What is the total heat evolved when a saturated solution of boric acid (H3BO3) in water is cooled from 100C to 20C? Note the specific heat capacity of the saturated solution is approximately that of water in that temperature range (4.20 J/g.K) and the specific heat capacity of the solid is approximately 0.

As we are not given mass do I use the equation q = m x c x ∆T and assume mass of 100g, or can I assume constant pressure and use the equation q(p) = C(p) x ∆T?

Thanks!

I don't think you can assume either. And q = mcdelta T IS q(p); i.e., q at constant p. Also, I don't think this problem can be solved without knowing the volume or mass of the saturated solution. Obviously a 200 g sample will evolve more heat than a 100 g sample.

To calculate the total heat evolved when a saturated solution of boric acid in water is cooled, you can use the equation q = m x c x ∆T, where q is the total heat evolved, m is the mass of the solution, c is the specific heat capacity of the solution, and ∆T is the change in temperature.

Since the specific heat capacity of the saturated solution is approximately the same as water, you can assume a value of c = 4.20 J/g.K. However, you are correct in noting that the mass is not given in the question.

If the mass is not given, you have two options. You can either assume a mass, typically 100g as you suggested, or you can use the constant pressure heat capacity equation q(p) = C(p) x ∆T.

The constant pressure heat capacity equation is typically used when you do not know the mass of the substance but know its heat capacity (C) instead. In this case, the solid boric acid has a heat capacity of approximately 0, meaning it does not require energy to change its temperature.

So, if you choose to use the constant pressure heat capacity equation, you would use q(p) = C(p) x ∆T, where q(p) is the total heat evolved, C(p) is the heat capacity of the solid (which is approximately 0 in this case), and ∆T is the change in temperature.

Both methods will give you the same result if you assume a mass of 100g. However, if you want to calculate the exact value, you would need to know the mass of the saturated solution.