Question

A) It takes 47.0J to raise the temperature of an 10.7g piece of unknown metal from 13.0∘C to 25.0∘C. What is the specific heat for the metal?

b) The molar heat capacity of silver is 25.35 J/mol⋅∘C. How much energy would it take to raise the temperature of 10.7g of silver by 15.2∘C?
c) What is the specific heat of silver?

Answer 1

a) 0.3660 J/g°C is the specific heat for the metal.

b) 37.7 Joules energy would it take to raise the temperature of 10.7 grams of silver by 15.2°C.

c)The specific heat of silver is 0.2347 J/g°C.

Step-by-step explanation:

Energy required to raise the temperature,Q = 47.0 J

Mass of the unknown metal = m = 10.7 g

Change in temperature = ΔT = 25.0°C - 13.0°C = 12°C

Specific heat of metal = c

`Q=mc\Delta T`

`47.0 J=10.7 g* c* 12^oC`

`c=(47.0 J)/(10.7 g* 12^oC)=0.3660 J/g^oC`

0.3660 J/g°C is the specific heat for the metal.

b) The molar heat capacity of silver =
`c_m=25.35 J/mol^oC`

Molar mass of silver ,M= 108 g/mol

Specific heat of silver = c =
`(c_m)/(M)=-(25.35 J/mol^oC)/(108 g/mol)=0.2347 J/g ^oC`

Given mass of silver = m = 10.7 g

Change in temperature = ΔT = 15°C

Energy required to raise the temperature of silver = Q

`Q=mc\Delta T`

`Q= 10.7 g* 0.2347 J/g ^oC* 15^oC`

Q = 37.7 Joules

37.7 Joules energy would it take to raise the temperature of 10.7 grams of silver by 15.2°C.

c) The specific heat of silver is calculated in (b) part above.

Specific heat of silver = c =
`(c_m)/(M)=-(25.35 J/mol^oC)/(108 g/mol)=0.2347 J/g ^oC`

Answer 2

The heat Q can be evaluated as:
Q=mcΔT
where:
m is the mass
c specific heat
ΔT change in temperature.
So:
a)
47=10.7c(25-13)
c=0.39 J/g°C
Using the same idea you get (I transformed g into moles using the molar mass of silver from the table of elements):
b) Q=(10.7/107.9)×25.35×15.2=38.21 J
where: Molar mass of Ag = 107.8682 g/mol
c) 38.21=10.7c15.2
c=specific heat of silver=0.235 J/g°C