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Adding 5.25 g of to 130 g of water in a coffee-cup calorimeter (with stirring to dissolve the salt) resulted in a decrease in temperature from 18.1 °C to 15.4 °C. Calculate the enthalpy change for dissolving in water in kJ/mol. Assume the solution (whose mass is 135.3 g) has a specific heat capacity of 4.2 J/g · K. (Cold packs take advantage of the fact that dissolving ammonium nitrate in water is an endothermic process.)

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Answer:

ΔHrxn =  - 1534.3 J

Explanation:

Given the assumptions and the formula for the change in enthalpy:

ΔHrxn = m x C x ΔT,  where

               m is the mass of solution given 135.4 g

               C is the heat capacity 4.2 J/g .K  and,

               ΔT is the change in temperature

we have ,

T₁ = ( 18.1 + 273) K = 291.1 K

T₂ = ( 15.4 +273) K = 288.4 K

ΔHrxn =  135.3 g x 4.2 J/gK x ( 288.4 -291.1 ) K = - 1534.3 J

After verifying our result has the correct unit, the answer is -1534.3 Joules, and the negative sign tells us it is an endothermic reaction decreasing the final temperature.

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