a 67 gram chunk of ice (Heat of Fusion = 6.0 kJ/mol) in a beaker immersed in a water bath. To produce just enough heat to melt the ice, how many moles of solid NaOH (Heat of Solution = -445.1 kJ/mol) must be added to this system to just melt the ice.
(Moles)
To solve this problem, we need to calculate the amount of heat required to melt the ice and then relating it to the heat released by dissolving NaOH.
Step 1: Calculate the heat required to melt the ice.
The heat required to melt the ice can be calculated using the formula:
q = m * ΔHf
Where:
q is the heat energy (in kJ)
m is the mass of the ice (in grams)
ΔHf is the heat of fusion (in kJ/mol)
Given:
m = 67 grams
ΔHf = 6.0 kJ/mol
To calculate the moles of ice, we need the molar mass of water (H2O) which is approximately 18 g/mol.
moles of ice = mass of ice / molar mass of water
moles of ice = 67 g / 18 g/mol
Step 2: Calculate the heat released by dissolving NaOH.
The heat released by dissolving NaOH can be calculated using the formula:
q = n * ΔHs
Where:
q is the heat energy (in kJ)
n is the moles of NaOH
ΔHs is the heat of solution (in kJ/mol)
Given:
ΔHs = -445.1 kJ/mol
Step 3: Equate the two equations to find the moles of NaOH.
Since the heat gained by the NaOH is equal to the heat lost by the ice, we can set up the equation as follows:
moles of ice * ΔHf = moles of NaOH * ΔHs
Substituting the values we have:
(moles of ice) * (ΔHf) = (moles of NaOH) * (ΔHs)
(67 g / 18 g/mol) * 6.0 kJ/mol = (moles of NaOH) * (-445.1 kJ/mol)
Simplifying the equation:
(67 / 18) * 6.0 = moles of NaOH * (-445.1)
moles of NaOH = (67 / 18) * 6.0 / (-445.1)
Calculating this expression gives us the answer for moles of NaOH needed to just melt the ice.