How much heat (in kJ) is required to warm 10.0 g of ice, initially at -10.0 °C, to steam at 110.0 °C? The heat capacity of ice is 2.09 J/g°C, and that of steam is 2.01 J/g°C.

Verified step by step guidance

1. Calculate the heat required to warm the ice from -10.0 °C to 0 °C using q = m * c * ΔT, where m is the mass, c is the specific heat capacity of ice, and ΔT is the temperature change.
2. Calculate the heat required to melt the ice at 0 °C to water using q = m * ΔH_fus, where ΔH_fus is the heat of fusion for water.
3. Calculate the heat required to warm the water from 0 °C to 100 °C using q = m * c * ΔT, where c is the specific heat capacity of water.
4. Calculate the heat required to vaporize the water at 100 °C to steam using q = m * ΔH_vap, where ΔH_vap is the heat of vaporization for water.
5. Calculate the heat required to warm the steam from 100 °C to 110 °C using q = m * c * ΔT, where c is the specific heat capacity of steam.

Key Concepts

Phase Changes

Phase changes refer to the transitions between solid, liquid, and gas states of matter. In this question, the ice must first melt into water, then the water must be heated to 100 °C, followed by vaporization into steam, and finally, the steam is heated to 110 °C. Each of these transitions involves specific heat values and latent heat, which are crucial for calculating the total heat required.

Specific Heat Capacity

Specific heat capacity is the amount of heat required to raise the temperature of a unit mass of a substance by one degree Celsius. Different substances have different specific heat capacities, which affect how much heat is needed to change their temperature. In this problem, the specific heat capacities of ice and steam are provided, and they will be used to calculate the heat required for temperature changes in each phase.

Latent Heat

Latent heat is the heat absorbed or released during a phase change without a change in temperature. For instance, when ice melts to water, it absorbs latent heat of fusion, and when water vaporizes to steam, it absorbs latent heat of vaporization. These values are essential for calculating the total heat required in the given problem, as they account for the energy needed to change the state of the substance.