In a polystyrene calorimeter, 8.0 g of ammonium nitrate is placed in 50.0 ml of water. the initial temperature of the water is 22.9 °c. the temperature of the solution drops to 12.4 °c. assume the specific heat of the solution is 1.00 cal/g·°c. which of the statements below is true?
the reaction is endothermic with a heat of solution of approximately 609 cal/mol. the reaction is exothermic with a heat of solution of approximately 6.09 kcal/mol. the reaction is endothermic with a heat of solution of approximately 6.09 kcal/mol
the reaction is endothermic with a heat of solution of approximately 609 kcal/mol.

The reaction is endothermic with a heat of solution of approximately 6.09 kcal/mol

Explanation:

First of all we will calculate the number of moles of ammonium nitrate.

Number of moles = mass/ molar mass

Number of moles = 8.0 g/ 80.0 g/mol

Number of moles = 0.1 mol

Formula:

q₁ + q₂ = 0 (1)

q₂

q₂ = mcΔT

ΔT = 12.4°C - 22.9°C

ΔT = -10.5°C

m = 8 g + 50 g = 58 g

c = 1.0 cal/g.°C

q₂ = mcΔT

q₂ = 58 g × 1.0 cal/g.°C ×-10.5°C

q₂ = -609 cal

q₁

q₁ = nΔH(sol)

q₁ = 0.1 mol × ΔH(sol)

Now we will put the values of q₁  and q₂ in equation 1

q₁ + q₂ = 0

0.1 mol × ΔH(sol) + ( -609 cal) = 0

ΔH(sol)  = +609 cal / 0.1 mol

ΔH(sol)  = +6090 cal/mol

cal to kcal

6090/1000

ΔH(sol)  = +6.09 kcal/mol