Question

A sample of polystyrene, which has a specific heat capacity of , is put into a calorimeter (see sketch at right) that contains of water. The polystyrene sample starts off at and the temperature of the water starts off at . When the temperature of the water stops changing it's . The pressure remains constant at . Calculate the mass of the polystyrene sample. Be sure your answer is rounded to significant digits.

Answer 1

This question is incomplete, the complete question is;

A sample of polystyrene, which has a specific heat capacity of 1.880 J.g⁻¹, is put into a calorimeter (see sketch at right) that contains 300.0 g of water. The polystyrene sample starts off at 94.9 °C and the temperature of the water starts off at 22.0. When the temperature of the water stops changing it's 27 °C . The pressure remains constant at 1 atm.

Calculate the mass of the polystyrene sample. Be sure your answer is rounded to 2 significant digits.

Answer:

the mass of the polystyrene sample is 57 g

Step-by-step explanation:

Given the data in the question;

mass of water m
`_{water` = 300 g

Temperature of water T
`_{water` = 22 °C

Specific heat capacity of water C
`_{water` = 4.184 J/g°C

mass of the polystyrene sample m
`_{polystyrene` = ?

T
`_{polystyrene` = 94.9 °C

Specific heat capacity of polystyrene; C
`_{polystyrene` = 1.880 J.g⁻¹.°C⁻¹

T = 27.7 °C

Now, using heat conservation equation

heat lost by polystyrene = heat gained by water

m
`_{polystyrene` × C
`_{polystyrene` × ( T
`_{polystyrene` - T ) = m
`_{water` × C
`_{water` × ( T - T
`_{water` )

We substitute

m
`_{polystyrene` × 1.880 × ( 94.9 - 27.7 ) = 300 × 4.184 × ( 27.7 - 22 )

m
`_{polystyrene` × 1.880 × 67.2 = 300 × 4.184 × 5.7

m
`_{polystyrene` × 126.336 = 7154.64

m
`_{polystyrene` = 7154.64 / 126.336

m
`_{polystyrene` = 56.63 ≈ 57 g { 2 significant figures }

Therefore, the mass of the polystyrene sample is 57 g