Calculating Heat of Fusion and Capacity for Water: 50g Ice to 22°C Liquid Water

Also, when converting grams to moles, you need to divide by the molar mass of water (18g/mol). So, your final answer should be 21.3kj. In summary, to convert 50g of ice at 0 degrees C to liquid water at 22 degrees C, you would need 21.3kj of heat. This is calculated by multiplying the heat capacity of liquid water (75.3 j/mol*k) by the change in temperature (22 degrees C), then adding the heat of fusion of water (6.01 kj/mol multiplied by 2.778 moles).
  • #1
Pinkchika88
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Homework Statement


the heat of fusion of water is 6.01 kj/mol. the heat capacity of liquid water is 75.3 j/mol*k. the conversion of 50g of ice at 0 degrees C to liquid water at 22 degrees C requires _____kj of heat.

The Attempt at a Solution


i converted grams of ice to mols and got 2.778
then i multiplied by the heat capacity of 75.3 and the change in temperature of 22
i then converted 4601.667j to 4.601kj and added the heat of fusion 6.01kj/mol
i got an answer of 10.611kj but my study guide says the answer should be 21.3kj and I am not sure where in my calculations i went wrong...could someone please help?
 
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  • #2
You are close.

Take note that the heat of fusion is given in units of energy per mole i.e. you need to multiply the 6.01 by the number of moles.
 

Related to Calculating Heat of Fusion and Capacity for Water: 50g Ice to 22°C Liquid Water

What is the heat of fusion of water?

The heat of fusion of water, also known as the enthalpy of fusion, is the amount of energy required to change one gram of solid water (ice) into liquid water at its melting point of 0°C.

Why is the heat of fusion of water important?

The heat of fusion of water is important because it is a crucial factor in determining the temperature at which ice will melt and water will freeze. It also plays a significant role in many industrial and environmental processes, such as melting and freezing of glaciers, sea ice, and ice caps.

What is the value of the heat of fusion of water?

The heat of fusion of water is 334 joules per gram (J/g) at its melting point of 0°C. This value is commonly used in scientific calculations and is considered a fundamental physical constant.

How does the heat of fusion of water compare to other substances?

The heat of fusion of water is relatively high compared to other substances, such as alcohol or oil, which have much lower values. This is due to the high amount of intermolecular forces present in water, which require more energy to break the bonds between water molecules in order for them to change from solid to liquid form.

Does the heat of fusion of water change under different conditions?

Yes, the heat of fusion of water can vary slightly depending on external factors such as pressure and impurities. For example, at higher pressures, the heat of fusion will decrease, meaning it will take less energy to melt ice. Additionally, impurities in water can also affect its heat of fusion, as they can disrupt the intermolecular forces and make it easier for the water to change from solid to liquid form.

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