Help me solve this

Question

You have dissolved 19.178g of barium chloride in water. If all of the Gibb's Free Energy liberated by this reaction is transferred to a 40.107g block of copper at 16.38°C, what is the final temperature of the copper block? The specific heat of copper is 0.3851J/g*°C .

Substance ΔG°f (kJ/mol)

BaCl2(s). -806.67

Ba+2(aq) -560.84

Cl-1(aq) -132.78

Answer 1

The first thing we have to do in the problem is to find the total amount of heat generated by dissolving 19.178 g BaCl2. Once we have that value, we can then proceed to find the final temperature of the copper block.

Dissolution of BaCl2

BaCl2(s) ==> Ba2+(aq) + 2Cl-(aq)

moles BaCl2 used = 19.178 g BaCl2 x 1 mol BaCl2 / 208.23 g = 0.09210 moles

∆Grxn = ∑products - ∑reactants = [(-560.84) + (2x -132.78)] - (-806.67)] x 0.09210

∆Grxn = (-826.4 + 806.67) x 0.09210

∆Grxn = -19.73 kJ/mol x 0.09210 mol = -1.817 kJ ... This is the heat generated by dissolving the BaCl2

Note the negative sign, which indicates an exothermic reaction. This heat will be transferred to the Cu.

Next, we can use the formula q = mC∆T

q = heat = 1.817 kJ = 1817 J

m = mass of Cu = 40.107 g

C = specific heat of Cu = 0.3851 J/gº (note units are in J, so we converted q to joules also)

∆T = change in temperature = ?

Solving for ∆T we have ...

∆T = q /mC = 1817 J / (40.107 g)(0.3851 J/gº)

∆T = 117.96º

Final temp of Cu = 16.38º + 117.96º = 134.34º

(be sure to check the math)