Consider a 67-g chunk of ice (∆Hfus = 6.0 kkJ/mol) in a beaker immersed in a water bath. To produce just enough heat to melt the ice, how many moles of solid NaOH (∆Hsoln = -445.1 kJ/mol) must you dissolve in the water bath?
Please show all work.
Thanks in advance.
Why did the ice go to therapy? Because it was feeling a bit melty!
Now, let's solve the problem at hand. To melt the ice, we need to provide enough heat to overcome its enthalpy of fusion (ΔHfus = 6.0 kJ/mol).
First, we need to determine how many moles of ice we have. The molar mass of ice (H2O) is approximately 18 g/mol. Therefore, we have:
67 g / 18 g/mol ≈ 3.72 mol of ice
Next, we need to calculate the amount of heat required to melt this ice. This can be done using the equation:
q = n × ΔHfus
where q is the heat transfer, n is the number of moles, and ΔHfus is the enthalpy of fusion.
q = 3.72 mol × 6.0 kJ/mol ≈ 22.32 kJ
Now, we need to find a solute that can provide enough heat to melt the ice. One option is solid NaOH, which has an enthalpy of solution (ΔHsoln) of -445.1 kJ/mol.
To calculate the number of moles of NaOH required, we can rearrange the equation and solve for n:
n = q / ΔHsoln
n = 22.32 kJ / -445.1 kJ/mol ≈ -0.0501 mol
Since moles cannot be negative, we can simply take the absolute value. Therefore, we would need approximately 0.0501 moles of solid NaOH to dissolve in the water bath.
Just a friendly reminder: make sure to add the solid NaOH gradually and stir well to ensure proper dissolution and heat transfer. And please, don't forget to wear protective equipment, including a lab coat and goggles!
Hope this helps, and remember, laughter is always the coolest reaction!
To determine the number of moles of solid NaOH required to produce enough heat to melt the ice, we need to calculate the amount of heat absorbed by the ice (∆Hice).
The equation for the heat absorbed by the ice is as follows:
q = ∆Hice * moles of ice
To calculate the number of moles of ice, we need to use the molar mass of water (H2O) and the mass of the ice.
Molar mass of H2O = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
Mass of ice = 67 g
Moles of ice = (mass of ice) / (molar mass of H2O)
Moles of ice = 67 g / 18.02 g/mol = 3.72 mol
Next, we need to determine the amount of heat absorbed by the ice. The equation for the heat absorbed by the ice is as follows:
q = ∆Hfus * moles of ice
Given: ∆Hfus = 6.0 kJ/mol
Moles of ice = 3.72 mol
q = 6.0 kJ/mol * 3.72 mol = 22.32 kJ
Now, we need to find the amount of heat released by dissolving solid NaOH (∆Hsoln) in the water bath. The equation for the heat released by dissolving NaOH is as follows:
q = ∆Hsoln * moles of NaOH
We want to find the moles of NaOH required to release 22.32 kJ of heat.
Given: ∆Hsoln = -445.1 kJ/mol
Moles of NaOH = ?
Rearranging the equation, we get:
moles of NaOH = q / ∆Hsoln
Moles of NaOH = 22.32 kJ / -445.1 kJ/mol = -0.05 mol
Note: The negative sign indicates that the reaction is exothermic, meaning it releases heat.
Therefore, in order to produce enough heat to melt the ice, you need to dissolve approximately 0.05 moles of solid NaOH in the water bath.
To solve this problem, we will use the principle of energy conservation. The heat absorbed by the solid NaOH must exactly equal the heat necessary to melt the ice.
The heat required to melt an amount of ice can be calculated using the formula:
q = m * ∆Hfus
Where:
q is the heat (in joules) required to melt the ice
m is the mass (in grams) of the ice
∆Hfus is the enthalpy of fusion (heat of fusion) of water, which is the amount of energy required to convert one mole of a solid substance to a liquid at its melting point
In this case, we have a 67-g chunk of ice, so m = 67 g.
To convert the mass of ice to moles, we need to know the molar mass of water. The molar mass of H2O is approximately 18 g/mol. Therefore, the number of moles of ice (n) is:
n = m / molar mass
n = 67 g / 18 g/mol
Now, we can calculate the heat required to melt the ice:
q = m * ∆Hfus
q = 67 g * (6.0 kkJ/mol / 1000 J/kJ) (convert kJ to J)
q = 67 g * 6.0 kJ/mol * (1 mol / 1000 J) (convert kJ to J)
q = 241.2 J
Now, let's calculate the number of moles of solid NaOH that will release this amount of heat when dissolved:
q = ∆Hsoln * n_NaOH
Where:
q is the heat released (in joules) when dissolving NaOH
∆Hsoln is the enthalpy of solution of NaOH (heat released per mole of NaOH dissolved in water)
n_NaOH is the number of moles of NaOH
Rearranging the equation:
n_NaOH = q / ∆Hsoln
n_NaOH = 241.2 J / (-445.1 kJ/mol * (1 mol / 1000 J)) (convert kJ to J)
n_NaOH = 241.2 J / (-445.1 J/mol)
n_NaOH = -0.542 mol
Note: The negative sign indicates that the dissolution of NaOH is exothermic and releases heat.
Therefore, you would need to dissolve approximately 0.542 moles of solid NaOH in the water bath to produce just enough heat to melt the ice.
Please note that the actual value might vary depending on the specific heat capacity of the water bath and any other factors that might affect the heat transfer.
67g of ice is 67/18 = 3.72moles. 6.0kJ/mol means it takes 6.0 kJ to convert 1mole of solid ice into liquid water. so, for 3.72moles requires 3.72x6= 22.333kJ energy input.
the energy released is 445.1kJ/mol from NaOH. so 22.333kJ energy from NaOH must be used/provided..isn't it???..that means we are to find how many mole of NaOH is required to produce 22.333kJ..getting there???...we know that 1mole of NaOH releases 445.1kJ..How many moles are required to release 22.333kJ????
hope that helps..