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. The total heat capacity of the calorimeter and solution is 448 J/°C. The observed increase in temperature is 21.1 °C at a constant pressure of one atm. Using these data, calculate the standard enthalpy of reaction.
-247 KJ/mol
q = Ccal x delta T
dHrxn/g Zn = q/2.50
dHrxn/mol Zn = (q/2.50) x (atomic mass Zn/mol) = ?
To calculate the standard enthalpy of reaction, we can use the equation:
ΔH_rxn = q_rxn / n
where ΔH_rxn is the standard enthalpy of reaction, q_rxn is the heat released or absorbed by the reaction, and n is the number of moles of the reactant.
First, let's calculate the heat released or absorbed by the reaction (q_rxn).
We can use the equation:
q_rxn = -CΔT
where q_rxn is the heat released or absorbed by the reaction, C is the total heat capacity of the calorimeter and solution, and ΔT is the change in temperature.
Given:
C = 448 J/°C
ΔT = 21.1 °C
Substituting the given values into the equation, we can calculate q_rxn:
q_rxn = -CΔT
q_rxn = -(448 J/°C × 21.1 °C)
q_rxn = -9,452.8 J
The negative sign indicates that heat is released by the reaction.
Next, let's calculate the number of moles of zinc (n).
The molar mass of zinc (Zn) is 65.38 g/mol.
Given:
Mass of zinc (Zn) = 2.50 g
Using the equation:
n = Mass / Molar mass
n = 2.50 g / 65.38 g/mol
n = 0.0382 mol
Now, we can substitute the values of q_rxn and n into the equation to calculate the standard enthalpy of reaction:
ΔH_rxn = q_rxn / n
ΔH_rxn = -9,452.8 J / 0.0382 mol
ΔH_rxn ≈ -247,168 J/mol
Therefore, the standard enthalpy of reaction is approximately -247,168 J/mol.
To calculate the standard enthalpy of reaction, we can use the formula:
ΔH = q / n
where ΔH is the standard enthalpy change, q is the heat released or absorbed, and n is the number of moles of the limiting reactant.
First, let's calculate the heat released (q) using the formula:
q = m × C × ΔT
where m is the mass of the limiting reactant, C is the heat capacity, and ΔT is the change in temperature.
In this case, the mass of the limiting reactant is the mass of zinc (2.50 g). The heat capacity is given as 448 J/°C, and the change in temperature is 21.1 °C.
Substituting these values into the equation, we get:
q = (2.50 g) × (448 J/°C) × (21.1 °C)
Next, we need to calculate the number of moles of the limiting reactant, which is zinc. To do this, we can use the molar mass of zinc (65.38 g/mol):
n = m / M
where n is the number of moles, m is the mass, and M is the molar mass.
Substituting the values, we get:
n = (2.50 g) / (65.38 g/mol)
Now, we can substitute the values of q and n into the formula for ΔH:
ΔH = q / n
Calculating this will give us the standard enthalpy of reaction.