How much heat in kJ is required to melt 54 grams of ice at 0 degrees C into water at 0 degrees C if delta Hvap for water = 6.01 kJ/mol?
To calculate the amount of heat required to melt a given quantity of ice, you need to use the following equation:
q = m * ΔHfus
where:
q is the heat (in Joules)
m is the mass (in grams)
ΔHfus is the heat of fusion (in Joules per gram)
First, let's convert the given mass of ice from grams to moles, since ΔHvap is provided in kJ/mol:
Molar mass of water (H2O) = 18.015 g/mol
moles of ice = mass of ice / molar mass of water
moles of ice = 54 g / 18.015 g/mol
Next, we need to convert ΔHvap from kJ/mol to J/g:
ΔHvap = 6.01 kJ/mol = 6.01 * 10^3 J/mol
Now we can calculate the amount of heat required to melt the ice:
q = moles of ice * ΔHfus
q = (54 g / 18.015 g/mol) * (6.01 * 10^3 J/mol)
q = 9.03 * 10^3 J
Finally, we can convert the heat from Joules to kilojoules:
q = 9.03 * 10^3 J = 9.03 kJ
Thus, the amount of heat required to melt 54 grams of ice at 0 degrees C into water at 0 degrees C is approximately 9.03 kJ.