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Instant cold packs, often used to ice athletic injuries on the field, contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the following endothermic reaction: NH4NO3(s)âNH+4(aq)+NOâ3(aq) In order to measure the enthalpy change for this reaction, 1.25 g of NH4NO3 is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 âC and the final temperature (after the solid dissolves) is 21.9 âC. Part A Calculate the change in enthalpy for the reaction in kilojoules per mole. (Use 1.0g/mL as the density of the solution and 4.18J/gâ âC as the specific heat capacity.) Express your answer to two significant figures and include the appropriate units. ÎHrxn = Â ??? kJ/mol
Answer:
26 kJ / mol
Explanation:
Given that;
The mass of NHâNOâ = 1.25 g
Number of moles of NHâNOâ = Mass of NHâNOâ / Molar Mass of NHâNOâ
Number of moles of NHâNOâ= 1.25 g / 80.043 g/mol
Number of moles of NHâNOâ= 0.016 mol
Volume of solution = 25.0 mL
Density of Solution = 1.0g/mL
Since; [tex]density = \frac {mass} {volume}[/tex]
Mass of Solution = Density x Volume
= 1.0g/mL Ă 25.0mL
= 25 g
Heat Generated (Q) Â = [tex]mc \delta T[/tex]
Q= 25g à 4.18 J/g°C x (25.8°C - 21.9°C)
Q = Â 407.55 J
Q = 407 Ă 10 â»Âł kJ
Q = 0.40755 kJ
Î [tex]H_{rxn}[/tex] = [tex]\frac{Heat generated(Q)}{number of molesof NH_4NO_3}[/tex]
= Â [tex]\frac {0.40755 kJ}{ 0.016 mol}[/tex]
= 25.47 kJ/ mol
~ 26 kJ / mol
Therefore, the change in enthalpy for the reaction in kilojoules per mole = 26 kJ / mol
The change in enthalpy for the chemical reaction is equal to 26.125 kJ/mol.
Given the following data:
- Density of solution = 1.0 g/mL
- Specific heat capacity of solution = 4.18 J/g°C.
- Mass of [tex]NH_4NO_3[/tex] = 1.25 g
- Initial temperature = 25.8°C
- Final temperature = 21.9°C
Scientific data:
The molar mass of [tex]NH_4NO_3[/tex] = 80.043 g/mol
To calculate the change in enthalpy for the chemical reaction:
First of all, we would determine the mass of the solution:
[tex]Mass\;of\;solution = density \times volume\\\\Mass\;of\;solution = 1.0 \times 25.0[/tex]
Mass of solution = 25 grams.
For the quantity of heat generated:
[tex]Q = mc\theta\\\\Q = 25 \times 4.18 \times (25.8 - 21.9)\\\\Q =25 \times 4.18 \times 3.9[/tex]
Q = 407.55 Joules.
Next, we would determine the number of moles of [tex]NH_4NO_3[/tex] used in the chemical reaction:
[tex]Number\;of\;moles = \frac{mass}{molar\;mass}\\\\Number\;of\;moles = \frac{1.25}{80.043}[/tex]
Number of moles = 0.0156 moles
Now, we can calculate the change in enthalpy for the chemical reaction:
[tex]\Delta H_{rxn} = \frac{Q}{n} \\\\\Delta H_{rxn} = \frac{407.55}{0.0156} \\\\\Delta H_{rxn} = 26125\;J/mol[/tex]
Note: In kJ/mol, we would divide by 1000.
[tex]\Delta H_{rxn} = \frac{26125}{1000} =26.125 \;kJ/mol[/tex]
Read more on change in enthalpy here: https://brainly.com/question/13197037
Complete Question:
Instant cold packs, often used to ice athletic injuries on the field, contain ammonium nitrate and water separated by a thin plastic divider. When the divider is broken, the ammonium nitrate dissolves according to the following endothermic reaction:
         [tex]NH_4NO_3(s)\rightarrow NH^+_4(aq)+NO^{-}_3(aq)[/tex]
In order to measure the enthalpy change for this reaction, 1.25 g of [tex]NH_4NO_3[/tex] is dissolved in enough water to make 25.0 mL of solution. The initial temperature is 25.8 âC and the final temperature (after the solid dissolves) is 21.9 âC.
Part A: Calculate the change in enthalpy for the reaction in kilojoules per mole. (Use 1.0g/mL as the density of the solution and 4.18J/gâ âC as the specific heat capacity.) Express your answer to two significant figures and include the appropriate units. ÎHrxn = Â ??? kJ/mol
