Answer:
A) 900 J
B) 27.96 J
C) 1,628 J ≅ 1.63 kJ
Explanation:
The heat absorbed by the metal (silver) - or energy required to heat it - is calculated as:
heat = mass x Cp x ΔT
Where Cp is the heat capacity (0.24 J/°C ·g) and ΔT is the change in temperature (final T - initial T).
A) Given:
mass = 150.0 g
final T = 298 K = 25°C
initial T = 273 K = 0°C
We calculate the energy in J to raise the temperature:
heat = mass x Cp x (final T - initial T)
= 150 .0 g x 0.24 J/°C ·g x (25°C - 0°C )
= 900 J
B) Given:
moles Ag= 1.0 mol
ΔT = 1.08°C
We first calculate the mass of silver (Ag) by multiplying the moles of Ag by the molar mass of Ag (MM = 107.9 g/mol)
mass = moles x MM = 1.0 mol Ag x 107.9 g/mol Ag = 107.9 g
Then, we calculate the heat required:
heat = mass x Cp x ΔT = 107.9 g x 0.24 J/°C ·g x 1.08°C = 27.96 J
C) Given:
heat = 1.25 kJ = 1,250 J
final T = 15.28°C
initial T = 12.08°C
We first calculate the change in temperature:
ΔT = final T - initial T = 15.28°C - 12.08°C = 3.2°C
Then, we calculate the mass of silver:
mass = heat/(Cp x ΔT) = 1,250 J/(0.24 J/°C ·g x 3.2°C) = 1,628 J ≅ 1.63 kJ
Taking into account the definition of calorimetry:
A) the energy required to raise the temperature of 150 g Ag from 273 K to 298 K is 900 J.
B) the energy required to raise the temperature of 1.0 mole of Ag by 1.08 °C is 27.96 J.
C) the mass of the sample of silver is 1627.60 g.
Calorimetry is the measurement and calculation of the amounts of heat exchanged by a body or a system.
Sensible heat is defined as the amount of heat that a body absorbs or releases without any changes in its physical state (phase change).
So, the expression that allows to calculate heat exchanges is:
Q = c× m× ΔT
where Q is the heat exchanged by a body of mass m, made up of a specific heat substance c and where ΔT is the temperature variation.
In this case, you know:
Replacing:
Q= 0.24[tex]\frac{J}{Cg}[/tex] × 150 g× 25 C
Solving:
Q= 900 J
In summary, the energy required to raise the temperature of 150 g Ag from 273 K to 298 K is 900 J.
In this case, you know:
Replacing:
Q= 0.24[tex]\frac{J}{Cg}[/tex] × 107.87 g× 1.08 C
Solving:
Q= 27.96 J
In summary, the energy required to raise the temperature of 1.0 mole of Ag by 1.08 °C is 27.96 J.
In this case, you know:
Replacing:
1250 J= 0.24[tex]\frac{J}{Cg}[/tex] × m× 3.2 C
Solving:
m= 1250 J÷ (0.24[tex]\frac{J}{Cg}[/tex] × 3.2 C)
m= 1627.6 g
In summary, the mass of the sample of silver is 1627.60 g.
Learn more about calorimetry:
