Clausius Clapeyron Equation of lead

In summary, the melting point of lead at atmospheric pressure is 327.0 degrees C, with a density decrease from 1.101 x 10^4 to 1.065 x 10^4 kg/m^3 and a latent heat of 24.5 kJ/kg. Using the Clausius-C equation, the estimated melting point of lead at a pressure of 100 atm is 600.754 K, assuming L/T(deltaV) is constant. This assumption would need to be verified for accurate results.
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Homework Statement



When lead is melted at atmospheric pressure the melting point is 327.0 degrees C, the density decreases from 1.101 x 10^4 to 1.065 x 10^4 kg/m^3 and the latent heat is 24.5 kJ/kg. Estimate the melting point of lead at a pressure of 100 atm.


Homework Equations





The Attempt at a Solution



Ok So i know how to get the right answer - which i think is 600.754 K as follows:

Clausius-C equation: dp/dT = L/T delta (V)

so i just say that delta p = L/T delta V delta T

Substituting in the values, I get the right answer..

My question is - why is this a valid move? surely it assumes L/T(deltaV) to be constant? Must it be?
 
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  • #2
Yes, it's assumed that this factor is constant. This is something you'd have to verify to make sure the calculation is accurate.
 

1. What is the Clausius-Clapeyron equation?

The Clausius-Clapeyron equation is a thermodynamic equation that describes the relationship between the vapor pressure and temperature of a substance. It is often used to predict the vapor pressure of a substance at different temperatures or to calculate the enthalpy of vaporization.

2. How is the Clausius-Clapeyron equation derived?

The Clausius-Clapeyron equation is derived from the combination of the ideal gas law and the Clausius-Clapeyron relation, which states that the rate of change of vapor pressure with respect to temperature is equal to the enthalpy of vaporization divided by the gas constant.

3. What is the significance of the Clausius-Clapeyron equation in chemistry?

The Clausius-Clapeyron equation is important in chemistry because it allows us to predict the behavior of substances at different temperatures, particularly in regards to phase changes between liquid and gas states. It is also useful in determining the stability of a substance and its boiling point at different pressures.

4. How does the Clausius-Clapeyron equation apply to lead?

The Clausius-Clapeyron equation can be applied to lead by using its vapor pressure and temperature data to calculate its enthalpy of vaporization. This information can then be used to understand the behavior of lead in different environments and predict its boiling point at different pressures.

5. Are there any limitations to the Clausius-Clapeyron equation?

While the Clausius-Clapeyron equation is a useful tool in predicting vapor pressure and phase changes, it does have some limitations. It assumes that the substance in question follows ideal gas behavior, which may not always be the case. It also does not take into account factors such as intermolecular forces and non-ideal behavior, which can affect the accuracy of its predictions.

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