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.
See your post below. no units.
To calculate the enthalpy change for the reaction per mole of the substance, we can use the formula:
ΔH = q / n
Where:
ΔH is the enthalpy change (in kilojoules per mole),
q is the heat transfer (in joules),
n is the number of moles of the substance involved in the reaction.
First, let's calculate the heat transfer, q. We can use the equation:
q = m * c * ΔT
Where:
q is the heat transfer (in joules),
m is the mass of the water (in grams),
c is the specific heat capacity of water (4.18 J/g·°C),
ΔT is the change in temperature (in °C).
Given data:
Mass of water, m = 20.0 g
Change in temperature, ΔT = (27.5 - 12.5) °C = 15.0 °C
Specific heat capacity, c = 4.18 J/g·°C
Plugging in these values:
q = (20.0 g) * (4.18 J/g·°C) * (15.0 °C)
q = 12540 J
Now, let's calculate the number of moles of the substance, n. We can use the formula:
n = mass / molar mass
Given data:
Mass of substance, mass = 2.20 g
Molar mass of substance = 59.0 g/mol
Plugging in these values:
n = 2.20 g / 59.0 g/mol
n ≈ 0.0373 mol
Finally, we can calculate the enthalpy change, ΔH, using the formula:
ΔH = q / n
Plugging in the values we obtained:
ΔH = 12540 J / 0.0373 mol
ΔH ≈ 336,301.34 J/mol
To express the change in enthalpy in kilojoules per mole to three significant figures, we convert the value to kilojoules and round it:
ΔH ≈ 336.3 kJ/mol
So, the enthalpy change for this reaction per mole of the substance is approximately 336.3 kJ/mol.