Question

Some hikers were climbing Mount McKinley and pitched camp part way up. While boiling eggs in water for breakfast, they noticed that the temperature of the boiling water was 85.0 °C. The ∆H(vap) of water is 40.7 kJ/mol. Atmospheric pressure at sea level is 760 torr. R = 8.314 ×10⁻³ kJ/mol･K. Calculate the atmospheric pressure (in torr) at their elevation.

Answer 1

To calculate the atmospheric pressure at the hikers’ elevation on Mount McKinley, we can use the Clausius-Clapeyron equation. By plugging in the temperature of boiling water on Mount McKinley (85.0 °C) and the ∆H(vap) of water (40.7 kJ/mol), we can solve for the atmospheric pressure at their elevation.

Step-by-step explanation:

At higher altitudes, the atmospheric pressure is lower, causing the boiling point of water to decrease. According to the information provided, the temperature of boiling water on Mount McKinley is 85.0 °C and the ∆H(vap) of water is 40.7 kJ/mol. To calculate the atmospheric pressure at their elevation, we can use the Clausius-Clapeyron equation:

ln(P2/P1) = (∆H(vap)/R) * (1/T1 - 1/T2)

Given that the temperature at their elevation is 85.0 °C, we can convert it to Kelvin by adding 273.15:

T1 = 85.0 °C + 273.15 = 358.15 K

From the equation, we can set P1 as the atmospheric pressure at sea level (760 torr) and T2 as 358.15 K. Plugging in the values, we can solve for P2, which represents the atmospheric pressure at their elevation:

P2 = P1 * e^[(∆H(vap)/R) * (1/T1 - 1/T2)]

Substituting the given values:

P2 = 760 torr * e^[(40.7 kJ/mol / (8.314 ×10^-3 kJ/mol･K)) * (1/358.15 K - 1/85.0 °C + 273.15 K)]

Calculating this expression would give us the atmospheric pressure at their elevation in torr.

Answer 2

The atmospheric pressure on top of Mt. Everest when water boils at a temperature of 70.0°C is approximately 671.29 torr.

Step-by-step explanation:

The boiling point of water is affected by the atmospheric pressure. At higher altitudes, the atmospheric pressure is lower, causing the boiling point of water to decrease. To determine the atmospheric pressure on top of Mt. Everest when water boils at a temperature of 70.0°C, we can use the vapor pressure of water at different temperatures and compare it to the given boiling temperature.

Using the given information, the ∆H(vap) of water, and the ideal gas law, we can calculate the atmospheric pressure in torr. First, we need to convert the given temperature to Kelvin by adding 273.15 to 70.0°C, which gives us 343.15 K. Next, we can use the Clausius-Clapeyron equation to calculate the vapor pressure of water at 343.15 K:

ln(P2/P1) = (∆H(vap) / R) * (1/T1 - 1/T2)

Since the boiling point of water at sea level is 100.0°C (373.15 K), we can use these values in the equation and solve for P2:

ln(P2/760) = (40.7 / 8.314 ×10⁻³) * (1/373.15 - 1/343.15)

Now, we can solve for P2 by multiplying both sides of the equation by 760:

P2 = 760 * e^[(40.7 / 8.314 ×10⁻³) * (1/373.15 - 1/343.15)]

Plugging in the values and solving, we find that P2 is approximately 671.29 torr. Therefore, the atmospheric pressure on top of Mt. Everest when water boils at 70.0°C is approximately 671.29 torr.