A 2.50-g sample of powdered zinc is added to 100.0 mL of a 2.00-M aqueous solution of hydrobromic acid in a calorimeter with a total heat capacity of 448 J/K. The observed increase in temperature is 21.1 K at a constant pressure of one bar. Using these data, calculate the standard enthalpy of reaction. Zn(s) + 2HBr(aq) ---> ZnBr2(aq) + H2(g)
heat emitted (absorbed by the calorimeter) = q
I am under the impression that 448 J/K is the Ccal WITHOUT the added water. You will need to adjust the answer if that isn't the case and 448 J/K is the total heat capacity of the SYSTEM.
Q = [mass H2O x specific heat H2O x 21.1] + [Ccal x 21.1] = ?
Then q/gram is q/2.5g Zn and q/mol = q/g x 65.39. You can change to kJ/mol which is the way they usually are reported.
How do you convert that to kJ/mol
To calculate the standard enthalpy of the reaction, we need to use the equation:
ΔH = q / n
Where:
ΔH is the change in enthalpy (standard enthalpy of reaction)
q is the heat absorbed or released by the system (calorimeter)
n is the number of moles of the limiting reactant (Zinc in this case)
Step 1: Calculate the heat absorbed or released by the system, q
q = C * ΔT
Where:
q is the heat absorbed or released by the system
C is the heat capacity of the calorimeter
ΔT is the change in temperature
q = 448 J/K * 21.1 K
q = 9448.8 J (Joules)
Step 2: Calculate the number of moles of Zinc (limiting reactant)
Given:
Mass of Zinc = 2.50 g
Molar mass of Zinc (Zn) = 65.38 g/mol
Number of moles of Zinc = Mass / Molar Mass
Number of moles of Zinc = 2.50 g / 65.38 g/mol
Number of moles of Zinc = 0.038 mol
Step 3: Calculate the standard enthalpy of reaction, ΔH
ΔH = q / n
ΔH = 9448.8 J / 0.038 mol
ΔH ≈ 248,900 J/mol (Joules per mole)
Note: Since the units of heat capacity, mass, and molar mass are in Joules per Kelvin (J/K), grams (g), and grams per mole (g/mol) respectively, the final result ΔH is also in Joules per mole (J/mol).
To calculate the standard enthalpy of reaction (ΔH°), we need to use the heat capacity of the calorimeter (C), the observed increase in temperature (ΔT), and the amount of substance reacting.
First, let's calculate the heat transferred during the reaction using the formula:
q = C * ΔT
In this case, the heat transferred (q) is the negative of the change in enthalpy (ΔH) because the reaction is exothermic. Therefore:
-ΔH = q = C * ΔT
Now we need to find the molar quantity of zinc reacting. We can do this using the mass of zinc and its molar mass.
Molar mass of zinc (Zn) = 65.38 g/mol
To convert grams to moles, we use the following formula:
moles = mass / molar mass
moles of zinc = 2.50 g / 65.38 g/mol
Next, we need to determine the amount of heat per mole of zinc reacting. This is done by dividing the heat transferred by the number of moles of zinc.
ΔH per mole of zinc = q / moles of zinc
Finally, we need to relate this to the stoichiometry of the reaction. The balanced equation shows that 1 mole of zinc reacts with 2 moles of hydrobromic acid to form 1 mole of zinc bromide and 1 mole of hydrogen gas.
Therefore, the standard enthalpy of reaction (ΔH°) can be calculated by dividing the heat per mole of zinc by the stoichiometric coefficient of zinc in the balanced equation.
ΔH° = (ΔH per mole of zinc) / balanced coefficient of zinc
Now you can plug in the values and calculate ΔH°.