Answer:
5.62 kJ
Explanation:
Let's consider the thermochemical equation for the dissolution of ammonium nitrate.
NH₄NO₃(s) ⇒ NH₄⁺(aq) + NO₃⁻(aq) ΔH° = 25.7 kJ
25.7 kJ are absorbed per 1.00 mole of NH₄NO₃. The enthalpy change when 17.5 g of NH₄NO₃ (M: 80.04 g/mol) are dissolved is:
17.5 g × 1 mol/80.04 g × 25.7 kJ/mol = 5.62 kJ
Considering the rule of three, if 17.5 grams of NH₄NO₃ are dissolved, the enthalpy change is 5.62 kJ.
In first place, the rule of three is a way of solving problems of proportionality between three known values and an unknown value, establishing a relationship of proportionality between all of them.
That is, what is intended with it is to find the fourth term of a proportion knowing the other three.
If the relationship between the magnitudes is direct, that is, when one magnitude increases, so does the other (or when one magnitude decreases, so does the other) , the direct rule of three must be applied.
To solve a direct rule of three, the following formula must be followed, being a, b and c known data and x the variable to be calculated:
a ⇒ b
c ⇒ x
So: [tex]x=\frac{cxb}{a}[/tex]
Being 80 g/mole the molar mass of NH₄NO₃, that is, the amount of mass that a substance contains in one mole, the number of moles that 17.5 g of the compound contain is calculated as:
[tex]17.5 gramsx\frac{1 mole}{80 grams} =[/tex] 0.21875 moles
Then it is possible to apply the following rule of three: if when 1.00 mol of NH₄NO₃ dissolves in water the enthalpy change is ΔH =+25.7 kJ, when 0.21875 moles of the compound dissolves in water, the enthalpy change will have what value?
[tex]enthalpy change=\frac{0.21875 molesx25.7 kJ}{1 mole}[/tex]
enthalpy change= 5.62 kJ
Finally, if 17.5 grams of NH₄NO₃ are dissolved, the enthalpy change is 5.62 kJ.
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