The vapour pressure of a liquid at 20 deg C is 0.57 atm but it raises to 0.65 at when the
temperature raises by 3 deg C . Calculate the enthalpy of vaporisation of this liquid (in
).

Ask by Schofield Reid. in Guyana

Nov 30,2024

Question

The vapour pressure of a liquid at 20 deg C is 0.57 atm but it raises to 0.65 at when the
temperature raises by 3 deg C . Calculate the enthalpy of vaporisation of this liquid (in
).

Ask by Schofield Reid. in Guyana

Nov 30,2024

UpStudy AI · Accepted Answer

To calculate the enthalpy of vaporization ($$ \Delta H_{vap} $$) of the liquid, we can use the Clausius-Clapeyron equation, which relates the change in vapor pressure with temperature to the enthalpy of vaporization:

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

Where:
- $$ P_1 $$ and $$ P_2 $$ are the vapor pressures at temperatures $$ T_1 $$ and $$ T_2 $$ respectively.
- $$ R $$ is the universal gas constant, approximately $$ 8.314 \, \text{J/(mol K)} $$.
- $$ T_1 $$ and $$ T_2 $$ are the absolute temperatures in Kelvin.

Given:
- $$ P_1 = 0.57 \, \text{atm} $$ at $$ T_1 = 20 \, \text{°C} = 293.15 \, \text{K} $$
- $$ P_2 = 0.65 \, \text{atm} $$ at $$ T_2 = 20 + 3 = 23 \, \text{°C} = 296.15 \, \text{K} $$

Now, we can plug in the values into the Clausius-Clapeyron equation:

1. Calculate $$ \ln\left(\frac{P_2}{P_1}\right) $$:

$$
\ln\left(\frac{0.65}{0.57}\right) = \ln(1.1404) \approx 0.1315
$$

2. Calculate $$ \frac{1}{T_2} - \frac{1}{T_1} $$:

$$
\frac{1}{T_2} - \frac{1}{T_1} = \frac{1}{296.15} - \frac{1}{293.15} \approx 0.003384 - 0.003410 \approx -0.000026
$$

3. Substitute these values into the Clausius-Clapeyron equation:

$$
0.1315 = -\frac{\Delta H_{vap}}{8.314} \times (-0.000026)
$$

4. Rearranging to solve for $$ \Delta H_{vap} $$:

$$
\Delta H_{vap} = \frac{0.1315 \times 8.314}{0.000026}
$$

5. Calculate $$ \Delta H_{vap} $$:

$$
\Delta H_{vap} \approx \frac{1.095}{0.000026} \approx 42115.38 \, \text{J/mol} \approx 42.12 \, \text{kJ/mol}
$$

Thus, the enthalpy of vaporization of the liquid is approximately:

$$
\Delta H_{vap} \approx 42.12 \, \text{kJ/mol}
$$
The enthalpy of vaporization of the liquid is approximately 42.12 kJ/mol.

The vapour pressure of a liquid at 20 deg C is 0.57 atm but it raises to 0.65 at when the
temperature raises by 3 deg C . Calculate the enthalpy of vaporisation of this liquid (in
).

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The vapour pressure of a liquid at 20 deg C is 0.57 atm but it raises to 0.65 at when the temperature raises by 3 deg C . Calculate the enthalpy of vaporisation of this liquid (in ).

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Latest Chemistry Questions

The vapour pressure of a liquid at 20 deg C is 0.57 atm but it raises to 0.65 at when the
temperature raises by 3 deg C . Calculate the enthalpy of vaporisation of this liquid (in
).