In a coffee cup calorimeter, 50.0 mL of 0.100 M
AgNO3 and 50.0 mL of 0.100 M HCl are mixed to yield
the following reaction:
Ag+ (aq) + Cl- (aq) -----------------> AgCl (s)
The two solutions were initially at 22.60 °C, and the final
temperature is 23.40 °C. Calculate the heat that
accompanies this reaction in kJ/mol of AgCl formed.
Assume that the combined solution has a mass of 100.0 g
and a specific heat of 4.18 J/g°C.
q rxn in J = mass soln x specific heat soln x delta T.
q rxn in kJ/mol = q rxn/0.005 = ?
(.005 comes from M x L = 0.1M x 0.05 L)
JKNIN
To calculate the heat that accompanies this reaction in kJ/mol of AgCl formed, we need to use the equation:
q = m * c * ΔT
where:
- q is the heat released or absorbed (in Joules)
- m is the mass of the solution (in grams)
- c is the specific heat capacity of the solution (in J/g°C)
- ΔT is the change in temperature (in °C)
Step 1: Calculate the mass of the solution.
Given that the combined solutions have a mass of 100.0 g, the mass of the solution is 100.0 g.
Step 2: Calculate the change in temperature (ΔT)
ΔT = Tfinal - Tinitial
ΔT = 23.40 °C - 22.60 °C
ΔT = 0.8 °C
Step 3: Calculate the heat released or absorbed (in Joules)
q = m * c * ΔT
q = 100.0 g * 4.18 J/g°C * 0.8 °C
q = 334.4 J
Step 4: Convert the heat to kilojoules (kJ)
1 kJ = 1000 J
q (kJ) = 334.4 J / 1000
q (kJ) = 0.3344 kJ
Step 5: Calculate the moles of AgCl formed
Since the reaction is a 1:1 ratio between Ag+ and Cl-, the moles of AgCl formed will be equal to the moles of AgNO3 used.
moles of AgNO3 = volume (L) * concentration (mol/L)
moles of AgNO3 = 0.050 L * 0.100 mol/L
moles of AgNO3 = 0.005 mol
Step 6: Calculate the heat per mole of AgCl formed
heat per mole of AgCl formed = q (kJ) / moles of AgCl
heat per mole of AgCl formed = 0.3344 kJ / 0.005 mol
heat per mole of AgCl formed = 66.88 kJ/mol
Therefore, the heat that accompanies this reaction is 66.88 kJ/mol of AgCl formed.
To calculate the heat that accompanies the reaction in kJ/mol of AgCl formed, we can use the equation:
q = m * c * ΔT
where:
q is the heat energy transferred in J,
m is the mass of the solution in g,
c is the specific heat capacity of the solution in J/g°C, and
ΔT is the change in temperature in °C.
First, let's calculate the mass of the solution. We are given that the combined solution has a mass of 100.0 g.
Next, let's calculate the change in temperature. It is the final temperature minus the initial temperature.
ΔT = 23.40 °C - 22.60 °C = 0.80 °C
Now, we can calculate the heat energy transferred (q).
q = m * c * ΔT
= 100.0 g * 4.18 J/g°C * 0.80 °C
= 334.4 J
To convert from joules (J) to kilojoules (kJ), we divide by 1000.
q = 334.4 J ÷ 1000
= 0.3344 kJ
Now, we need to find the number of moles of AgCl formed.
To do this, we can use the balanced equation:
Ag+ (aq) + Cl- (aq) → AgCl (s)
The equation shows that 1 mole of Ag+ reacts with 1 mole of Cl- to form 1 mole of AgCl.
Since the initial concentrations of AgNO3 and HCl are both 0.100 M, and the volumes of the solutions are both 50.0 mL (or 0.050 L), the moles of Ag+ and Cl- are both calculated as follows:
moles of Ag+ and Cl- = initial concentration * volume
= 0.100 M * 0.050 L
= 0.005 mol
Therefore, the number of moles of AgCl formed is also 0.005 mol, as Ag+ and Cl- react in a 1:1 ratio.
Finally, we divide the heat energy transferred by the number of moles of AgCl formed to calculate the heat per mole of AgCl formed.
heat per mole of AgCl formed = q / moles of AgCl
= 0.3344 kJ / 0.005 mol
= 66.88 kJ/mol
Thus, the heat that accompanies the reaction in kJ/mol of AgCl formed is 66.88 kJ/mol.