The latent heat of fusion for ice is 6.0 kJ/mole. In order to melt 36 g of ice (solid #H_2O#) at 0°C, how much energy is required?

Answer 1

#"12 kJ"#

The molar latent heat of fusion, which is an alternative name given to the enthalpy of fusion, tells you how much heat is required in order to convert a specific amount of a given substance, either a gram or a mole, from solid at its melting point to liquid at its melting point.

Ice is said to have a molar enthalpy of fusion equal to

#DeltaH_"fus" = "6.0 kJ mol"^(-1)#
This means that in order to melt #1# mole of ice at its normal melting point of #0^@"C"#, you must supply it with #"6.0 kJ"# of heat.
Now, your sample of ice has a mass of #"36 g"#, so the first thing to do here is to convert it to moles by using the molar mass of water
#36 color(red)(cancel(color(black)("g"))) * ("1 mole H"_2"O")/(18.015color(red)(cancel(color(black)("g")))) = "1.998 moles H"_2"O"#

You can now use the molar enthalpy of fusion as a conversion factor to help you figure out how much heat must be supplied to your sample

#1.998 color(red)(cancel(color(black)("moles ice"))) * "6.0 kJ"/(1color(red)(cancel(color(black)("mole ice")))) = color(darkgreen)(ul(color(black)("12 kJ")))#

The answer is rounded to two sig figs.

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Answer 2

To calculate the energy required to melt 36 g of ice, we first need to convert the mass of ice from grams to moles using the molar mass of water (H2O). Then, we can use the given latent heat of fusion to determine the energy required.

  1. Calculate the number of moles of ice: ( \text{Molar mass of water (H}_2\text{O)} = 18.015 , \text{g/mol} ) ( \text{Number of moles of ice} = \frac{36 , \text{g}}{18.015 , \text{g/mol}} )

  2. Use the given latent heat of fusion to calculate the energy required: ( \text{Energy required} = \text{number of moles of ice} \times \text{latent heat of fusion} )

Substitute the values into the equation: ( \text{Energy required} = (\text{number of moles of ice}) \times 6.0 , \text{kJ/mol} )

Finally, calculate the energy required in kilojoules.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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