Mercury is the only metal that is a liquid at room temperature. When mercury vapor is inhaled, it is readily absorbed by the lungs, causing significant health risks. The enthalpy of vaporization of mercury is 59.1 kJ/mol. The normal boiling point of mercury is 357°C.

What is the vapor pressure of mercury at 43°C? Assume the enthalpy of vaporization does not depend on temperature.

To calculate the vapor pressure of mercury at 43°C using the Clausius-Clapeyron equation, convert the given temperature and the boiling point to Kelvin, then apply the equation with the given enthalpy of vaporization and solve for the vapor pressure.

Explanation:

The question asks for the calculation of the vapor pressure of mercury at 43°C given that the enthalpy of vaporization is 59.1 kJ/mol and that the normal boiling point is 357°C. To find the vapor pressure at a temperature other than the boiling point, one can use the Clausius-Clapeyron equation:

P = P0 × exp(-ΔHvap / (R × (1/T - 1/T0)))

Where P is the vapor pressure at the desired temperature, P0 is the vapor pressure at the boiling point (which is 1 atm by definition at the normal boiling point), ΔHvap is the enthalpy of vaporization, R is the gas constant (8.314 J/mol·K), T is the temperature at which the vapor pressure is to be calculated (in Kelvin), and T0 is the normal boiling point (in Kelvin).

First, one needs to convert the temperatures from Celsius to Kelvin by adding 273.15 to each. T = 43°C = 316.15 K and T0 = 357°C = 630.15K. Then we can use the Clausius-Clapeyron equation to calculate P:

P = 1 atm × exp(-(59.1 kJ/mol) / (8.314 J/mol·K × (1/316.15 K - 1/630.15 K)))

After calculation, the resultant P will give us the vapor pressure of mercury at 43°C.

MerylStreep MerylStreep · Answer 2 · 2023-07-17T03:47:42-04:00

Final answer:

The vapor pressure of mercury at 43°C is approximately 7.65 Pa.

Explanation:

To calculate the vapor pressure of mercury at 43°C, we can use the Clausius-Clapeyron equation:

ln(P2/P1) = (ΔHvap/R) × (1/T1 - 1/T2)

Let P1 be the vapor pressure at the normal boiling point of mercury (357°C) and P2 be the vapor pressure at 43°C.
Substitute the given values into the equation: ΔHvap = 59.1 kJ/mol, T1 = 357 + 273 = 630 K, and T2 = 43 + 273 = 316 K.
Solve for ln(P2/P1) and convert it to P2 to find the vapor pressure at 43°C.

The vapor pressure of mercury at 43°C is approximately 7.65 Pa.

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