Question

When 150 g of ammonium nitrate dissolves in 450 g of water, the temperature of the solution decreases from 22 °C to 6.9 °C. What is the enthalpy of solution in joules per gram of ammonium nitrate?

Assume that the specific heat capacity of the solution is the same as that of pure water.

Answer 1

The enthalpy of solution is 250 J/g.

Explanation:

There are two heat transfers involved in this problem.

`"heat of solution of NH"_4"NO"_3 + "heat lost by water" = 0`
`color(white)(mmmmmmm)q_1color(white)(mmmmml) +color(white)(mmmm) q_2color(white)(mmmm) = 0`
`color(white)(mmmmml)m_1Δ_text(sol)Hcolor(white)(mmmll) + color(white)(mmll)m_2CΔT color(white)(mm)= 0`

Let's calculate the heats separately.

`m_1 = "150 g"`

`q_1 = m_1Δ_text(sol)H = 150Δ_text(sol)Hcolor(white)(l) "g"`

`m_2 = "(150 + 450) g" = "600 g"`
`C = "4.18 J·g·°C"^"-1"`
`ΔT = "(6.9 - 22) °C" = "-15.1 °C"`

`q_2 = m_2CΔT = 600 color(red)(cancel(color(black)("g"))) × "4.184J"·color(red)(cancel(color(black)("g"^"-1"·"°C"^"-1"))) × ("-15.1") color(red)(cancel(color(black)("°C"))) = "-37 900 J"`

`q_1 + q_2 = 150Δ_text(sol)Hcolor(white)(l) "g" - "37 870 J"" = 0`

`Δ_text(sol)H = "37 900 J"/"150 g" = "250 J/g"`

Note: The answer can have only two significant figures, because that is we have for the value of `ΔT`.