Physical Chemistry - vapor pressures

In summary, the question is asking for the temperature at which isopropanol and carbon tetrachloride have the same vapor pressure, given their respective boiling points and standard enthalpies of vaporization. The Clapeyron equation can be used to find this temperature, with the external pressure being 1 atm. The given information is enough to find any pressure and temperature pair for the two substances.
  • #1
belltos
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Homework Statement



At what temperature will isopropanol (Tbp = 82.5C) and carbon tetrachloride (Tbp = 76.7C) have the same vapour pressure? For isopropanol and carbon tetrachloride, the standard enthalpies of vaporization are 32.54 kJ mol-1 and 44.0 kJ mol-1, respectively.

Homework Equations


Clapeyron Equation?


The Attempt at a Solution


I don't really know how to get started.

Homework Statement




Homework Equations





The Attempt at a Solution



 
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  • #2
You are right about using Clapeyron equation.

What does boiling point mean? How is it related to vapor pressure?

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  • #3
The only relationship I know between boiling point and vapor pressure is that the boiling point is the temperature where the vapor pressure of a liquid is equal to external pressure.
 
  • #4
External pressure is 1 atm - that means you are given p1, T1 and vaporization enthalpy for each substance. That's enough to find any p2/T2 pair.
 
  • #5


To solve this problem, we can use the Clausius-Clapeyron equation, which relates the vapor pressure of a substance to its temperature and enthalpy of vaporization. This equation is as follows:

ln(P2/P1) = -(ΔHvap/R)((1/T2) - (1/T1))

Where P1 and P2 are the vapor pressures at temperatures T1 and T2 respectively, ΔHvap is the enthalpy of vaporization, and R is the gas constant.

In this case, we want to find the temperature at which the vapor pressures of isopropanol and carbon tetrachloride are equal. This means that P1 = P2, so we can rewrite the equation as:

ln(1) = -(ΔHvap/R)((1/T2) - (1/T1))

Now we can substitute in the values given in the problem:

ln(1) = -((32.54 kJ/mol)/(8.314 J/mol•K))((1/T2) - (1/T1))

We can simplify this to:

0 = -(3.9155)(1/T2 - 1/T1)

Next, we can rearrange the equation to solve for T2:

1/T2 = 1/T1 + (0/3.9155)

T2 = T1

So, at the same temperature, the vapor pressures of isopropanol and carbon tetrachloride will be equal. Therefore, the temperature at which this occurs is 82.5°C.
 

FAQ: Physical Chemistry - vapor pressures

1. What is vapor pressure?

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid form at a specific temperature. It is a measure of the tendency of a substance to escape from its liquid or solid state and enter the gas phase.

2. How is vapor pressure related to temperature?

As temperature increases, the vapor pressure of a substance also increases. This is because higher temperatures provide more energy for the molecules to overcome the attractive forces holding them in the liquid or solid state and escape into the gas phase.

3. What factors affect vapor pressure?

The main factors that affect vapor pressure are temperature, intermolecular forces, and the nature of the substance. Substances with weaker intermolecular forces have higher vapor pressures, while substances with stronger intermolecular forces have lower vapor pressures.

4. How is vapor pressure measured?

Vapor pressure can be measured using various techniques, such as the Knudsen effusion method, the static method, or the dynamic method. These methods involve measuring the rate of evaporation of a substance and using mathematical equations to determine its vapor pressure.

5. What is the significance of vapor pressure?

Vapor pressure plays a crucial role in many physical and chemical processes, such as evaporation, boiling, and condensation. It also affects the properties of mixtures, such as the boiling point and composition. In industrial and environmental contexts, vapor pressure is important for understanding the behavior and transport of substances in the gas phase.

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