When 1.07E-1 g of Zn(s) combines with 5.64E1 mL of HCl(aq) in a coffee cup calorimeter, all of the zinc reacts, which increases the temperature of the HCl solution from 2.32E1 °C to 2.48E1 °C:
Zn(s) + 2HCl(aq) → ZnCl_2(aq) + H_2(g)
Calculate the enthalpy change of the reaction ΔH°rxn in J/mol. (Assume the volume of the solution doesn't change, density of the solution is 1.00 g/mL and the specific heat capacity of solution is 4.184 J/g°C; the calorimetry constant is assumed to be negligible.)
2. When 2.00 g of calcium metal reacts with 100.00 g of 1.00 M HCl in a coffee-cup calorimeter, the temperature rises from 18.1ºC to 66.8ºC. The heat capacity of the calorimeter apparatus is 131 J/K. Calculate ∆H (in kJ) for the reaction:
Ca(s) + 2HCl(aq) → CaCl2(aq) + H2(g)
Assume the specific heat of the solution is 4.18 J/K∙g.
[Hint: the solution contains all the reactants.]
Why did the chemist open a bakery? Because they wanted to mix some compounds and bake a reaction! Now let's mix some numbers and bake some calculations to find the enthalpy change.
For the first problem, we need to calculate the heat gained or lost by the HCl solution, which can be calculated using the equation:
q = m × C × ΔT
where q is the heat gained/lost, m is the mass of the solution, C is the specific heat capacity of the solution, and ΔT is the change in temperature.
Given that the mass of the HCl solution is 5.64E1 g (which is the same as 5.64 mL due to the density of 1.00 g/mL), the specific heat capacity is 4.184 J/g°C, and the temperature change is 2.48E1°C - 2.32E1°C = 0.16°C, we can substitute these values into the equation:
q = (5.64E1 g) × (4.184 J/g°C) × (0.16°C)
Now, for the number crunching: *drumroll*
q = 37.624 J
Since the reaction involves 1.07E-1 g of Zn, we can calculate the moles of Zn using its molar mass (supplemental joke: Why was Avogadro so rich? Because he was the mole-ionaire!). The molar mass of Zn is 65.38 g/mol.
moles of Zn = (1.07E-1 g) / (65.38 g/mol) = 1.638E-3 mol
Now it's time to calculate the enthalpy change of the reaction ΔH°rxn in J/mol. We can use the equation:
ΔH°rxn = q / moles of Zn
Substituting the values:
ΔH°rxn = (37.624 J) / (1.638E-3 mol)
And the moment of truth:
ΔH°rxn = 2.2976E4 J/mol
For the second problem, we will follow a similar process. First, we need to calculate the heat gained or lost by the HCl solution using the equation:
q = m × C × ΔT
Given that the mass of the HCl solution is 100.00 g, the specific heat capacity is 4.18 J/K∙g, and the temperature change is 66.8ºC - 18.1ºC = 48.7ºC, we can substitute these values into the equation:
q = (100.00 g) × (4.18 J/K∙g) × (48.7ºC)
Calculating further:
q = 20146 J
Since the reaction involves 2.00 g of Ca, we can calculate the moles of Ca using its molar mass. The molar mass of Ca is 40.08 g/mol.
moles of Ca = (2.00 g) / (40.08 g/mol) = 0.0499 mol
Now we can calculate the total heat released or absorbed by the reaction, including the heat absorbed by the calorimeter apparatus. Let's call this ∆H_total.
∆H_total = q + heat capacity of calorimeter
∆H_total = 20146 J + 131 J = 20277 J
Finally, to calculate the enthalpy change of the reaction ∆H in kJ, we divide ∆H_total by the moles of Ca.
∆H = ∆H_total / moles of Ca
∆H = (20277 J) / (0.0499 mol)
Calculating, calculating...
∆H = 4.06E5 J/mol
And converting to kilojoules (kJ):
∆H ≈ 406 kJ
Hope these calculations didn't cause a chemical reaction of confusion!
To calculate the enthalpy change of the reaction (∆H°rxn) in Joules per mole (J/mol), you can use the formula:
∆H°rxn = q / n
Where:
- q is the heat absorbed or released by the reaction in Joules (J)
- n is the number of moles of the limiting reactant (the reactant with the smallest number of moles involved)
Let's calculate the enthalpy change for each problem step by step:
For the first problem:
Step 1: Convert grams to moles for Zn(s) using its molar mass.
Molar mass of Zn = 65.38 g/mol
moles = mass / molar mass
moles of Zn = 1.07E-1 g / 65.38 g/mol
Step 2: Calculate the heat absorbed or released by the reaction (q).
q = mcΔT
m = mass of solution = 5.64E1 mL * 1.00 g/mL = 5.64E1 g
c = specific heat capacity of the solution = 4.184 J/g°C
ΔT = temperature change = 2.48E1 °C - 2.32E1 °C
Step 3: Calculate the number of moles of HCl based on its volume and concentration.
Volume of HCl = 5.64E1 mL = 5.64E1 g (since density = 1.00 g/mL)
Molarity of HCl = 1.00 M
moles of HCl = volume of HCl (in L) * molarity of HCl
Step 4: Determine the limiting reactant and the number of moles involved (n).
From the balanced equation:
Zn(s) + 2HCl(aq) → ZnCl2(aq) + H2(g)
1 mole of Zn reacts with 2 moles of HCl
So, the number of moles of HCl involved = 2 * moles of Zn
Step 5: Calculate ∆H°rxn.
So, q = mcΔT
∆H°rxn = q / n
Plug in the values to calculate ∆H°rxn.
For the second problem:
Step 1: Convert grams to moles for Ca(s) using its molar mass.
Molar mass of Ca = 40.08 g/mol
moles = mass / molar mass
moles of Ca = 2.00 g / 40.08 g/mol
Step 2: Calculate the heat absorbed or released by the reaction (q).
q = mcΔT
m = mass of solution + mass of Ca = 100.00 g + 2.00 g
c = specific heat capacity of the solution = 4.18 J/K∙g
ΔT = temperature change = 66.8°C - 18.1°C
Step 3: Calculate the number of moles of HCl based on its volume and concentration.
Volume of HCl = 100.00 g (since density = 1.00 g/mL)
Molarity of HCl = 1.00 M
moles of HCl = volume of HCl (in L) * molarity of HCl
Step 4: Determine the limiting reactant and the number of moles involved (n).
From the balanced equation:
Ca(s) + 2HCl(aq) → CaCl2(aq) + H2(g)
1 mole of Ca reacts with 2 moles of HCl
So, the number of moles of HCl involved = 2 * moles of Ca
Step 5: Calculate ∆H°rxn.
So, q = mcΔT
∆H°rxn = q / n
Plug in the values to calculate ∆H°rxn in kJ.
To calculate the enthalpy change of a reaction, you can use the formula:
ΔH°rxn = q / n
where ΔH°rxn is the enthalpy change of the reaction in J/mol, q is the heat transferred in J, and n is the number of moles of the limiting reactant.
To solve the first problem, we need to follow the following steps:
Step 1: Calculate the mass of the HCl(aq) solution.
Given volume = 5.64E1 mL = 5.64E1 g (since the density is 1.00 g/mL)
Hence, the mass of the solution is 5.64E1 g.
Step 2: Calculate the heat transferred (q).
q = mcΔT
where m is the mass of the solution and c is the specific heat capacity of the solution.
Given that c = 4.184 J/g°C, ΔT = (2.48E1 - 2.32E1) °C, and m = 5.64E1 g, we can calculate q.
q = (5.64E1 g) * (4.184 J/g°C) * (2.48E1 - 2.32E1) °C
Step 3: Calculate the number of moles of Zn(s).
We need to convert the mass of Zn(s) to moles.
Given that the molar mass of Zn is approximately 65.38 g/mol, we can calculate the number of moles.
moles of Zn(s) = (1.07E-1 g) / (65.38 g/mol)
Step 4: Calculate the enthalpy change of the reaction (ΔH°rxn).
Using the formula ΔH°rxn = q / n, we can plug in the values we have calculated so far.
ΔH°rxn = q / n
ΔH°rxn = [(5.64E1 g) * (4.184 J/g°C) * (2.48E1 - 2.32E1) °C] / [(1.07E-1 g) / (65.38 g/mol)]
Solving this expression will give you the enthalpy change of the reaction (ΔH°rxn) in J/mol.
To solve the second problem, we need to follow similar steps:
Step 1: Calculate the mass of the HCl(aq) solution.
Given that the mass of HCl is 100.00 g, we don't need to make any conversions.
Step 2: Calculate the heat transferred (q).
q = mcΔT
where m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the temperature change.
Given that c = 4.18 J/K∙g, ΔT = (66.8 - 18.1) °C, and m = 100.00 g, we can calculate q.
q = (100.00 g) * (4.18 J/K∙g) * (66.8 - 18.1) °C
Step 3: Calculate the number of moles of Ca(s).
We need to convert the mass of Ca(s) to moles.
Given that the molar mass of Ca is approximately 40.08 g/mol, we can calculate the number of moles.
moles of Ca(s) = (2.00 g) / (40.08 g/mol)
Step 4: Calculate the enthalpy change of the reaction (ΔH°rxn).
Using the formula ΔH°rxn = q / n, we can plug in the values we have calculated so far.
ΔH°rxn = q / n
ΔH°rxn = [(100.00 g) * (4.18 J/K∙g) * (66.8 - 18.1) °C] / [(2.00 g) / (40.08 g/mol)]
Solving this expression will give you the enthalpy change of the reaction (ΔH°rxn) in J/mol.