How much heat (in kJ) is required to convert 100 g of ice (H2O) at 253 K to steam (H2O) at 393 K? Assume the following values: specific heat of ice = 2.09 J/g·K, specific heat of liquid water = 4.18 J/g·K, specific heat of steam = 2.01 J/g·K, enthalpy of fusion = 334 J/g, enthalpy of vaporization = 2260 J/g. The melting point of ice is 273 K and the boiling point of water is 373 K.

• A. Approximately 326 kJ
• B. Approximately 226 kJ
• C. Approximately 452 kJ
• D. Approximately 178 kJ

Answer: (A)

Verified step by step guidance

1. Identify the different stages involved in converting 100 g of ice at 253 K to steam at 393 K. These stages are: heating the ice from 253 K to 273 K (melting point), melting the ice at 273 K, heating the liquid water from 273 K to 373 K (boiling point), vaporizing the water at 373 K, and finally heating the steam from 373 K to 393 K.
2. Calculate the heat required to raise the temperature of the ice from 253 K to 273 K using the formula \(q = m \times C_{ice} \times \Delta T\), where \(m\) is the mass, \(C_{ice}\) is the specific heat capacity of ice, and \(\Delta T\) is the temperature change.
3. Calculate the heat required to melt the ice at 273 K using the formula \(q = m \times \Delta H_{fusion}\), where \(\Delta H_{fusion}\) is the enthalpy of fusion.
4. Calculate the heat required to raise the temperature of the liquid water from 273 K to 373 K using \(q = m \times C_{water} \times \Delta T\), where \(C_{water}\) is the specific heat capacity of liquid water.
5. Calculate the heat required to vaporize the water at 373 K using \(q = m \times \Delta H_{vaporization}\), and then calculate the heat required to raise the temperature of the steam from 373 K to 393 K using \(q = m \times C_{steam} \times \Delta T\). Finally, sum all these heat values to find the total heat required.