Question

Considering the reaction shown below, how much thermal energy would be required to run the reaction with 5.0 g of hydrogen and 25 g of iodine?

H2(g) + I2(g) --> 2HI(g)
deltaH(rxn) = +53 kJ

I happen to know the answer is 5.2 kJ, but I'm not sure how to get to it. I'm studying for finals and need help. Thank you!

Answer 1

`"5.2 kJ"`

Explanation:

The thermochemical equation given to you tells you how much heat is needed in order to produce `2` moles of hydrogen iodide.

In other words, you know that in order to produce `2` moles of hydrogen iodide, you need `1` mole of hydrogen gas, `1` mole of iodine, and `"53 kJ"` of heat.

`DeltaH_"rxn" = + "53 kJ"`

The plus sign tells you that this reaction taken is `"53 kJ"` of heat, i.e. the reaction is endothermic.

`color(blue)(ul(color(black)("1 mole I"_2 color(white)(.)"and 1 mole H"_2 -> "53 kJ of heat consumed")))`

So, convert the samples of hydrogen gas and iodine to moles by using the molar masses of the two reactants.

`5.0 color(red)(cancel(color(black)("g"))) * "1 mole H"_2/(2.016color(red)(cancel(color(black)("g")))) = "2.48 moles H"_2`

`25 color(red)(cancel(color(black)("g"))) * "1 mole I"_2/(253.81color(red)(cancel(color(black)("g")))) = "0.0985 moles I"_2`

The reaction consumes hydrogen gas and iodine in a `1:1` mole ratio, so you can say that iodine will act as a limiting reagent here because you have fewer moles of iodine than of hydrogen gas.

Therefore, the reaction will consume `0.0985` moles of iodine and of hydrogen gas and produce.

This means that the reaction will require

`0.0985 color(red)(cancel(color(black)("moles I"_2))) * "53 kJ"/(1color(red)(cancel(color(black)("mole I"_2)))) = color(darkgreen)(ul(color(black)("5.2 kJ")))`

of heat. The answer is rounded to two sig figs. You can thus say that you have

`DeltaH_ ("rxn for 0.0985 moles I"_2 color(white)(.)"and H"_2) = + "5.2 kJ"`