# Standard entropy of liquid lead at 500C?

• magnesium12
In summary: Entropy is not conserved; it can change with temperature.In summary, the standard entropy of liquid lead at 500C can be calculated using the equation ΔS(500) = S(298) + ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT, which takes into account the initial entropy at 25C. This is because entropy is a state function and the standard entropy is the change in entropy from the state of pure elements at 25C. The entropy can change with temperature, so the ∫(Cp(s)/T)dT term should be included in the calculation.
magnesium12

## Homework Statement

The standard entropy of lead at 25C is S(298)=64.80 J/Kmol.
The heat capacity of solid lead is Cp(s) = 22.13 + .01172T + 0.96x105T-2.
The heat capacity of liquid lead is Cp(l) = 32.51 - 0.00301T
Melting point is 327.4C
Heat of fusion is 4770J/mol.
Calculate the standard entropy of liquid lead at 500C.

## Homework Equations

ΔS(500) = S(298) + ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT
ΔS(500) = ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT

## The Attempt at a Solution

I'm just wondering which equation to use?
At first I thought the equation was just ΔS(500) = ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT but the question includes the standard entropy at 25C, so do I have to account for that too by using ΔS(500) = S(298) + ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT? But shouldn't the initial entropy not matter since entropy is a state function?
And if I do have to account for entropy at 25C, does that entropy stay the same up to the melting point so I wouldn't need to account for the ∫(Cp(s)/T)dT

magnesium12 said:

## The Attempt at a Solution

I'm just wondering which equation to use?
At first I thought the equation was just ΔS(500) = ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT but the question includes the standard entropy at 25C, so do I have to account for that too by using ΔS(500) = S(298) + ∫(Cp(s)/T)dT + ΔHfus/T + ∫(Cp(l)/T)dT?
Yes.
But shouldn't the initial entropy not matter since entropy is a state function?
When you are talking about the "standard entropy," you are talking about the change in entropy from the state of pure elements comprising the compound at 25 C.
And if I do have to account for entropy at 25C, does that entropy stay the same up to the melting point so I wouldn't need to account for the ∫(Cp(s)/T)dT
What would make you think this?

## 1. What is the standard entropy of liquid lead at 500C?

The standard entropy of liquid lead at 500C is 21.0 J/mol*K.

## 2. Why is the standard entropy of liquid lead at 500C important?

The standard entropy of a substance at a specific temperature provides important information about its molecular disorder and energy distribution, which can impact its physical and chemical properties.

## 3. How is the standard entropy of liquid lead at 500C measured?

The standard entropy is typically measured experimentally using calorimetry or through theoretical calculations based on thermodynamic principles.

## 4. How does the standard entropy of liquid lead at 500C compare to other substances?

The standard entropy of liquid lead at 500C is relatively low compared to other substances, such as water (70.0 J/mol*K) or carbon dioxide (213.6 J/mol*K).

## 5. Does the standard entropy of liquid lead at 500C change with pressure or volume?

No, the standard entropy is an intrinsic property of a substance and is not affected by pressure or volume changes. However, the standard entropy may change with temperature.

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