A calorimeter contains 20.0 of water at 12.5 . When 2.20 of (a substance with a molar mass of 59.0 ) is added, it dissolves via the reaction and the temperature of the solution increases to 27.5 .

Calculate the enthalpy change, , for this reaction per mole of .

Assume that the specific heat and density of the resulting solution are equal to those of water [4.18 and 1.00 ] and that no heat is lost to the calorimeter itself, nor to the surroundings.

Express the change in enthalpy in kilojoules per mole to three significant figures.

You don't have any units. 12.5 what? 2.20 what? etc.

To calculate the enthalpy change per mole of the substance, we can use the equation:

ΔH = q / n

Where:
ΔH is the change in enthalpy
q is the heat absorbed or released in the reaction
n is the number of moles of the substance involved in the reaction

Now let's break down the steps to find the values we need to calculate the enthalpy change:

Step 1: Calculate the heat absorbed or released in the reaction (q)
We can use the equation:

q = mcΔT

Where:
q is the heat absorbed or released
m is the mass of the solution (water + substance)
c is the specific heat of the solution (water)
ΔT is the change in temperature of the solution

Given:
Mass of water (m) = 20.0 g
Change in temperature (ΔT) = 27.5 °C - 12.5 °C = 15.0 °C
Specific Heat of water (c) = 4.18 J/g°C (Since the density and specific heat of the resulting solution are equal to water)

Plugging in the values:

q = (20.0 g + 2.20 g) * 4.18 J/g°C * 15.0 °C

Step 2: Calculate the number of moles of the substance (n)
We can use the equation:

n = mass / molar mass

Given:
Mass of the substance = 2.20 g
Molar mass of the substance = 59.0 g/mol

Plugging in the values:

n = 2.20 g / 59.0 g/mol

Step 3: Calculate the enthalpy change (ΔH)

ΔH = q / n

Plugging in the values from step 1 and step 2:

ΔH = q / n
ΔH = [(20.0 g + 2.20 g) * 4.18 J/g°C * 15.0 °C] / (2.20 g / 59.0 g/mol)

Step 4: Convert the result to kilojoules per mole (kJ/mol)
Divide the answer by 1000 to convert from joules to kilojoules:

ΔH (kJ/mol) = ΔH (J/mol) / 1000

Performing the calculations will give you the enthalpy change per mole of the substance. Make sure to round the answer to three significant figures, as specified in the question.