What is the final temperature and state of water when 8.50 kJ of energy is added to 10.0 g of ice at 0 degree Celsius.

Helpful information:

Cs (ice)= 2.1 J/g•C

Heat of vaporization (water)= 40.7kJ/mol

Ca (water)= 4.184 J/g•C

Heat of fusion (water)= 6.02 kJ/mol

Cs (steam) = 2.0 J/g• C

To determine the final temperature and state of water when energy is added to ice, we need to consider the phase changes involved and calculate the amount of energy required for each step.

First, we need to determine the energy required to heat the ice from 0°C to its melting point (0°C) and convert it into water at 0°C. This requires two steps:

1. Energy required to heat the ice:
The specific heat capacity of ice (Cs) is given as 2.1 J/g•C. We have 10.0 g of ice, so the energy required to raise its temperature from -273.15°C to 0°C can be calculated using the formula:
Energy = mass (g) x specific heat capacity (J/g•C) x temperature change (°C)

Energy = 10.0 g x 2.1 J/g•C x (0 - (-273.15))
Energy = 5671.55 J

2. Energy required for melting:
The heat of fusion (ΔHf) for water is given as 6.02 kJ/mol. Since we have the mass of ice in grams, we need to convert it to moles using the molar mass:
Molar mass of water (H2O) = 18.015 g/mol

moles of ice = mass (g) / molar mass (g/mol)
moles of ice = 10.0 g / 18.015 g/mol ≈ 0.555 mol

Now, we can calculate the energy required to melt the ice:
Energy = moles of ice x heat of fusion (ΔHf)
Energy = 0.555 mol x 6.02 kJ/mol
Energy = 3.34 kJ

So, the total energy required to raise the temperature of ice to its melting point and melt it is:
Total energy = Energy required to heat ice + Energy required for melting
Total energy = 5.67 kJ + 3.34 kJ
Total energy = 8.01 kJ

Since 8.50 kJ of energy is added, the remaining energy will be used to heat the water. The final temperature can be calculated by dividing the remaining energy by the specific heat capacity of water (Ca) and the mass of water:

Remaining energy = 8.50 kJ - 8.01 kJ
Remaining energy = 0.49 kJ

Final temperature = Remaining energy / (mass x specific heat capacity of water)
Final temperature = 0.49 kJ / (10.0 g x 4.184 J/g•C)
Final temperature ≈ 0.0117 °C

So, the final temperature of water is approximately 0.0117 °C. Since the energy added is not enough to cause a phase change, the state of the water remains in the liquid phase.