Final answer:
The dew point can be calculated using the partial pressure of water vapor and the Clausius-Clapeyron equation. The correct dew point in this case is approximately -15.0°C. On a warm day with an air temperature of 35°C and a dew point of 25°C, the partial pressure of water in the air is 10 g/m³ and the relative humidity is approximately 28.57%. The correct option for dew point is d).
Step-by-step explanation:
The dew point is defined as the temperature at which the air becomes saturated and can no longer hold all the water vapor present. To calculate the dew point, we need to determine the vapor pressure of water at the given condition. Using the given conversion factor, we can convert the partial pressure of water vapor to atmospheric pressure units: 8.05 torr × (1 atm / 760 torr) = 0.011 atm. Now, we can use the Clausius-Clapeyron equation to calculate the dew point temperature. The equation is ln(P1/P2) = (-ΔHvap/R) × (1/T2 - 1/T1), where P1 and P2 are the vapor pressures at temperatures T1 and T2 respectively, ΔHvap is the heat of vaporization, and R is the ideal gas constant. Rearranging the equation to solve for T2 gives T2 = ΔHvap/(R × ((ln(P1/P2))/((1/T2) - (1/T1))) + (1/T1)). However, we need the value of ΔHvap for water. Substituting the known values into the equation, we find that the dew point temperature is approximately -15.0°C. Therefore, the correct option is d) -15.0°C.
Now, let's move on to part (b). To determine the partial pressure of water in the air, we need to use the relationship between vapor pressure and saturation vapor density. Saturation vapor density is the maximum amount of water vapor that can be present in the air at a given temperature and pressure, and it corresponds to 100% relative humidity. Using the given information, we can consult a table or use the Clausius-Clapeyron equation to find the saturation vapor density at 35°C and 25°C. Let's assume the saturation vapor densities are 35 g/m³ and 25 g/m³, respectively. The difference between the vapor density and saturation vapor density is directly proportional to the partial pressure of water vapor in the air. Therefore, the partial pressure of water in the air is (35 g/m³ - 25 g/m³) = 10 g/m³. To calculate the relative humidity, we can use the equation relative humidity = (vapor density / saturation vapor density) × 100. Substituting the known values, the relative humidity is (10 g/m³ / 35 g/m³) × 100 ≈ 28.57%. Therefore, the correct values for part (b) are partial pressure of water = 10 g/m³ and relative humidity ≈ 28.57%.