If 1 mol of ice melts at its melting point of 273 K, the entropy change for the ice is 22.0 J/K. If the ice melts in someone’s hand at 34°C, what is the change in the entropy of the universe? Assume a final temperature for the water of 0°C. The enthalpy of fusion for ice is 6.01 kJ/mol

a. +19.6 J/K
b. –19.6 J/K
c. +2.4 J/K
d. –2.4 J/K
e. +41.5 J/K

If 1 mol of ice melts at its melting point of 273 K, the entropy change for the ice is 22.0 J/K. If the ice melts in someone’s hand at 34°C, what is the change in the entropy of the universe? Assume a final temperature for the water of 0°C. The enthalpy of fusion for ice is 6.01 kJ/mol

a. +19.6 J/K
b. –19.6 J/K
c. +2.4 J/K
d. –2.4 J/K
e. +41.5 J/K

To determine the change in entropy of the universe, we need to consider the entropy change of the ice and the surroundings when it melts in someone's hand.

First, let's calculate the entropy change of the ice. We are given that when 1 mol of ice melts at its melting point of 273 K, the entropy change is 22.0 J/K.

Next, let's calculate the entropy change of the surroundings. We can use the equation:

ΔS_surroundings = -ΔH/T

where ΔH is the enthalpy change and T is the temperature in Kelvin.

The enthalpy of fusion for ice is given as 6.01 kJ/mol. To convert this to J/mol, we multiply by 1000, which gives us 6010 J/mol.

The initial temperature, provided as 34°C, needs to be converted to Kelvin by adding 273 to it. Thus, the initial temperature is 34 + 273 = 307 K.

The final temperature, provided as 0°C, is also converted to Kelvin by adding 273 to it. The final temperature is 0 + 273 = 273 K.

Now, we can calculate the entropy change of the surroundings:

ΔS_surroundings = -ΔH/T
ΔS_surroundings = -(6010 J/mol) / (307 K)
ΔS_surroundings = -19.6 J/K

Finally, to find the change in entropy of the universe, we can simply add the entropy changes of the ice and surroundings:

ΔS_universe = ΔS_ice + ΔS_surroundings
ΔS_universe = 22.0 J/K + (-19.6 J/K)
ΔS_universe = 2.4 J/K

Therefore, the change in entropy of the universe is +2.4 J/K. Thus, the correct answer is option c: +2.4 J/K.