The molar heat of solution of NaOH is -445.1KJ/mol. in a certain experiment,5g of NaOH is completely dissolved in 1L of water at 20°C in foam cup calorimeter. Assuming no heat loss, calculate Tf?

To calculate the final temperature (Tf) of the solution, we can use the equation:

q = m × C × ΔT

Where:
q = heat gained or lost by the solution (in this case, it will be negative since heat is lost)
m = mass of the solution (in this case, it is the mass of water + mass of NaOH)
C = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature (Tf - 20°C)

First, let's calculate the mass of the solution:
Mass of water = volume × density = 1 L × 1 g/mL = 1000 g
Mass of NaOH = 5 g

Total mass of the solution = mass of water + mass of NaOH = 1000 g + 5 g = 1005 g

Next, let's calculate the heat lost by the solution:
q = -445.1 kJ/mol × (1 mol NaOH / 40.0 g NaOH) × (5 g NaOH / 1 mol NaOH) = -55.6375 kJ

Since 1 kJ = 1000 J, we convert the heat to joules:
q = -55.6375 kJ × 1000 J/kJ = -55637.5 J

Now, let's calculate the change in temperature:
q = m × C × ΔT
-55637.5 J = 1005 g × 4.18 J/g°C × (Tf - 20°C)

Simplifying the equation:
-55637.5 J = 4198.5 g°C × (Tf - 20°C)
-55637.5 J = 4198.5 g°C × Tf - 83970 g°C
4198.5 g°C × Tf = -55637.5 J + 83970 g°C
4198.5 g°C × Tf = 28332.5 g°C
Tf = 28332.5 g°C / 4198.5 g°C
Tf ≈ 6.75°C

Therefore, the final temperature (Tf) of the solution is approximately 6.75°C.