A calorimeter contains 32.0mL of water at 13.0∘C . When 2.30g of X (a substance with a molar mass of 82.0g/mol is added, it dissolves via the reaction
X(s)+H2O(l)�¨X(aq)
and the temperature of the solution increases to 30.0∘C .
Calculate the enthalpy change, ĢH for this reaction per mole of X .
Assume that the specific heat of the resulting solution is equal to that of water [4.18 J/(g⋅∘C) ], that density of water is 1.00 g/mL , and that no heat is lost to the calorimeter itself, nor to the surroundings.
Do you want enthalpy/grams or enthalpy/mol. Most prefer it to be kJ/mol.
q = g H2O x specific heat H2O x (Tfinal-Tinitial)
That gives you q/2.30g X = ? J/g
If you want J/mol it is J/g x 82.0 = ? J/mol. You can change that to kJ/mol if you wish.
To calculate the enthalpy change (∆H) for the reaction per mole of X, we can use the equation:
∆H = q / moles of X
Where q is the heat transferred and moles of X is the amount of substance X.
First, we need to calculate the heat transferred (q) using the equation:
q = m × c × ∆T
Where:
- m is the mass of the water and X
- c is the specific heat capacity of water (since the specific heat of the resulting solution is assumed to be the same as water)
- ∆T is the change in temperature
To determine the mass (m) in the equation, we can use the density of water to find the mass of water and subtract it from the total mass of the solution.
1. Calculate the mass of water:
density = mass / volume
mass_water = density_water × volume_water
Given that the density of water is 1.00 g/mL and the volume of water is 32.0 mL:
mass_water = 1.00 g/mL × 32.0 mL = 32.0 g
2. Calculate the mass of X:
mass_X = 2.30 g
3. Calculate the total mass of the solution:
mass_solution = mass_water + mass_X
4. Calculate the heat transferred (q):
q = mass_solution × c × ∆T
Given:
c = 4.18 J/(g⋅∘C)
∆T = (final temperature - initial temperature) = 30.0∘C - 13.0∘C = 17.0∘C
Substituting the values:
q = (mass_water + mass_X) × c × ∆T
5. Calculate moles of X:
moles_X = mass_X / molar mass_X
Given:
molar mass_X = 82.0 g/mol
mass_X = 2.30 g
Substituting the values:
moles_X = 2.30 g / 82.0 g/mol
6. Calculate ∆H:
∆H = q / moles_X
Substituting the calculated values:
∆H = q / (2.30 g / 82.0 g/mol)
By evaluating this equation, you can determine the enthalpy change (∆H) for this reaction per mole of X.