Question

A 4.00 m solution of KCl was prepared using 1.00 kg of water at 25.0 ∘C. Once the solid had all dissolved, the temperature of the solution was 12.3 ∘C. Calculate the heat of solution, ΔHsoln, of KCl. Assume that the specific heat of the solution is identical to that of water, 4.18 J/(g⋅∘C).

Answer 1

The heat of solution, ΔHsoln, of KCl can be calculated using the formula: ΔHsoln = q / n. The specific heat of the solution is assumed to be the same as water. In this case, the heat of solution is approximately -993.28 kJ/mol.

Step-by-step explanation:

The heat of solution, ΔHsoln, of KCl can be calculated using the formula:

ΔHsoln = q / n

Where q is the amount of heat transferred and n is the number of moles of solute. In this case, the mass of water is given as 1.00 kg, which can be converted to grams by multiplying by 1000:

1.00 kg * 1000 g/kg = 1000 g

Assuming the specific heat of the solution is the same as water, we can use the equation:

q = m * C * ΔT

Where m is the mass, C is the specific heat, and ΔT is the temperature change:

ΔT = final temperature - initial temperature = 12.3 °C - 25.0 °C = -12.7 °C

Substituting the given values:

q = 1000 g * 4.18 J/(g⋅∘C) * -12.7 °C = -53260 J

Converting to kilojoules:

-53260 J / 1000 J/kJ = -53.26 kJ

To find the number of moles of KCl, we can use the formula:

n = m/M

Where m is the mass and M is the molar mass.

The molar mass of KCl is 74.55 g/mol. Substituting the values:

n = 4.00 m / 74.55 g/mol ≈ 0.0536 mol

Finally, substituting the values back into the formula for ΔHsoln:

ΔHsoln = -53.26 kJ / 0.0536 mol ≈ -993.28 kJ/mol

Answer 2

The heat of solution of KCl is 17.2 kJ

Step-by-step explanation:

Step 1: given data

We have a 4m solution of KCl prepared in 1kg of water

⇒molality = number of moles / kg of solute

⇒ in this case it means 4 moles / 1kg of water = 4

Specific heat of water = 4.18J/g °C

KCl has a molar mass of 75.55g/mole

Step 2: calculate mass and change of temperature

Heat of solution = mass (g) * specific heat (j/g °C) * change of temperature

mass of KCl we can calculate through te formula mass = moles * Molar mass

⇒ m(KCl) = 4 moles * 74.55g/mole = 298.2g

⇒ total mass = 298.2g of KCl + 1000g of water = 1298.2g

Change of temperature = Final temperature T2 - initial temperature T1 = 12.3°C - 25°C = -12.7 °C ⇔ this means the temperature reduces with 12.7 °C

Step3 : calculating heat of solution

heat of solution (q) = mass * specific heat * change in temperature

q = (1298g) * (4.18J/g °C ) * (-12.7) = -68910 J = -68.910 kJ

We will use the positve value of this

ΔH = q / moles = 68.91 kJ / 4 moles = 17.2 kJ

The heat of solution of KCl is 17.2 kJ