Question

In a constant-pressure calorimeter, 60.0 mL of 0.330 M Ba(OH)2 was added to 60.0 mL of 0.660 M HCl. The reaction caused the temperature of the solution to rise from 21.67 °C to 26.17 °C. If the solution has the same density and specific heat as water (1.00 g/mL and 4.184 J/g·°C, respectively), what is ΔH for this reaction (per mole of H2O produced)? Assume that the total volume is the sum of the individual volumes.

Answer 1

Given,

Concentration of Ba(OH)₂ = 0.330 M

The volume of Ba(OH)₂ = 60.0 mL x ( 1L /1000 mL) = 0.06 L

Concentration of HCl = 0.660 M

Volume of HCl = 60.0 mL x ( 1L /1000 mL) = 0.06 L

Also given,

Initial temperature of solution = 21.67 ^oC

Final solution of temperature = 26.17 ^oC

specific heat of solution = 4.184 J/g ^oC

Density of solution = 1.00 g /mL

Now, We know the formula,

q = m x C x T

Calculating the mass of solution,

= [ 60 mL x ( 1 g / 1 mL)] + [ 60 mL x ( 1 g / 1 mL)]

= 120 g solution

T = T_f - T_i

T = 26.17 ^oC - 21.67 ^oC

T = 4.5 ^oC

Now, calculating the value of "q",

q = 120 g x 4.184 J/g ^oC x 4.5 ^oC

q = 2260.44 J x ( 1kJ/1000 J)

q = 2.2604 kJ

Now, the balanced chemical reaction between Ba(OH)₂ and HCl is,

Ba(OH)₂(aq) + 2HCl(aq) BaCl₂(aq) + 2H₂O(l)

Now, calculating the number of moles of Ba(OH)₂ and HCl,

= 0.06 L x 0.330 M = 0.0198 mol Ba(OH)₂

Similarly,

= 0.06 L x 0.660 M = 0.0396 mol HCl

Calculating the number of moles of H₂O by using the each mole of reactants and the mole ratio from the balanced chemical reaction,

= 0.0198 mol Ba(OH)₂ x ( 2 mol H₂O / 1 mol Ba(OH)₂)

= 0.0396 mol H₂O

Similarly,

= 0.0396 mol HCl x ( 1 mol H₂O / 1 mol HCl)

= 0.0396 mol H₂O

Thus, we know

H = -q / n(moles)

H = - 2.2604 kJ / 0.0396 mol

H = -57.1 kJ /mol of H₂O