{18.01} mol * °C\right )}=75.2818 J/mol * °C\)

Exercise \(\PageIndex{2}\)

Exactly 149.6 J will raise the temperature of 10.0 g of a metal from 25.0 °C to 60.0 °C. What is the specific heat capacity of the metal?

Answer: 0.427 J/(g *°C)

Exercise \(\PageIndex{3}\)

A 100 g sample of each of the following metals is heated from 35°C to 45°C. Which metal absorbs the lowest amount of heat energy?

Metal Specific Heat Capacity

Copper 0.385 J/(g*°C)

Magnesium 1.02 J/(g*°C)

Mercury 0.138 J/(g*°C)

Silver 0.237 J/(g*°C)

Lead 0.129 J/(g*°C)

Answer: Lead

Exercise \(\PageIndex{4}\)

35.0 kJ raises the temperature of an gold object from 22^oC to its melting point of 1064.18^oC. What is the mass of the gold object?

Answer: \[q=mc\Delta T\\m=\frac{q}{c\left ( T_f-T_i \right )}=\frac{35kJ\left ( \frac{1000J}{kJ} \right )}{\frac{0.129J}{g\cdot ^{o} C}\left (1064.18^{o}C-22^{o}C \right )}=260. g \nonumber\]

Exercise \(\PageIndex{5}\)

What is the specific heat capacity in cal/g^oC of a substance if it takes 5.09 kJ to raise a 30.1 g mass sample of the material from 25.0 to 400.0^oC?

Answer: \[q=mc\Delta T\\c=\frac{q}{m\left ( T_f-T_i \right )}=\frac{5.09kJ\left ( \frac{1000J}{kJ} \right )\left ( \frac{cal}{4.184J} \right )}{30.1g\left (400.0^{o}C-25.0^{o}C \right )}=0.108\left ( \frac{cal}{g\cdot^{o}C} \right ) \nonumber\]

Exercise \(\PageIndex{7}\)

Does it take more or less energy to raise 100.0 g of gold or 100.0 g of water from 10.0^oC to 100.0^oC?

Calculate Heat required to raise the gold to 100.0^oC.
Calculate the Heat required to raise the water to 100.0^oC.
Give the ratio of the heat required to raise the water to the gold, and the ratio of the heat capacities of water to gold.
Explain why these are the same.

Answer a: sulfur tetrafluoride

Answer b: diphosphorus pentasulfide

Answer c: dinitrogen tetraoxide

Answer d: tetraphosphorus decasulfide

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