Final answer:
The ΔH per mole of H+ reacting is 19664.8 J/mol. To calculate the ΔH per mole of H+ reacting, we can use the equation: q = mCΔT. First, calculate the mass of the solution. Next, calculate the heat transferred using the equation q = mCΔT. Finally, calculate the number of moles of H+ reacting and divide the heat transferred by the moles of H+ to get the ΔH per mole of H+ reacting.
Step-by-step explanation:
To calculate the ΔH per mole of H+ reacting, we can use the equation:
q = mCΔT
where q is the heat transferred, m is the mass of the solution, C is the specific heat of the solution, and ΔT is the change in temperature.
First, let's calculate the mass of the solution.
We can assume the density of the final solution is equal to the density of water, which is 0.998 g/mL.
Since we have 50.0 mL of NaOH and 75.0 mL of H3PO4, the total volume of the solution is 125.0 mL or 125.0 g.
This is because the density of water is 1 g/mL.
Next, let's calculate the heat transferred using the equation q = mCΔT.
Since we know the specific heat of all solutions is 4.184 J/gK and the change in temperature is 7°C (from 22°C to 29°C), we can calculate q:
q = 125.0 g * 4.184 J/gK * 7°C
= 3688.2 J
Finally, let's calculate the number of moles of H+ reacting.
We can use the stoichiometry of the balanced chemical equation for the reaction between NaOH and H3PO4:
NaOH + H3PO4 → Na3PO4 + H2O
From the equation, we can see that 1 mole of NaOH reacts with 1 mole of H3PO4 to produce 1 mole of H+.
Since we have 50.0 mL of NaOH with a concentration of 3.75 M, we can calculate the number of moles as follows:
moles of NaOH = 50.0 mL * 3.75 M
= 0.1875 moles
Therefore, the ΔH per mole of H+ reacting is:
ΔH = q / moles of H+
ΔH = 3688.2 J / 0.1875 moles =
19664.8 J/mol