Question

Sunita performed a calorimetry experiment to determine ΔH (enthalpy change) for the dissolving of potassium permanganate in water according to the reaction:

KMnO4(s) → K+ (aq) + MnO4- (aq)

Her calorimeter contained 50.0 g of water at an initial temperature of 20.4 °C. After adding 4.23 g of KMnO4, the temperature fell to 16.1°C. The specific heat capacity of the solution was 4.18 J/g°C. What value of ΔH will Sunita obtain from her data in J/g and in J/mol?

A) ΔH = -2424.21 J/g, ΔH = -154.75 kJ/mol
B) ΔH = -154.75 J/g, ΔH = -2424.21 kJ/mol
C) ΔH = -2143.36 J/g, ΔH = -136.28 kJ/mol
D) ΔH = -136.28 J/g, ΔH = -2143.36 kJ/mol

Answer 1

The calculated enthalpy change per gram of potassium permanganate is 212.58 J/g and per mole is 33.59 kJ/mol. No provided option matches the calculated results, indicating a discrepancy.

Step-by-step explanation:

To calculate the enthalpy change ΔH for the dissolution of potassium permanganate in water, we need to use the heat capacity of the solution and the mass and temperature change of the water. We know that the specific heat capacity is 4.18 J/g°C, the mass of the water is 50.0 g, and the temperature change is 20.4°C - 16.1°C = 4.3°C. The heat absorbed or released by the solution (q) can be calculated using the formula q = m × c × ΔT.

First, calculate the amount of heat (q) in joules:

q = 50.0 g × 4.18 J/g°C × 4.3°C = 898.7 J

Since the temperature decreased, the dissolution process is endothermic and the heat is absorbed by the solution. Therefore, ΔH is positive:

ΔH = +898.7 J

To find the ΔH per gram of KMnO4, divide the heat by the mass of KMnO4:

ΔH per gram = 898.7 J / 4.23 g = 212.58 J/g

Next, calculate the molar enthalpy change using the molar mass of KMnO4, which is approximately 158.04 g/mol:

ΔH per mole = 212.58 J/g × 158.04 g/mol = 33,591.55 J/mol or 33.59 kJ/mol

The closest answer in the given options is:

ΔH = -136.28 J/g, ΔH = -2143.36 kJ/mol

However, this doesn't match the calculated results, which suggests there could be an error either in the calculation (such as forgetting to consider the sign) or in the provided options.