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?
Look up the vapor pressure of H2O at various temperatuares. I assume you have a table in your text/notes; otherwise, you can look on the web. Look for a vapor pressure of 520 mm and the temperature that produces that will be the boiling point. WHY? Because boiling point is defined as the temperature at which the vapor pressure of a liquid is the same as atmospheric pressure.
is there any formula that I can use to find out the vapor pressure at a certain temperature without using the table?
Is there a formula used to calculate this problem, or should I only look at the table in my book?
To determine the approximate boiling point of water at a given air pressure, you can refer to a boiling point vs. atmospheric pressure chart or use a mathematical equation known as the Clausius-Clapeyron equation.
The boiling point of a liquid depends on the pressure applied to the liquid. As the pressure decreases, the boiling point also decreases. Conversely, as the pressure increases, the boiling point rises.
At sea level, where atmospheric pressure is approximately 760 mmHg, water boils at 100 degrees Celsius (212 degrees Fahrenheit). However, since you are at a certain elevation in a mountain range with an atmospheric pressure of 520 mmHg, the boiling point will be lower.
To find the approximate boiling point of water at 520 mmHg, you can use a boiling point vs. atmospheric pressure chart specific to water or use the Clausius-Clapeyron equation.
The Clausius-Clapeyron equation is:
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 (8.314 J/(mol·K)),
T1 and T2 are the initial and final temperatures respectively.
Assuming that the enthalpy of vaporization (ΔHvap) and the initial temperature (T1) are constant, we can simplify the equation as:
ln(P1/P2) = 1/T2 - 1/T1
Since you want to find the boiling point, we can assume that the final temperature (T2) is 100 degrees Celsius (373 Kelvin). Rearranging the equation, we get:
ln(520/760) = 1/373 - 1/T1
Now, solve for T1:
1/T1 = 1/373 - ln(520/760)
Taking the reciprocal of both sides:
T1 = 1 / (1/373 - ln(520/760))
Using a scientific calculator to solve this equation, you will find the approximate boiling point of water at an air pressure of 520 mmHg in the mountain range.