Solving a Vapor Pressure Problem: Find Hydrogen Volume at 23°C

In summary, the problem involves finding the volume of a hydrogen sample at a different temperature, assuming the barometric pressure remains constant. Using the equation PV/T = PV/T and plugging in the given values, the final volume is calculated to be 0.396 liters. The concept of barometric pressure is clarified and its role in finding the partial pressure of hydrogen gas is explained. Alternative methods for checking the accuracy of the answer are also discussed.
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Qube
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Homework Statement



A 425-mL sample of hydrogen is collected above water at 35°C and 763 torr. Find the volume of the
hydrogen sample when the temperature falls to 23°C, assuming the barometric pressure does not change. (vapor pressures of water : at 35°C, 42.2 torr ; at 23°C, 21.1 torr)

Homework Equations



Okay, we're looking a vapor pressure problem. Therefore the partial pressure of the gas above water is found by subtracting the vapor pressure from the total, barometric (?) pressure. I'm assuming that's what barometric pressure refers to in this problem - that the total pressure of 763 torr is the barometric pressure, and it doesn't change.

We're also looking at a problem that has three variables changing - the pressure (note the drop in vapor pressure) - the temperature (note the change in temperature stated in the problem) and the volume (the variable we're solving for). Therefore we should use PV/T = PV/T.

The Attempt at a Solution



Okay. Initial scenario:

Pressure of hydrogen gas is 763 torr - 42.2 torr.
Temperature = 35 + 273 K
Volume = 0.425 L

Final scenario:

Pressure: 763 minus 21.1 torr. (Barometric (total?) pressure does not change according to the problem.)
Temperature = 23 + 273 K
Volume = variable we're solving for.

Now, PV/T = PV/T. That's pretty simple and I just plugged it all into my graphing calculator.

V = 0.396 liters.

Questions:

1) I know I got the right answer. Is my line of reasoning and process right?

2) What exactly is barometric pressure? I think it's referring to total pressure within the closed system. This makes finding the partial pressure of hydrogen gas a lot easier because we can just do 763 (barometric pressure) minus the partial pressure of water vapor at whatever temperature instead of having to account for both changing barometric and vapor pressures at different temperatures.
 
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Is that right? 3) Is there a way to check if my answer is correct without just depending on the accuracy of my calculator?
 

Related to Solving a Vapor Pressure Problem: Find Hydrogen Volume at 23°C

1. How do I calculate vapor pressure?

To calculate vapor pressure, you will need the temperature, pressure, and the vapor pressure constant for the substance. The equation for calculating vapor pressure is: P = P° × e^(−ΔHvap/RT), where P is the vapor pressure, P° is the vapor pressure constant, ΔHvap is the enthalpy of vaporization, R is the gas constant, and T is the temperature in Kelvin.

2. What is the ideal gas law?

The ideal gas law is a mathematical equation that describes the relationship between pressure, volume, temperature, and the number of moles of a gas. It is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature in Kelvin.

3. How do I find the volume of hydrogen at 23°C?

To find the volume of hydrogen at 23°C, you will need to use the ideal gas law equation and solve for V. You will also need to know the number of moles of hydrogen, which can be calculated by dividing the mass of hydrogen by its molar mass. The temperature must be converted to Kelvin by adding 273.15 to the Celsius temperature.

4. What is the vapor pressure constant for hydrogen?

The vapor pressure constant for hydrogen is 13.81 kPa at 20°C. This value may vary slightly depending on the source, as it is an experimentally determined value.

5. How does temperature affect vapor pressure?

As temperature increases, so does the vapor pressure. This is because as temperature increases, more molecules have enough energy to overcome the intermolecular forces holding them in the liquid phase and escape into the gas phase, increasing the vapor pressure. Therefore, at higher temperatures, the volume of hydrogen will also increase at a faster rate.

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