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  • Calculate the heat capacity of 500 g of water at 25°C, given that the molar heat capacity

Calculate the heat capacity \mathrm{C_{p} of 500 g of water at 25°C, given that the molar heat capacity\mathrm{C_{p,m}} of water is 75 J/(mol·K) and the molar mass of water is 18.015 g/mol.

 

Option: 1

2080 J/K
 


Option: 2

2087 J/K
 


Option: 3

2300 J/K
 


Option: 4

2400 J/K


Answers (1)

best_answer

The heat capacity\mathrm{(Cp)} of a substance is related to its molar heat capacity \mathrm{(Cp,m)} and molar mass (M) by the formula:

\mathrm{C_p=C_{p, m} \times \frac{m}{M}}

where m is the mass of the substance and M is the molar mass.
Given:

 \mathrm{\begin{aligned} C_{p, m} & =75 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K}) \\ m & =500 \mathrm{~g} \\ M & =18.015 \mathrm{~g} / \mathrm{mol} \end{aligned}}

Substituting the values:

\mathrm{C_p=75 \mathrm{~J} /(\mathrm{mol} \cdot \mathrm{K}) \times \frac{500 \mathrm{~g}}{18.015 \mathrm{~g} / \mathrm{mol}} \approx 2086.7 \mathrm{~J} / \mathrm{K}}

Therefore, the heat capacity (Cp) of 500 g of water at 25°C is approximately
2086.7 J/K.

 

Posted by

Deependra Verma

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