Consider the following reaction

AgNO3 (aq) + NaCl (aq) → AgCl (s) +
NaNO3 (aq) DH = -66 kJ
Suppose that 100.0 mL of 0.100M AgNO3 is added to 200.0 mL of 0.100 M NaCl in a coffee
cup calorimeter. Assuming that the initial temperature of the solution is 25.000C calculate the
final temperature of the solution. You may assume that the specific heat capacity of the solution
is 4.18 J/g 0C and that the density of the solution is 1.00 g/mL. Also assume that the heat
capacity of the cup itself and the precipitate is negligible.

You will have 300 mL of solution and 0.01 mol of AgCl.

q = 66,000 = mass H2O x specific heat H2O x (Tfinal-Tinitial).
Solve for Tf.

To calculate the final temperature of the solution, we'll use the equation:

q = mcΔT

Where:
q = heat transferred
m = mass of the solution
c = specific heat capacity of the solution
ΔT = change in temperature

Step 1: Calculate the moles of AgNO3 and NaCl

Given:
Volume of AgNO3 = 100.0 mL
Concentration of AgNO3 = 0.100 M

Step 1.1: Calculate the moles of AgNO3
Volume (in liters) = 100.0 mL / 1000 = 0.100 L
Moles of AgNO3 = Concentration x Volume
= 0.100 M x 0.100 L
= 0.0100 moles

Step 1.2: Calculate the moles of NaCl
Volume of NaCl = 200.0 mL
Concentration of NaCl = 0.100 M

Volume (in liters) = 200.0 mL / 1000 = 0.200 L
Moles of NaCl = Concentration x Volume
= 0.100 M x 0.200 L
= 0.0200 moles

Step 2: Find the limiting reactant
To find the limiting reactant, we compare the moles of AgNO3 and NaCl. The reactant with fewer moles will be the limiting reactant.

From Step 1.1, we have 0.0100 moles of AgNO3.
From Step 1.2, we have 0.0200 moles of NaCl.

Since AgNO3 has fewer moles, it is the limiting reactant.

Step 3: Calculate the heat transferred (q)
Given: DH = -66 kJ
We need to convert it to Joules.

1 kJ = 1000 J

DH = -66 kJ x 1000 J/kJ
= -66,000 J

The heat transferred (q) is -66,000 J since the reaction is exothermic.

Step 4: Calculate the mass of the solution
Given: Density of the solution = 1.00 g/mL
Volume of the solution = Volume of AgNO3 + Volume of NaCl
= 100.0 mL + 200.0 mL
= 300.0 mL

Mass of the solution = Density x Volume
= 1.00 g/mL x 300.0 mL
= 300.0 g

Step 5: Calculate the change in temperature (ΔT)
q = mcΔT

Rearranging the equation:
ΔT = q / (mc)

Specific heat capacity of the solution = 4.18 J/g°C

ΔT = -66,000 J / (300.0 g x 4.18 J/g°C)
= -49.699 °C

Step 6: Calculate the final temperature
Final temperature = Initial temperature + ΔT
= 25.000 °C + (-49.699 °C)
= -24.699 °C

Since the resulting temperature is negative, and assuming no heat is lost to the surroundings, the final temperature of the solution would be 0 °C.

To calculate the final temperature of the solution, we can use the principle of heat exchange. The heat released by the reaction can be calculated using the enthalpy change (ΔH) and the moles of reactants.

Step 1: Calculate the moles of AgNO3 and NaCl
First, we need to determine the moles of AgNO3 and NaCl present in the solution. We can use the given volumes and concentrations:
Volume of AgNO3 = 100.0 mL = 0.100 L
Concentration of AgNO3 = 0.100 M
Moles of AgNO3 = Volume × Concentration = 0.100 L × 0.100 mol/L = 0.010 mol

Volume of NaCl = 200.0 mL = 0.200 L
Concentration of NaCl = 0.100 M
Moles of NaCl = Volume × Concentration = 0.200 L × 0.100 mol/L = 0.020 mol

Step 2: Calculate the heat released by the reaction
The enthalpy change (ΔH) for the reaction is given as -66 kJ. However, we need to convert it to joules to match the units of heat capacity later on.
ΔH = -66 kJ = -66,000 J

Step 3: Calculate the total mass of the solution
To calculate the total mass of the solution, we need to consider both the mass of the AgNO3 solution and the NaCl solution. We can assume the density of the solution is 1.00 g/mL, and since the total volume is 300.0 mL, the total mass will be:
Total mass of solution = Density × Volume = 1.00 g/mL × 300.0 mL = 300.0 g

Step 4: Calculate the heat capacity of the solution
The heat capacity (C) of the solution is given as 4.18 J/g°C. To find the total heat capacity of the solution, we multiply it by the total mass of the solution:
Heat capacity of the solution = Total mass × Heat capacity = 300.0 g × 4.18 J/g°C = 1254 J/°C

Step 5: Apply the principle of heat exchange
According to the principle of heat exchange, the heat released by the reaction (q) is equal to the heat absorbed by the solution:
q = m × C × ΔT

Where:
q = heat released by the reaction = -66,000 J
m = mass of the solution = 300.0 g
C = heat capacity of the solution = 1254 J/°C
ΔT = change in temperature

Solving for ΔT:
-66,000 J = 300.0 g × 1254 J/°C × ΔT
ΔT = -66,000 J / (300.0 g × 1254 J/°C)
ΔT ≈ -0.174 °C

Step 6: Calculate the final temperature
The final temperature can be found by subtracting the change in temperature from the initial temperature of the solution:
Final temperature = Initial temperature + ΔT
Final temperature ≈ 25.000 °C - 0.174 °C
Final temperature ≈ 24.826 °C

Therefore, the final temperature of the solution is approximately 24.826 °C.