Question

The specific heat capacity of silver is 0.24 J/°C ·g.(a) Calculate the energy (J) required to raise thetemperature of 150.0 g Ag from 273 Kto 295 K.(b) Calculate the energy required to raise the temperature of1.0 mol Ag by 1.0°C (called the molar heat capacity of silver(J/mol°C)(c) It takes 1.15 kJ of energy toheat a sample of pure silver from 12.0°C to 14.9°C. Calculate the mass of the sample ofsilver (g).

Answer 1

(a) 792.0 J

(b) 25.89 J/molºC

(c) 1652 g

Step-by-step explanation:

(a) We are given the specific heat for silver, and also know that

Q= mx c x ΔT, where Q is the heat energy ,

m is the mass ,

c is the specific heat, and

ΔT is the change in temperature.

We are given the specific heat , the mass and ΔT. So we have all that is required to calculate for Q, but first we will need to compute the temperature in º C since the specific heat is given in Kelvin.

T₀ = (273 -273) ºC = 0 ºC

T₁ = (295 - 273) ºC = 22 ºC

ΔT = (22 - 0) ºC = 22 ºC

Q = 150.0 g x 0.24 J/ºC·g x ( 22 ºC) = 792.0 J

(b) We know the specific heat per gram, and we need to calculate the molar heat capacity per mol. So our strategy here is to convert the given specifi heat to molar heat capacity:

0.24 J /ºC·g x 107.87 g/mol = 25.89 J/molºC

(c) In this part we need to calculate the mass given the heat energy and the change in temperature. Since we want our answer in grams, we will be using the specific heat of 0.24 J/ºC·g. Again convert Q to J to be consistent in our units.

Q = 1.15 kJ x 1000 J/kj = 1150 J

Q = m x c x ΔT ⇒ m = Q / (c x ΔT)

m = 1150 J / (0.24 J/°C ·g x (14.9 - 12.0)ºC) = 1652 g