How many calories must be added to 3 g of ice at 0°C to convert it completely to water vapor at 100°C?

• A. 5400 calories
• B. 2047 calories
• C. 2250 calories
• D. 22500 calories

Answer: (D)

Verified step by step guidance

1. Identify the three stages involved in converting 3 g of ice at 0°C to water vapor at 100°C: (1) melting ice to liquid water at 0°C, (2) heating the liquid water from 0°C to 100°C, and (3) vaporizing the water at 100°C to steam.
2. Calculate the heat required to melt the ice using the formula \(q = m \times \Delta H_{fus}\), where \(m\) is the mass of ice and \(\Delta H_{fus}\) is the heat of fusion of ice (approximately 80 cal/g).
3. Calculate the heat required to raise the temperature of the liquid water from 0°C to 100°C using \(q = m \times C_{water} \times \Delta T\), where \(C_{water}\) is the specific heat capacity of water (1 cal/g°C) and \(\Delta T\) is the temperature change (100°C - 0°C).
4. Calculate the heat required to vaporize the water at 100°C using \(q = m \times \Delta H_{vap}\), where \(\Delta H_{vap}\) is the heat of vaporization of water (approximately 540 cal/g).
5. Add the three amounts of heat calculated in the previous steps to find the total calories needed to convert 3 g of ice at 0°C completely to water vapor at 100°C.