A calorimeter contains 21.0 mL of water at 14.0 degreesC. When 1.90 g of X (a substance with a molar mass of 70.0 g/mol) is added, it dissolves via the reaction
X(s)+H_2O(l)reacts to make X(aq)
and the temperature of the solution increases to 28.5degreesC.
Calculate the enthalpy change, Delta H, for this reaction per mole of X.
Assume that the specific heat and density of the resulting solution are equal to those of water [4.18 J/degrees C) and 1.0g/mL] and that no heat is lost to the calorimeter itself, nor to the surroundings.
To calculate the enthalpy change (ΔH) for the reaction per mole of X, we need to use the equation:
ΔH = q / n
where:
ΔH is the enthalpy change per mole of X
q is the heat exchanged during the reaction
n is the number of moles of X
To find the heat exchanged during the reaction (q), we can use the equation:
q = m × c × ΔT
where:
q is the heat exchanged
m is the mass of the solution in grams
c is the specific heat capacity of water (assumed to be equal to the solution's specific heat capacity – 4.18 J/g°C)
ΔT is the change in temperature (final temperature - initial temperature)
First, let's determine the mass of the solution. We know that the density of the solution is equal to the density of water, which is 1.0 g/mL. The volume of water is given as 21.0 mL, so the mass of the water is:
mass = volume × density
mass = 21.0 mL × 1.0 g/mL
mass = 21.0 g
Since the specific heat capacity of the solution is equivalent to the specific heat capacity of water, we can use 4.18 J/g°C for the value of c.
ΔT is the change in temperature, which is 28.5°C - 14.0°C = 14.5°C.
Now we can calculate the heat exchanged during the reaction (q):
q = mass × c × ΔT
q = 21.0 g × 4.18 J/g°C × 14.5°C
q = 1372.37 J
Next, we need to find the number of moles of X. To do this, we'll use the given mass (1.90 g) and the molar mass of X (70.0 g/mol).
n = mass / molar mass
n = 1.90 g / 70.0 g/mol
n ≈ 0.02714 mol
Finally, we can calculate the enthalpy change (ΔH) per mole of X using:
ΔH = q / n
ΔH = 1372.37 J / 0.02714 mol
ΔH ≈ 50594 J/mol
So, the enthalpy change (∆H) for this reaction per mole of X is approximately 50594 J/mol.