Find the specific latent heat of vaporisation of 1.25 g of nitrogen (in Jg -1 ), if it releases 250 Joules of heat when it condenses at its boiling point of 196° C.
200
Calculating Specific Latent Heat of Vaporisation
The question asks us to find the specific latent heat of vaporisation of nitrogen. We are given the amount of heat released when a certain mass of nitrogen condenses at its boiling point. The specific latent heat of vaporisation (or condensation) is defined as the amount of heat energy absorbed or released per unit mass during a phase change (from liquid to gas or gas to liquid) at a constant temperature (the boiling point).
Understanding Latent Heat of Vaporisation/Condensation
When a substance changes phase from liquid to gas (vaporisation) or from gas to liquid (condensation) at a constant temperature (its boiling point), it either absorbs or releases energy. This energy is called latent heat. Specifically:
- Vaporisation: Energy is absorbed by the substance to overcome the intermolecular forces holding the liquid together and change into a gas. This is called the latent heat of vaporisation.
- Condensation: Energy is released by the substance as the gas molecules come closer together to form a liquid. This is also related to the latent heat of vaporisation (the same amount of energy per unit mass is involved).
The relationship between the heat energy (\(Q\)), the mass of the substance (\(m\)), and the specific latent heat (\(L\)) is given by the formula:
\(Q = mL\)
Where:
- \(Q\) is the heat energy absorbed or released (in Joules, J).
- \(m\) is the mass of the substance (in grams, g, or kilograms, kg).
- \(L\) is the specific latent heat of vaporisation or condensation (in J/g or J/kg).
Applying the Formula to Nitrogen Condensation
We are given the following information:
- Mass of nitrogen, \(m = 1.25\) g
- Heat released during condensation, \(Q = 250\) J
- Boiling/condensation point of nitrogen = -196°C (This temperature information confirms the phase change is happening at the boiling point, but is not needed for the calculation itself, only the heat and mass are needed).
We need to find the specific latent heat of vaporisation, \(L\). We can rearrange the formula \(Q = mL\) to solve for \(L\):
\(L = \frac{Q}{m}\)
Step-by-Step Calculation
Substitute the given values into the rearranged formula:
\(L = \frac{250 \text{ J}}{1.25 \text{ g}}\)
Now, perform the division:
\(L = \frac{250}{1.25} \text{ J/g}\)
\(L = 200 \text{ J/g}\)
So, the specific latent heat of vaporisation of nitrogen is 200 Jg\(^{-1}\).
Verification with Options
Let's compare our calculated value with the given options:
- Option 1: 469 Jg\(^{-1}\)
- Option 2: 500 Jg\(^{-1}\)
- Option 3: 312.5 Jg\(^{-1}\)
- Option 4: 200 Jg\(^{-1}\)
Our calculated value of 200 Jg\(^{-1}\) matches Option 4.
| Quantity | Symbol | Value Given |
|---|---|---|
| Mass of Nitrogen | \(m\) | 1.25 g |
| Heat Released (Condensation) | \(Q\) | 250 J |
| Specific Latent Heat | \(L\) | ? |
Calculation summary:
\(L = \frac{Q}{m} = \frac{250 \text{ J}}{1.25 \text{ g}} = 200 \text{ J/g}\)
Revision Table: Specific Latent Heat Concepts
| Concept | Definition | Formula | Units |
|---|---|---|---|
| Latent Heat | Energy absorbed or released during a phase change at constant temperature. | \(Q\) | Joules (J) |
| Specific Latent Heat | Latent heat per unit mass of a substance. | \(L = Q/m\) | J/g or J/kg |
| Latent Heat of Fusion | Energy per unit mass for melting (solid to liquid) or freezing (liquid to solid). | \(L_f\) | J/g or J/kg |
| Latent Heat of Vaporisation | Energy per unit mass for vaporisation (liquid to gas) or condensation (gas to liquid). | \(L_v\) | J/g or J/kg |
Additional Information: Phase Changes and Energy
Phase changes, like melting, freezing, boiling, and condensation, involve energy transfer without a change in temperature. This is because the energy is used to change the potential energy between the molecules rather than increasing their kinetic energy (which corresponds to temperature). For example, during boiling, the energy supplied is used to break the bonds holding molecules in the liquid phase, allowing them to escape as a gas, instead of increasing the speed of the molecules.
- Vaporisation: Liquid absorbs latent heat to become gas. Molecules gain enough energy to overcome intermolecular forces.
- Condensation: Gas releases latent heat to become liquid. Molecules lose energy and intermolecular forces pull them together.
- Fusion (Melting): Solid absorbs latent heat to become liquid. Energy breaks down the rigid structure of the solid.
- Freezing: Liquid releases latent heat to become solid. Molecules arrange into a more ordered structure.
The specific latent heat is a property of the substance itself and depends on the type of phase change (fusion or vaporisation) and the specific substance (like water, nitrogen, etc.).
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