A calorimeter contains 16.0ml of water at 15.0degrees celsius. When 1.60g of X(a substance with a molar mass of 46.0g/mol) is added, it dissolves via the reaction
X(s)+H20(l)->X(aq)
and the temperature of the solution increases to 25.0degrees celsius.
Calculate the enthalpy change for this reaction per mole of X.
Assume that the specific heat and density of the resulting solution are equal to those of water [4.18j/g*C and 1.00g/ml] and that no heat is lost to the calorimeter itself, nor to the surroundings.
find the heat evolved:
heatevolved=totalmass*specificheat*deltatemp
Now, divide that heat by the number of moles of X you had, and you have the enthalpy change per mole.
To calculate the enthalpy change per mole of X, we need to use the equation:
ΔH = q / n
Where:
ΔH is the enthalpy change per mole of X (in J/mol)
q is the heat absorbed by the solution (in J)
n is the number of moles of X
To calculate q, we need to use the equation:
q = m × c × ΔT
Where:
q is the heat absorbed by the solution (in J)
m is the mass of the solution (in g)
c is the specific heat capacity of the solution (in J/g°C)
ΔT is the change in temperature (in °C)
First, let's calculate the mass of the solution.
We know that the density of the solution is equal to that of water, which is 1.00 g/ml. Therefore, the mass of the solution is equal to its volume multiplied by its density.
Volume of the solution = volume of water = 16.0 ml
Density of the solution = 1.00 g/ml
Mass of the solution = volume of the solution × density of the solution
Mass of the solution = 16.0 ml × 1.00 g/ml
Mass of the solution = 16.0 g
Next, we can calculate ΔT by subtracting the initial temperature from the final temperature:
ΔT = final temperature - initial temperature
ΔT = 25.0°C - 15.0°C
ΔT = 10.0°C
Now, we can calculate q using the equation:
q = m × c × ΔT
q = 16.0 g × 4.18 J/g°C × 10.0°C
q = 668.8 J
Finally, we can calculate the enthalpy change per mole of X using the equation:
ΔH = q / n
We know that the mass of X is 1.60 g and its molar mass is 46.0 g/mol. Therefore, we can calculate the number of moles of X:
n = mass of X / molar mass of X
n = 1.60 g / 46.0 g/mol
n = 0.0348 mol
Now we can calculate the enthalpy change per mole of X:
ΔH = 668.8 J / 0.0348 mol
ΔH ≈ 19,201 J/mol
So, the enthalpy change for this reaction per mole of X is approximately 19,201 J/mol.