The enthalpy of solution is the amount of energy absorbed or released when a solute is dissolved in a solvent. Suppose a 650 g ‘cold pack’ drops in temperature from 24 Celsius to -15 Celsius when its constituents mix. Assuming the specific heat of this aqueous solution is close to that of pure water, 4.18 J/g-C, what is the enthalpy of solution for the cold pack’s components? Is this enthalpy a positive or negative number? Explain.

Is the 650 grams the solvent-water or cold pack? It's the water temperature that drops, not the mass of cold pack. So, I'm assuming the mass value is that of water into which the cold pack was added. Also, when measuring changes of temperature, one is actually measuring the change occurring in the surroundings not the system. The results 'observed' are typically interpreted in terms of the system (in this case the cold pack).

So, using the 650g as the mass of water-solvent losing heat to the dissolution of the cold pack salts, Q = mcΔT = (650g)(4.184j/g∙⁰C)(-15 - 24)⁰C = - 106,064.4 Joules energy lost from solvent-water, or -1.10E+5 Joules (2-Sig.Figs.)… which means that the cold pack material on dissolution gained (endothermic) the 1.1 x 10⁵ Joules.

That is, the reaction is exothermic with respect to the water-solvent but endothermic with respect to the cold pack.

To find the enthalpy of solution for the cold pack's components, we first need to calculate the heat gained or lost by the solution using the equation:

q = m * c * ΔT

Where:
- q is the heat gained or lost by the solution
- m is the mass of the solution (650 g in this case)
- c is the specific heat capacity of the solution (assumed to be 4.18 J/g-C, which is close to that of pure water)
- ΔT is the change in temperature (final temperature minus initial temperature)

In this case, the initial temperature is 24 Celsius, and the final temperature is -15 Celsius. However, since we are interested in the magnitude of temperature change (|ΔT|), we can neglect the negative sign. Therefore,

|ΔT| = |-15 - 24| = 39 Celsius

Now, plugging in the values into the equation:

q = 650 g * 4.18 J/g-C * 39 Celsius
= 103,247.4 J

So, the heat gained or lost by the solution (enthalpy change) is approximately 103,247.4 J.

To determine whether this enthalpy change is positive or negative, we need to consider the sign convention. When heat is absorbed by the system (endothermic process), the enthalpy change is positive. On the other hand, when heat is released by the system (exothermic process), the enthalpy change is negative.

In this case, since the temperature of the solution decreased, it indicates that heat was released by the system. Therefore, the enthalpy change for the cold pack's components is negative.