Knowing that delta h vaporization for water is 40.7 kj/ mol calculate p vaporation of water at 37 degress
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Can't you use the Clausius-Clapeyron equation? You have delta H, you know T1 and T2 and P(at boiling point is 760 mm), calculate p at 37 C.
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To calculate the vapor pressure of water at 37 degrees Celsius, you can use the Clausius-Clapeyron equation, which relates vapor pressure to the enthalpy of vaporization, the temperature, and the gas constant. The equation is as follows:
ln(P2/P1) = (∆Hvap/R) * (1/T1 - 1/T2)
Where:
P1 = vapor pressure at temperature T1
P2 = vapor pressure at temperature T2
∆Hvap = enthalpy of vaporization
R = gas constant
T1 = initial temperature (in Kelvin)
T2 = final temperature (in Kelvin)
First, let's convert the temperature from degrees Celsius to Kelvin. The formula for converting Celsius to Kelvin is K = °C + 273.15.
Therefore, T1 = 37 + 273.15 = 310.15 K.
Now, we need to know the initial vapor pressure at this temperature (P1). In this case, we assume it to be the vapor pressure of water at its boiling point, which is about 100 degrees Celsius or 373.15 Kelvin. The vapor pressure of water at its boiling point is approximately 1 atmosphere or 101.325 kPa; you can use this value for P1.
Using the given values and substituting them into the Clausius-Clapeyron equation:
ln(P2/101.325) = (40.7 / R) * (1/310.15 - 1/T2)
Now, we can rearrange the equation to solve for P2:
P2 = 101.325 * e^[(40.7 / R) * (1/310.15 - 1/T2)]
The value for R in the equation is the ideal gas constant, which is approximately 8.314 J/(mol·K). So, substituting that into the equation:
P2 = 101.325 * e^[(40.7 / 8.314) * (1/310.15 - 1/T2)]
You can now calculate the value for P2 by substituting the final temperature (T2) into the equation and evaluating the expression.