10g of ice at 273K is added to 20 g of water at 900 C in an insulated flask. The heat of fusion of ice is 6 Kj/mol and the specific heat capacity of water is 4.2 J/K/g. ignoring the heat capacity of the flask; Determine ∆S of the system.
water @ 900 C?
To determine the change in entropy (∆S) of the system, we need to look at the heat transfer during the process.
Step 1: Determine the heat transferred during the process.
The heat required to raise the temperature of the water from 27°C to 90°C can be calculated using the formula:
q1 = m1 * c1 * ∆T1
Where:
m1 = mass of water = 20 g
c1 = specific heat capacity of water = 4.2 J/K/g
∆T1 = change in temperature of water = 90°C - 27°C = 63°C
q1 = 20 g * 4.2 J/K/g * 63°C
q1 = 5292 J
The heat released during the phase change of ice from solid to liquid at its melting point can be calculated using the formula:
q2 = n * ΔHf
Where:
n = moles of ice
ΔHf = heat of fusion of ice = 6 kJ/mol = 6000 J/mol
To determine the number of moles of ice, we need to use the molar mass of water (H2O):
Molar mass of H2O = 2(atomic mass of hydrogen) + atomic mass of oxygen = 2(1 g/mol) + 16 g/mol = 18 g/mol
Number of moles of ice = mass of ice (in grams) / molar mass of water
Number of moles of ice = 10 g / 18 g/mol
Number of moles of ice = 0.556 mol
q2 = 0.556 mol * 6000 J/mol
q2 = 3336 J
The total heat transferred during the process is:
Total heat transferred = q1 + q2
Total heat transferred = 5292 J + 3336 J
Total heat transferred = 8628 J
Step 2: Calculate the change in entropy.
The change in entropy (∆S) is given by:
∆S = q / T
Where:
q = heat transferred
T = temperature in Kelvin
Since the flask is insulated, there is no heat exchange with the surroundings, so we can consider the temperature of the system to remain constant throughout the process.
T = 273 K (temperature of ice)
∆S = 8628 J / 273 K
∆S = 31.67 J/K
Therefore, the change in entropy (∆S) of the system is 31.67 J/K.
To determine the change in entropy (∆S) of the system, we need to calculate the heat transferred in the process and divide it by the temperature.
First, let's calculate the heat transferred during the process.
1. Calculate the heat required to increase the temperature of the water from 273 K to 900 K:
The specific heat capacity of water is given as 4.2 J/g/K.
The mass of water is 20 g.
The change in temperature is 900 K - 273 K = 627 K.
Heat transferred = mass × specific heat capacity × change in temperature
= 20 g × 4.2 J/g/K × 627 K
≈ 52692 J
2. Calculate the heat released when the ice is converted into water at 273 K:
The heat of fusion of ice is given as 6 kJ/mol.
To convert grams of ice into moles, we need to know the molar mass of water.
The molar mass of water (H₂O) is approximately 18 g/mol.
Moles of ice = mass ÷ molar mass
= 10 g ÷ 18 g/mol
≈ 0.5556 mol
Heat released = heat of fusion × moles of ice
= 6 kJ/mol × 0.5556 mol
≈ 3.333 kJ
= 3.333 × 10^3 J
Now, let's calculate the total heat transferred in the process by considering the heat absorbed and released:
Total heat transferred = Heat absorbed - Heat released
= 52,692 J - 3,333 J
≈ 49,359 J
Finally, we can calculate the change in entropy (∆S) of the system using the formula:
∆S = Heat transferred / T
∆S = 49,359 J / 900 K
≈ 54.84 J/K
Therefore, the change in entropy (∆S) of the system is approximately 54.84 J/K.