Energetics Calculations (Edexcel IGCSE Chemistry)

Calculate Heat Energy Change

Spec point — calculate the heat energy change from a measured temperature change using the expression Q = mcΔT

Calculating heat energy change

• In order to calculate heat energy changes you need to know:

  • The mass of the substance being heated
  • The temperature change
  • The specific heat capacity of the substance

• Specific heat capacity, c, is the energy needed to raise the temperature of 1 g of a substance by 1 °C

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

• Heat energy change, Q, can be calculated using the formula:

$Q=m\times c\times\Delta T$

• Where:

  • Q = the heat energy change, J
  • m = the mass of the substance being heated, g
  • c = the specific heat capacity, J/g/°C
  • ΔT = the temperature change, °C

• The temperature change in degrees Celsius is the same as the temperature change in Kelvin

Worked Example Excess iron powder was added to 100.0 cm³ of 0.200 mol dm^-3 copper(II) sulfate solution in a calorimeter.

The reaction equation was as follows.

Fe (s) + CuSO₄ (aq) → FeSO₄ (aq) + Cu (s)

The maximum temperature rise was 7.5 ^oC. Determine the heat energy change of the reaction, in kJ.

Answer:

The solution is assumed to have the same density as water, so 100.0 cm³ has a mass of 100 g

• State the equation:

Q = m x c x ΔT

• Known values:

  • m = 100 g
  • c = 4.18 J/g/°C
  • ΔT = 7.5 ^oC

• Substitute the values into the equation:

Q = 100 g x 4.18 J/g/°C x 7.5 ^oC

• Solve the equation:

Q = 3135 J

• Apply the sign:

  • The temperature increased
  • So, the reaction is exothermic (energy was released to the surroundings)
  • Exothermic reactions have a negative enthalpy change:

Q = -3135 J

• Convert from J to kJ (divide by 1000):

Q = $\frac{-3135}{1000}$ = -3.14 kJ(to 3 significant figures)

• The temperature increased indicating an exothermic reaction so the value must be negative

Worked Example 1.023 g of propan-1-ol (M = 60.11 g mol^-1) was burned in a spirit burner and used to heat 200 g of water in a copper calorimeter. The temperature of the water rose by 30 ^oC.

Calculate the heat energy change for the combustion of propan-1-ol using this data.

Answer:

• State the equation:

Q = m x c x ΔT

• Known values:

  • m = 200 g
  • c = 4.18 J/g/°C
  • ΔT = 30 ^oC

• Substitute the values into the equation:

Q = 200 g x 4.18 J/g/°C x 30 ^oC

• Solve the equation:

Q = 25080 J

• Apply the sign:

  • Combustion reactions are always exothermic:

Q = -25080 J

• Convert from J to kJ (divide by 1000):

Q = $\frac{-25080}{1000}$ = -25.1 kJ(to 3 significant figures)

• Combustion reactions are always exothermic so your answer must be negative

Calculate Molar Enthalpy Change

Spec point — calculate the molar enthalpy change (ΔH) from the heat energy change, Q

Calculating molar enthalpy change

• We can compare the amount of energy released per gram and per mole for different fuels
• In both cases, the energy released (Q) is calculated first
• To calculate the energy released per gram of fuel:

energy released per gram =$\frac{\mathrm{energy} \mathrm{released}}{\mathrm{mass} \mathrm{of} \mathrm{fuel} \mathrm{burned}}$

• To calculate the energy released per mole of fuel:

energy released per mole =$\frac{\mathrm{energy} \mathrm{released}}{\mathrm{number} \mathrm{of} \mathrm{moles}}$

$ΔH=\frac{Q}{n}$

• The energy released per mole is also known as the molar enthalpy change
• The units are kJ / mol

Worked Example The energy from 0.01 mol of propanol was used to heat up 250 g of water.

The temperature of the water rose from 25 °C to 37 °C .

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

a) Calculate the energy released per gram.

b) Calculate the enthalpy change in kJ/mol.

Answer:

• State the equation:

Q = m x c x ΔT

• Known values:

  • m = 250 g
  • c = 4.18 J/g/°C
  • ΔT = 37 – 25 °C = 12 °C

• Substitute the values into the equation:

Q = 250 g x 4.18 J/g/°C x 12 ^oC

• Solve the equation:

Q = 12540 J

• Apply the sign:

  • The temperature increased, so the reaction is exothermic:

Q = -12540 J

• Convert from J to kJ (divide by 1000):

Q = $\frac{-12540}{1000}$ = -12.54 kJ

a) To calculate the energy released per gram:

• Find the mass of propanol burned:

mass = moles × M_r

mass = 0.01 mol × 60.11 g mol^-1

mass = 0.601 g

• Apply the formula:

energy released per gram = $\frac{\mathrm{energy} \mathrm{released}}{\mathrm{mass} \mathrm{of} \mathrm{fuel} \mathrm{burned}}$

energy released per gram = $\frac{-12.54\mathrm{kJ}}{0.601g}$

energy released per gram = −20.9 kJ/g (to 3 s.f.)

b) To calculate the enthalpy change in kJ/mol:

• Calculate the energy released per mole:

ΔH = $\frac{Q}{n}$

ΔH = $\frac{12.540\mathrm{kJ}}{0.01\mathrm{mol}}$

ΔH = – 1254 kJ/mol

Exam Hint When you determine Q your answer will be in joules, but enthalpy change is measured in kJ/mol. Make sure you convert Q to kilojoules by dividing by 1000.

Exothermic reactions release energy to the surroundings, causing the temperature to rise. By convention, enthalpy changes for exothermic reactions are always negative, which reflects the fact that the reaction loses energy. If the temperature increased in your experiment, your final answer must be negative.