Instant cold packs used to treat athletic injuries contain solid NH4NO3 and a pouch of water. When the pack is squeezed, the pouch breaks and the solid dissolves, lowering the tem-perature because of the endothermic reaction NH4NO31s2 ¡ NH4NO31aq2 ∆H = +25.7 kJ What is the final temperature in a squeezed cold pack that contains 50.0 g of NH4NO3 dissolved in 125 mL of water? Assume a specific heat of 4.18 J/(g C) for the solution, an initial temperature of 25.0 °C, and no heat transfer between the cold pack and the environment.

Video transcript

Hey everyone, we're told that a 26 g compound with a molar mass of 85 g per mole was dissolved in water with a final volume of 67 mL. If the temperature decreased from 24.7 degrees Celsius to 22. degrees Celsius. What is the change in entropy of the dissolution? And were provided our density and our specific heat. So determining the mass of our solution. We can go ahead and take 67 ml and we can use our density in our dimensional analysis. So we know that we have 1.09 g per one mil leader. Now this will get us to a value of 73.03 g. Now let's go ahead and determine our q of our solution And our formula for this is going to be our mass times. Our specific heat times are changing temperature. So plugging in those values, we have 73.03 g Times are specific heat of 4.186 jewels over g times degrees C Times are changing temperature which is 22.4°C -24.7°C. Now, when we calculate this out and cancel out our units, we end up with the heat of negative .118, 2 jewels. Now, in order to find our change in entropy, we need to determine the moles of our compound. So taking 26.0 g of our compound. We're going to use our dimensional analysis here and use its molar mass of 85.0 g per one mole of compound. This will get us to a mole of 0.30588. Now, in order to determine our change in entropy, all we need to do is take our cue which was negative 703.1182 jewels and divide that by its moles which was zero 30588 Mole. This will get us to a change in entropy of negative 2,298.65 jewels over mole. And we can go ahead and change this into killer jewels by using Are dimensional analysis and we know that we have 10 to the third jewel per one killer jewels. This will get us to negative 2.298 kg joules per mole. And this is going to be our final answer. Now I hope that made sense. And let us know if you have any questions