vapor enthalpy energies kj/mol 40.66, specific heat capacities j/g degrees c s(s) 2.1, fus 6.01 enthalpy energies kj/mol 6.01 specifi heat j/g degrees c s(1) 4.2, s(g) 2.0 how much energy is needed to convert 64.0 grams of ice at 0.00 degress c to water at 80 degrees c
To calculate the amount of energy needed to convert 64.0 grams of ice at 0.00 degrees Celsius to water at 80 degrees Celsius, we need to consider the different stages involved: the heating of ice, the phase change from ice to water, and the heating of water.
Here's the step-by-step calculation:
1. Determine the energy required to raise the temperature of ice from -273.15 degrees Celsius (absolute zero) to 0 degrees Celsius. To do this, we use the equation:
Energy = mass * specific heat capacity * temperature change
Given:
- mass of ice = 64.0 grams
- specific heat capacity of ice (s(s)) = 2.1 J/g°C
- temperature change = 0°C - (-273.15°C) = 273.15°C
Energy = 64.0 g * 2.1 J/g°C * 273.15°C
2. Calculate the energy required for the phase change from ice to water. The enthalpy of fusion (fus) indicates the amount of energy required to convert one mole of ice to water at 0°C. One mole of any substance contains Avogadro's number (6.022 x 10^23) of particles.
Given:
- enthalpy of fusion (fus) = 6.01 kJ/mol
To convert this enthalpy to energy per gram of ice, divide by the molar mass of ice (18 g/mol):
Energy per gram = (6.01 kJ/mol) / (18 g/mol)
3. Multiply the energy per gram by the mass of ice to obtain the energy required for the phase change:
Energy = Energy per gram * mass of ice
4. Determine the energy required to raise the temperature of water from 0°C to 80°C. Use the equation:
Energy = mass * specific heat capacity * temperature change
Given:
- mass of water = mass of ice (since the ice is fully converted to water)
- specific heat capacity of water (s(1)) = 4.2 J/g°C
- temperature change = 80°C - 0°C = 80°C
Energy = mass of water * specific heat capacity of water * temperature change
5. Sum up all the energies calculated in steps 1, 2, and 4 to get the total energy required.
Total Energy = Energy (step 1) + Energy (step 2) + Energy (step 4)
Now you can substitute the given values into these equations and calculate the final answer.