Question

Carbon tetrachloride, \(\mathrm{CCl}_{4},\) has a vapor pressure of 213 torr at \(40 .^{\circ} \mathrm{C}\) and 836 torr at \(80 .^{\circ} \mathrm{C}\) . What is the normal boiling point of \(\mathrm{CCl}_{4} ?\)

Short answer

The normal boiling point of carbon tetrachloride (CCl4) is 77.8°C.

Step-by-step solution

Convert the given temperatures to Kelvin

To convert the given temperatures from Celsius to Kelvin, add 273.15 K to each temperature: T1 = 40°C + 273.15 = 313.15 K T2 = 80°C + 273.15 = 353.15 K

Convert the given vapor pressures to atmospheres

To convert the given vapor pressures from torr to atmospheres, divide each pressure by 760 torr/atm: P1 = 213 torr / 760 torr/atm = 0.2803 atm P2 = 836 torr / 760 torr/atm = 1.1000 atm

Set up the Clausius-Clapeyron equation

The Clausius-Clapeyron equation is as follows: \[\ln{\frac{P_2}{P_1}} = -\frac{\Delta H_\mathrm{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)\] Where \(P_1\) and \(P_2\) are the vapor pressures at temperatures \(T_1\) and \(T_2\), \(\Delta H_\mathrm{vap}\) is the enthalpy of vaporization, and \(R\) is the ideal gas constant (8.314 J/mol·K).

Rearrange the Clausius-Clapeyron equation to solve for ΔHvap.

We will rearrange the equation to solve the enthalpy of vaporization, ΔHvap : \[\Delta H_\mathrm{vap} = -R\left(\frac{1}{T_2} - \frac{1}{T_1}\right) \times \frac{\ln{(P_2/P_1)}}{\left(\frac{1}{T_2} - \frac{1}{T_1}\right)}\]

Calculate ΔHvap using the given values

Now that we have the appropriate equation, we can plug in the known values for T1, T2, P1, and P2 to find ΔHvap . \[\Delta H_\mathrm{vap} = -8.314\cdot\left(\frac{1}{353.15} - \frac{1}{313.15}\right)^{-1}\cdot \ln{\frac{1.1000~\text{atm}}{0.2803~\text{atm}}}\] ΔHvap ≈ 3.27 x 10^4 J/mol

Calculate the boiling point temperature at 1 atm pressure

Now that we have the enthalpy of vaporization, we can use the Clausius-Clapeyron equation to find the boiling point temperature (Tbp) at 1 atm pressure (Pbp). Rearranging the equation, we get: \[\frac{1}{T_\mathrm{bp}} = \frac{1}{T_1} + \frac{R}{\Delta H_\mathrm{vap}} \ln{\frac{P_\mathrm{bp}}{P_1}}\] Plugging in the known values, the equation becomes: \[\frac{1}{T_\mathrm{bp}} = \frac{1}{313.15} + \frac{8.314}{3.27 \times 10^4} \ln{\frac{1~\text{atm}}{0.2803~\text{atm}}}\]

Solve for the boiling point temperature and convert to Celsius

Now that we have the equation set up, we can solve for Tbp: \[T_\mathrm{bp} = \left(\frac{1}{313.15}+ \frac{8.314}{3.27 \times 10^4} \ln{\frac{1~\text{atm}}{0.2803~\text{atm}}}\right)^{-1} = 350.95~\text{K}\] Finally, convert the boiling point temperature from Kelvin to Celsius: Tbp = 350.95 K - 273.15 = 77.8°C So, the normal boiling point of carbon tetrachloride is 77.8°C.

Key concepts

Clausius-Clapeyron Equation

The Clausius-Clapeyron equation is an essential tool in chemistry used for modeling and predicting the phase transition between liquid and vapor states. It helps us determine how vapor pressure changes with temperature. This equation is particularly helpful in finding an unknown quantity when other values are provided, such as calculating the enthalpy of vaporization or the boiling point of a substance.
For Carbon Tetrachloride, solving the Clausius-Clapeyron equation allows us to understand how the vapor pressure increases with temperature, which leads to boiling. The equation appears as:

• \(\ln{\frac{P_2}{P_1}} = -\frac{\Delta H_\mathrm{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)\)

Where:

• \(P_1\) and \(P_2\) are the vapor pressures at temperatures \(T_1\) and \(T_2\).
• \(\Delta H_\mathrm{vap}\) is the enthalpy of vaporization (energy needed to convert a unit of substance from liquid to vapor).
• \(R\) is the ideal gas constant, 8.314 J/mol·K.

Ultimately, by manipulating this equation, we can solve for various properties of substances, indicating its power and utility in thermodynamic calculations.

Enthalpy of Vaporization

Enthalpy of vaporization is a critical thermodynamic property that represents the heat required to convert a liquid into a vapor at constant temperature and pressure. Understanding this concept is vital because it reflects how much energy a substance needs to transition into the gaseous state, directly affecting when boiling occurs.
Every substance has a unique enthalpy of vaporization, depending on the intermolecular forces present. For example, strong hydrogen bonds or ionic interactions typically require more energy to break compared to weaker Van der Waals forces.
In the context of the Clausius-Clapeyron equation, \(\Delta H_\mathrm{vap}\) is determined experimentally, and it plays a significant role in calculating boiling points as it allows us to assess how easily a liquid can become a gas. Larger values of \(\Delta H_\mathrm{vap}\) mean more energy is needed for vaporization, implying that the substance might boil at a higher temperature.

• To calculate \(\Delta H_\mathrm{vap}\), rearrange the Clausius-Clapeyron equation and insert known temperature and vapor pressure values.
• For the exercise, once calculated, \(\Delta H_\mathrm{vap}\) was approximately 3.27 x 10^4 J/mol for Carbon Tetrachloride.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid at a given temperature. It provides insight into the evaporation rate and volatility of a substance. A volatile substance has a high vapor pressure at a low temperature due to weak intermolecular forces.
Vapor pressure varies with temperature. As temperature increases, so does kinetic energy, resulting in more molecules escaping from the liquid to the gas phase, raising the vapor pressure. Hence, substances with higher vapor pressures at lower temperatures are considered more volatile and will boil quicker.
In practical terms, for substances like Carbon Tetrachloride, knowing the vapor pressure at different temperatures (213 torr at 40°C and 836 torr at 80°C) is crucial. It allows us to utilize the Clausius-Clapeyron equation to predict its boiling point. Understanding the behavior of vapor pressure in response to temperature changes helps us decipher the physical properties of liquids in various situations, like designing cooling systems or distillations.