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Copper (II) Sulphate reacts with Barium Chloride. Given the reaction details, calculate the temperature change of the solution.

Chemistry

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Answer

1.69 ∘C1.69 \text{ }^\circ\text{C}

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Here's how to calculate the temperature change:

Question 7:
Copper (II) Sulphate reacts with Barium Chloride according to the equation:
CuSO4(aq)+BaCl2(aq)→CuCl2(aq)+BaSO4(s)\text{CuSO}_4(\text{aq}) + \text{BaCl}_2(\text{aq}) \rightarrow \text{CuCl}_2(\text{aq}) + \text{BaSO}_4(\text{s})
ΔH=−17.7 kJ/mol\Delta H = -17.7 \text{ kJ/mol}
Volume of 1 M CuSO4=900 cm31\text{ M CuSO}_4 = 900 \text{ cm}^3
Volume of 1 M BaCl2=600 cm31\text{ M BaCl}_2 = 600 \text{ cm}^3
Heat capacity of solution c=4.2 J/g∘Cc = 4.2 \text{ J/g}^\circ\text{C}
Density of solution ρ=1 g/cm3\rho = 1 \text{ g/cm}^3

  1. Calculate the moles of each reactant.

    Convert volumes from cm3\text{cm}^3 to L\text{L}:
    900 cm3=0.900 L900 \text{ cm}^3 = 0.900 \text{ L}
    600 cm3=0.600 L600 \text{ cm}^3 = 0.600 \text{ L}

    Moles of CuSO4\text{CuSO}_4:

    Moles=Concentration×Volume\text{Moles} = \text{Concentration} \times \text{Volume} Moles of CuSO4=1 mol/L×0.900 L=0.900 mol\text{Moles of CuSO}_4 = 1 \text{ mol/L} \times 0.900 \text{ L} = 0.900 \text{ mol}

    Moles of BaCl2\text{BaCl}_2:

    Moles of BaCl2=1 mol/L×0.600 L=0.600 mol\text{Moles of BaCl}_2 = 1 \text{ mol/L} \times 0.600 \text{ L} = 0.600 \text{ mol}
  2. Determine the limiting reactant.

    From the balanced equation, CuSO4\text{CuSO}_4 and BaCl2\text{BaCl}_2 react in a 1:11:1 molar ratio.
    Since 0.600 mol0.600 \text{ mol} of BaCl2\text{BaCl}_2 is less than 0.900 mol0.900 \text{ mol} of CuSO4\text{CuSO}_4, BaCl2\text{BaCl}_2 is the limiting reactant.
    Therefore, 0.600 mol0.600 \text{ mol} of reaction occurs.

  3. Calculate the total heat released (qq).

    The enthalpy change for the reaction is ΔH=−17.7 kJ/mol\Delta H = -17.7 \text{ kJ/mol}.

    q=Moles reacted×∣ΔH∣q = \text{Moles reacted} \times |\Delta H| q=0.600 mol×17.7 kJ/molq = 0.600 \text{ mol} \times 17.7 \text{ kJ/mol} q=10.62 kJq = 10.62 \text{ kJ}

    Convert to Joules:

    q=10.62×1000 J=10620 Jq = 10.62 \times 1000 \text{ J} = 10620 \text{ J}
  4. Calculate the total mass of the solution.

    Total volume of solution:

    Total volume=900 cm3+600 cm3=1500 cm3\text{Total volume} = 900 \text{ cm}^3 + 600 \text{ cm}^3 = 1500 \text{ cm}^3

    Mass of solution:

    Mass=Total volume×Density\text{Mass} = \text{Total volume} \times \text{Density} m=1500 cm3×1 g/cm3=1500 gm = 1500 \text{ cm}^3 \times 1 \text{ g/cm}^3 = 1500 \text{ g}
  5. Calculate the temperature change (ΔT\Delta T).

    Use the formula q=mcΔTq = mc\Delta T:

    ΔT=qmc\Delta T = \frac{q}{mc} ΔT=10620 J1500 g×4.2 J/g∘C\Delta T = \frac{10620 \text{ J}}{1500 \text{ g} \times 4.2 \text{ J/g}^\circ\text{C}} ΔT=106206300 ∘C\Delta T = \frac{10620}{6300} \text{ }^\circ\text{C} ΔT=1.6857... ∘C\Delta T = 1.6857... \text{ }^\circ\text{C}

    Rounding to three significant figures:

    ΔT=1.69 ∘C\Delta T = 1.69 \text{ }^\circ\text{C}

    The temperature change is 1.69 ∘C1.69 \text{ }^\circ\text{C}.

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