Calculate the increase of entropy (in J/K) when 75 g of ice melts at 0 ºC and 1 atm. (The heat of fusion for ice is 6,000 J/mol.)
dG = dH - TdS
At equilibrium dG = 0 and the melting point you have equilibrium.
Substitute heat fusion for dH and T and solve for dS. Watch the signs.
To calculate the increase in entropy when ice melts, you can use the formula:
ΔS = Q / T
Where:
ΔS is the change in entropy (in J/K),
Q is the heat transferred (in J),
T is the temperature (in K).
First, let's calculate the heat transferred during the melting process. The heat transferred is given by the formula:
Q = n * ΔH
Where:
Q is the heat transferred (in J),
n is the number of moles, and
ΔH is the enthalpy change (in J/mol).
To find the number of moles (n), we can use the molar mass (M) and mass (m) of the substance:
n = m / M
The molar mass of water (H2O) is approximately 18.015 g/mol.
n = 75 g / 18.015 g/mol
n ≈ 4.16 mol
Now, let's calculate the heat transferred (Q):
Q = n * ΔH
= 4.16 mol * 6000 J/mol
= 24960 J
The temperature (T) remains constant during the phase change, so T = 0 ºC + 273.15 = 273.15 K.
Finally, we can calculate the change in entropy (ΔS):
ΔS = Q / T
= 24960 J / 273.15 K
≈ 91.3 J/K
Therefore, the increase in entropy when 75 g of ice melts at 0 ºC and 1 atm is approximately 91.3 J/K.