Question

The combustion of 20 g of a fuel in a calorimeter increases the temperature of 200 g of water by 5 °C. What is the enthalpy of combustion per gram of fuel?

The specific heat capacity of water is `"4.184 J·°C"^"-1""g"^"-1"`.

Answer 1

The enthalpy of combustion of the fuel is -0.84 kJ/g.

Explanation:

There are two heat transfers involved.

`"heat of combustion of fuel + heat gained by water = 0"`

`color(white)(mmmmmm)q_1 color(white)(mmmmmmll)+color(white)(mmmmm) q_2 color(white)(mmmm)= 0`

`color(white)(mmmmm)m_1Δ_ cHcolor(white)(mmmmm) + color(white)(mmmll)m_2CΔTcolor(white)(mm) = 0`

In this problem,

`m_1 = "20 g"`

`m_2 = "200 g"`

`C color(white)(ll)= "4.184 J·""°C"^"-1""g"^"-1"`

`ΔT = "5.0 °C"`

`q_1 = mΔ_cH = 5 Δ_cHcolor(white)(l) "g"`

`q_2 = m_2CΔT = 200 color(red)(cancel(color(black)("g"))) × "4.184 J"·color(red)(cancel(color(black)("g"^"-1""°C"^"-1"))) × 5.0 color(red)(cancel(color(black)("°C"))) = "4180 J" = "4.18 kJ"`

`q_1 + q_2 =5 Δ_cHcolor(white)(l) "g" + "4..18 kJ" = 0`

`Δ_cH = ("-4.18 kJ")/("5.0 g") = "-0.84 kJ/g"`