Calculate the mass of the polystyrene sample.

Question

A sample of polystyrene, which has a specific heat capacity of 1.880 J*g^-1 * C^-1, is put into a calorimeter that contains 300.0 g of water. The polystyrene sample starts off at 88.6 C and the temperature of the water starts off at 23.0 C. When the temperature of the water stops changing it's 28.2. The pressure remains constant at 1 atm.

Calculate the mass of the polystyrene sample. Be sure your answer is rounded to the correct number of significant digits.

I know how to calculate the temperature now but not the mass.

Answer 1

If you know how to calculate the temperature, calculating the mass is basically the same, but you rearrange the equation to get m on the left side.

Heat lost by the polystyrene = heat gained by the water (conservation of mass)

heat lost by polystyrene = q = mC∆T

heat gained by water = q - mC∆T

Final temperature of both = 28.2º (equilibrium)

(m)(1.880 J/gº)(88.6º - 28.2º) = (300.0 g)(4.184 J/gº)(28.2º - 23.0º)

(113.55 J/g)(m) = 6527 J

m = 6527 J / 113.55 J/g

m = 57.5 g of polystyrene (3 sig. figs. based on temperature readings)