Final answer:
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.