Video: Change in the Entropy of the Universe during the Melting of Ice

The melting of ice is represented by the equation H₂O(s) ⟶ H₂O(l). The standard molar entropy change for this process is 22.1 J/K ⋅ mol and each mole of water absorbs 6.012 kJ from the surroundings. Calculate the change in the entropy of the universe when 1.00 mole of ice melts at −10°C.

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Video Transcript

The melting of ice is represented by the equation H₂O solid forming H₂O liquid. The standard molar entropy change for this process is 22.1 joules per kelvin per mole and each mole of water absorbs 6.012 kilojoules from the surroundings. Calculate the change in the entropy of the universe when 1.00 mole of ice melts at minus 10 degrees Celsius.

We can calculate the entropy change of the universe by adding together the entropy change of our system to the entropy change of our surroundings. In this case, our system is the ice that’s melting, and the surroundings is the environment around it. First, let’s find the entropy change for our system. We can do this by multiplying the standard molar entropy change for the melting of ice, which is 22.1 joules per kelvin per mole, by the amount of ice that’s melting, which is one mole. This gives us 22.1 joules per kelvin for the entropy change of our system.

Now, let’s calculate the entropy change of the surroundings. The entropy change of the surroundings will be equal to the heat that’s absorbed or released by the surroundings divided by the temperature. The question tells us that each mole of water absorbs 6.012 kilojoules from the surroundings. This means that energy in the form of heat is being transferred from the surroundings to the system. This means that the heat transferred by the surroundings is 6.012 kilojoules. You should be careful about the sign here. Heat is defined as positive when it’s absorbed. Because the surroundings gave off heat to the system, the sign of the heat here is negative.

Before we continue, let’s quickly convert the units of our heat from kilojoules to joules, so that it will later match the units in the entropy change of our system. We can do this conversion by multiplying by 1000, since there are 1000 joules in a kilojoule. This gives us 6012 joules. The temperature is minus 10 degrees Celsius. But we need this to be in units of kelvin. We can convert to kelvin by adding 273.15, which gives us 263.15 kelvin. This gives us the entropy change of the surroundings to be negative 22.84628 joules per kelvin.

We now have everything we need to calculate the entropy change of the universe. The entropy change of the system was 22.1 joules per kelvin, and the entropy change of the surroundings was negative 22.84628 joules per kelvin. This gives us negative 0.74628 joules per kelvin.

We should express our answers to three significant figures because the standard molar entropy change was given to three significant figures. So, the entropy change of the universe for the melting of ice at negative 10 degrees Celsius is negative 0.746 joules for kelvin. We know that our answer makes sense because the entropy change of the universe should be positive for a spontaneous process. And, ice does not melt spontaneously below zero degrees Celsius.

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