Question

When 9.85 grams of potassium hydroxide (KOH) are dissolved in 150.0 grams of water at 25.0 ∘ C in an insulated container, the temperature of the water increases to 40.1 ∘C. Assuming that the specific heat of the solution is 4.184 J/ (g ∘C) and that no heat is gained or lost by the container, what is the ΔH of solution of KOH in kJ/mol ?

Answer 1

The ∆H of solution of KOH is 53.93 kJ/mol. To find this, the energy absorbed by the water due to the dissolved KOH was calculated using the mass of water, the specific heat capacity, and the temperature change. Then, the number of moles of KOH was used to determine the ∆H per mole.

Step-by-step explanation:

To calculate the ∆H of solution of KOH in kJ/mol, we first determine the amount of energy absorbed by the water when the KOH dissolves. We can use the formula q = mc∆T, where m is the mass of the water, c is the specific heat capacity, and ∆T is the change in temperature.

First, we compute the energy change:

Mass of water (m) = 150.0 g

Specific heat capacity of water (c) = 4.184 J/(g°C)

Change in temperature (∆T) = 40.1 °C - 25.0 °C = 15.1 °C

Using these values, the energy absorbed (q) is calculated as follows: q = mc∆T = (150.0 g)(4.184 J/g°C)(15.1 °C) = 9471.84 J

Now, we convert the energy absorbed into kilojoules by dividing by 1000 (since 1 kJ = 1000 J):

q = 9471.84 J / 1000 = 9.47184 kJ

To find the ∆H of solution per mole, we first calculate the number of moles of KOH.

The molar mass of KOH is 39.10 (K) + 16.00 (O) + 1.01 (H) = 56.11 g/mol.

Therefore, the number of moles of 9.85 g of KOH is given by:

moles of KOH = 9.85 g / 56.11 g/mol = 0.1756mol

Finally, to find the ∆H of solution per mole, we divide the energy change by the number of moles:

∆H of solution = 9.47184 kJ / 0.1756 mol = 53.93 kJ/mol

The ∆H of solution of KOH is 53.93 kJ/mol, and since the temperature increased upon dissolving, the reaction is exothermic.

Answer 2

To find the ΔH of solution for KOH, we calculate the heat change due to temperature increase when KOH is dissolved in water and then divide it by the number of moles of KOH to get the enthalpy change per mole in kJ/mol. ΔH = 9.47484 kJ /(9.85 g / 56.11 g/mol)

Step-by-step explanation:

When 9.85 grams of potassium hydroxide (KOH) are dissolved in 150.0 grams of water, causing the temperature of the solution to increase from 25.0 °C to 40.1 °C, we can calculate the heat change (q) associated with the dissolution process. The formula for calculating the heat evolved or absorbed during a process is q = mCΔT, where 'm' is the mass of the solution, 'C' is the specific heat capacity, and 'ΔT' is the change in temperature.

q = mass of water × specific heat capacity × change in temperature
q = 150.0 g × 4.184 J/(g°C) × (40.1 °C - 25.0 °C)
q = 150.0 g × 4.184 J/(g°C) × 15.1 °C
q = 9474.84 J

Since 1 kJ = 1000 J, we convert the heat change into kilojoules:
q = 9474.84 J × (1 kJ/1000 J) = 9.47484 kJ

To find the enthalpy change (ΔH) of the solution per mole of KOH, we use the molar mass of KOH, which is 56.11 g/mol:
ΔH = heat change (q)/number of moles of KOH
ΔH = 9.47484 kJ /(9.85 g / 56.11 g/mol)

This gives us the ΔH of solution of KOH in kJ/mol, which quantifies the heat released or absorbed when one mole of a substance dissolves in a solvent.