To calculate the molar enthalpy of this dilution, we can use the equation:
q = mcΔT
where q is the heat gained or lost by the solution, m is the mass of the solution, c is the specific heat capacity of the solution, and ΔT is the change in temperature.
First, we need to calculate the mass of the solution. The density of water is 1 g/mL, so the mass of 175 mL of water is:
mass of water = density × volume
mass of water = (1 g/mL) × (175 mL)
mass of water = 175 g
Next, we need to calculate the specific heat capacity of the solution. Since the solution is primarily water, we can assume that the specific heat capacity of the solution is the same as that of water, which is 4.18 J/g·°C.
Now, we can calculate the heat gained or lost by the solution, q:
q = (mass of water + mass of sulfuric acid) × c × ΔT
Substituting the given values:
q = (175 g + 49 g) × (4.18 J/g·°C) × (14.9°C - 10.0°C)
q = 224 g × 4.18 J/g·°C × 4.9°C
q = 4645.632 J
Next, we need to convert the heat gained or lost by the solution, q, to kilojoules:
q = 4645.632 J ÷ 1000
q = 4.645632 kJ
Finally, we can calculate the molar enthalpy of the dilution:
moles of sulfuric acid = volume of sulfuric acid × concentration of sulfuric acid
moles of sulfuric acid = 49 mL × (1 L/1000 mL) × 17.8 mol/L
moles of sulfuric acid = 0.8702 mol
molar enthalpy of dilution = heat gained or lost (q) ÷ moles of sulfuric acid
molar enthalpy of dilution = 4.645632 kJ ÷ 0.8702 mol
molar enthalpy of dilution ≈ 5.34 kJ/mol
Therefore, the molar enthalpy of this dilution is approximately 5.34 kJ/mol.
When sulfuric acid dissolves in water, a great deal of heat is given off. The enthalpy change for this process is called the enthalpy of solution. To measure it, 175 mL of water was placed in a coffee-cup calorimeter and chilled to 10oC. Then 49.0 mL of pure sulfuric acid, also at 10.0oC was added, and the mixture was quickly stirred with a thermometer. The temperature rose rapidly to 14.9oC Pure sulfuric acid has a concentration of 17.8 mol/L Calculate the molar enthalpy of this dilution kJ/mol
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