Final answer:
The exact mass of the solution cannot be calculated with the information provided because the heat absorbed or released (q) and the initial mass of water are not given, and assumptions beyond the given data would be needed.
Step-by-step explanation:
To calculate the mass of the solution (in grams) given that the specific heat of the solution is 4.19 J/g°C, the mass of NaOH pellets is 20.0g, the initial water temperature is 20.0°C, and the final solution temperature is 51.29°C, with a temperature change (∆°C) of 31.29°C, you can use the concept of heat transfer. Since the mass of NaOH is given, it's assumed that it is completely dissolved in the water.
Firstly, calculate the heat absorbed or released using the formula q = mass × specific heat × ∆T. ∆T is the change in temperature, which is 31.29°C. However, since we are missing the mass of the water, we cannot directly calculate the heat (q).
What we can infer is that the total mass of the solution is the mass of the NaOH plus the mass of the water. If the specific heat of the final solution is the same as that of water (which is given in this case), we can suppose that all the mass comes from the water, as NaOH becomes aqueous and assumes the properties of the solution.
Given the lack of information about the heat absorbed or released (q), and assuming no heat is lost to the surroundings (the system is isolated), we cannot calculate the exact mass of the solution without making additional assumptions, which are not provided in the information given.