A 100.0 mL sample of 0.300 M Ca(OH)2 is mixed with 100.0 mL of 0.700 M H3PO4 in a coffee cup calorimeter. If both solutions were initially at 35.0 degrees celsius and the resulting solution had a temperature that was recorded at 39.7 degrees celsius, determine the delta Hrxn in units of kj/mol. Assume the solution has the same specific heat and density as water.
No table is given for standard enthalpy of the solutions so where do I even start then?
To determine the enthalpy change (ΔHrxn) for the reaction between Ca(OH)2 and H3PO4, you can use the concept of calorimetry and the equations involving heat transfer.
Here are the steps to calculate ΔHrxn:
1. Calculate the heat transfer in the reaction using the equation: q = mcΔT
- Define q as the heat transfer (in joules).
- Define m as the mass (in grams) of the resulting solution. Given that the total volume is 200.0 mL and the density of water is approximately 1 g/mL, the mass can be determined as 200.0 g.
- Define c as the specific heat capacity of water (assumed to be the same as the solution), which is approximately 4.184 J/g°C.
- Determine ΔT, the change in temperature, which is the final temperature minus the initial temperature. In this case, ΔT = 39.7°C - 35.0°C.
Therefore, q = (200.0 g) × (4.184 J/g°C) × (39.7°C - 35.0°C).
2. Convert the calculated heat transfer (q) from joules to kilojoules by dividing by 1000: q = q / 1000.
3. Calculate the number of moles of limiting reactant (Ca(OH)2 or H3PO4) used in the reaction. Since both solutions have equal volumes, the moles of limiting reactant can be calculated using the relation:
Moles = Molarity × Volume (in liters)
- For Ca(OH)2: Moles of Ca(OH)2 = (0.300 M) × (0.100 L) = 0.0300 mol (because 100.0 mL is equal to 0.100 L).
- For H3PO4: Moles of H3PO4 = (0.700 M) × (0.100 L) = 0.0700 mol.
The limiting reactant is the one with fewer moles, which in this case is Ca(OH)2, with 0.0300 mol.
4. Calculate ΔHrxn by dividing the heat transfer (q) by the moles of limiting reactant:
ΔHrxn = q / moles of limiting reactant.
Therefore, ΔHrxn = (q / 1000) / 0.0300.
This will give you the value of ΔHrxn in units of kilojoules per mole (kJ/mol).
As for the missing table of standard enthalpies of the solutions, you don't actually need it to calculate ΔHrxn using calorimetry. Calorimetry measures the heat transfer occurring in the particular reaction and does not require standard enthalpy data.