Question

How do I find ΔHrxn for this reaction?

Zinc metal reacts with hydrochloric acid according to the following balanced equation.
`"Zn(s)+2HCl(aq)→ZnCl"_2"(aq)+H"_2"(g)"`
When 0.105 g of Zn(s) is combined with enough HCl to make 50.0 mL of solution in a coffee-cup calorimeter, all of the zinc reacts, raising the temperature of the solution from 21.5 ∘C to 24.3 ∘C.
Find ΔHrxn for this reaction as written. (Use 1.0 g/mL for the density of the solution and 4.18 J/g⋅∘C as the specific heat capacity.)

Answer 1

`Δ_text(rxn)H = "-360 kJ·mol"^"-1"`

There are two heat transfers to consider:

`"heat released by reaction + heat absorbed by water" = 0`

`q_1 color(white)(m)+ color(white)(m)q_2 = 0`

`color(white)(mll)nΔ _text(rxn)H + mcΔT = 0`

In this problem,

`n = 0.105 color(red)(cancel(color(black)("g Zn"))) × "1 mol Zn"/(65.38 color(red)(cancel(color(black)("g Zn")))) = "0.001 606 mol Zn"`

`Δ_text(r)H = x`

`m = "mass of water" = 50.0 color(red)(cancel(color(black)("mL"))) × "1.0 g"/(1 color(red)(cancel(color(black)("mL")))) = "50.0 g"`

`c = "4.18 J°C"^"-1""g"^"-1"`

`ΔT = "24.3 °C - 21.5 °C = 2.8 °C"`

`q_1 = "0.001 606" "mol" × x = "0.001 606"xcolor(white)(l) "mol"`

`q_2 = 50.0 cancel("g") × "4.18 J"color(red)(cancel(color(black)("°C"^"-1""g"^"-1"))) × 2.8 color(red)(cancel(color(black)("°C"))) = "585 J"`

`q_1 + q_2 = "0.001 606"xcolor(white)(l) "mol" + "585 J" = 0`

`x = "-585 J"/"0.001 606 mol" = "-360 000 J·mol"^"-1" = "-360 kJ·mol"^"-1"`

∴ `Δ_text(r)H = "-360 kJ·mol"^"-1"`

Note: The answer can have only two significant figures, because that is all you gave for the density of the solution and for the change in temperature.