In a constant-pressure calorimeter, 70.0 mL of 0.330 M Ba(OH)2 was added to 70.0 mL of 0.660 M HCl. The reaction caused the temperature of the solution to rise from 21.27 °C to 25.77 °C. If the solution has the same density and specific heat as water, what is ÄH for this reaction (per mole of H2O produced)? Assume that the total volume is the sum of the individual volumes.

To find the ÄH for this reaction, we need to use the equation:

ÄH = q / n

where ÄH is the enthalpy change, q is the heat absorbed or released by the reaction, and n is the number of moles of water produced in the reaction.

First, let's calculate the heat absorbed or released by the reaction using the equation:

q = m * C * ΔT

where q is the heat, m is the mass of the solution, C is the specific heat capacity of water, and ΔT is the change in temperature.

Since the density of the solution is the same as water and we have 70.0 mL + 70.0 mL = 140.0 mL of the solution, we can assume the mass of the solution to be equal to its volume, which is 140.0 g.

The specific heat capacity of water is 4.18 J/g°C.

Now, we can calculate q:

q = 140.0 g * 4.18 J/g°C * (25.77 °C - 21.27 °C)

Next, we need to determine the number of moles of water produced in the reaction. From the balanced equation:

Ba(OH)2 + 2HCl -> BaCl2 + 2H2O

we can see that for every 1 mole of Ba(OH)2 reacted, 2 moles of H2O are produced.

Since we have 0.0700 L (70.0 mL) of 0.330 M Ba(OH)2, we can find the number of moles of Ba(OH)2:

moles of Ba(OH)2 = volume (L) * concentration (M)

Now, we can calculate the number of moles of H2O:

moles of H2O = 2 * moles of Ba(OH)2

Finally, we can calculate the ÄH for the reaction:

ÄH = q / (moles of H2O)

Substitute the calculated values to find the ÄH (per mole of water produced).

To calculate the enthalpy change (ΔH) for this reaction per mole of water produced, we need to use the equation:

ΔH = q / n

where q is the heat absorbed or released by the reaction and n is the number of moles of water produced.

Step 1: Calculate the moles of Ba(OH)2 and HCl used in the reaction.

Moles of Ba(OH)2 = volume (in liters) x molarity
= 0.070 L x 0.330 mol/L
= 0.0231 mol

Moles of HCl = volume (in liters) x molarity
= 0.070 L x 0.660 mol/L
= 0.0462 mol

Step 2: Calculate the heat absorbed or released by the reaction.

Since the reaction is carried out in a constant-pressure calorimeter, the heat absorbed or released by the reaction can be calculated using the equation:

q = m × C × ΔT

where q is the heat, m is the mass, C is the specific heat, and ΔT is the temperature change.

Given that the solution has the same density and specific heat as water, we can assume that the density is 1 g/mL and the specific heat is 4.18 J/g°C.

Mass of solution = volume of solution x density
= (70.0 mL + 70.0 mL) x 1 g/mL
= 140 g

ΔT = final temperature - initial temperature
= 25.77 °C - 21.27 °C
= 4.5 °C

q = 140 g × 4.18 J/g°C × 4.5 °C
= 2658.6 J

Step 3: Calculate the number of moles of water produced.

The reaction between Ba(OH)2 and HCl produces 2 moles of water for every 1 mole of Ba(OH)2. Therefore, the number of moles of water produced is equal to twice the number of moles of Ba(OH)2 used.

n = 2 × 0.0231 mol
= 0.0462 mol

Step 4: Calculate the enthalpy change (ΔH) per mole of water produced.

ΔH = q / n
= 2658.6 J / 0.0462 mol
= 57525 J/mol

Therefore, the enthalpy change (ΔH) for this reaction per mole of water produced is 57525 J/mol.