You are in a mountain range with atmospheric air pressure of 520 mmHg, and you wish to boil some eggs. What is the approximate boiling point of the water at this air pressure?
Use ln(p1/p1) = dHvap/R (1/T1-1/T2)
p1 = 522
p2 = 760
T1 = ?
T2 = 273.15
dHvap = 40,650
To determine the approximate boiling point of water at a specific atmospheric pressure, we can use the Clausius-Clapeyron equation:
ln(P1/P2) = (ΔHvap/R) * (1/T1 - 1/T2)
Where:
P1 = initial pressure (normal atmospheric pressure, 760 mmHg)
P2 = pressure at the mountain range (520 mmHg)
ΔHvap = enthalpy of vaporization (40.7 kJ/mol for water)
R = ideal gas constant (8.314 J/(mol*K))
Rearranging the equation to solve for T2:
T2 = (1 / ((ln(P1/P2) * R / ΔHvap) + (1/T1)))
Let's substitute the values into the equation:
P1 = 760 mmHg
P2 = 520 mmHg
ΔHvap = 40.7 kJ/mol = 40.7 * 10^3 J/mol
R = 8.314 J/(mol*K)
T1 = boiling point of water at normal atmospheric pressure (100°C or 373.15 K)
T2 = (1 / ((ln(760/520) * 8.314 J/(mol*K) / (40.7 * 10^3 J/mol)) + (1/373.15 K)))
Calculating this expression will give us the approximate boiling point of water at the given air pressure in the mountain range.
To determine the approximate boiling point of water at a given air pressure, we can use the relationship between atmospheric pressure and boiling point. This relationship is described by the Clausius–Clapeyron equation:
ln(P1/P2) = ΔHvap/R * (1/T2 - 1/T1)
Where:
P1 and P2 are the initial and final pressures respectively.
ΔHvap is the enthalpy of vaporization.
R is the ideal gas constant.
T1 and T2 are the initial and final temperatures respectively.
In this case, P1 is the atmospheric pressure at the mountain range (520 mmHg) and T1 is the boiling point of water at standard atmospheric pressure (100 °C or 373 K).
We can rearrange the equation to solve for T2:
T2 = 1/ ((1/T1) - (R/ΔHvap) * ln(P1/P2))
Given that the boiling point of water at standard atmospheric pressure is 100 °C or 373 K, and the atmospheric pressure at the mountain range is 520 mmHg, we can substitute these values into the equation:
T2 = 1/ ((1/373) - (R/ΔHvap) * ln(760/520))
Now we need to determine the ΔHvap value for water and the ideal gas constant (R) to calculate the boiling point at the given air pressure. The enthalpy of vaporization (ΔHvap) of water is approximately 40.7 kJ/mol, and the ideal gas constant (R) is approximately 8.314 J/(mol*K).
Substituting these values into the equation:
T2 = 1/ ((1/373) - (8.314/40.7) * ln(760/520))
Calculating this equation will give us the approximate boiling point of water at the given air pressure in the mountain range.