Mass flow control and ideal gas calculation

[Enigmata]

Homework Statement

I have an experimental setup consisting of a 755ml stainless steel cylinder being fed with Hydrogen from atmospheric unitl 10 bar. I am using a Brooks Mass flow controller to measure and control the flow of Hydrogen into the cylinder while at the same time recording the flow rate. Once flow stop a separate pressure transmitter indicates 10 bar pressure, therefore the cylinder should be full. The recorded amount of Hydrogen show 12.8L.

Homework Equations

In order to prove the above, I have done the following calculation:
T=297.15K P=1000kPa Z=1.001 R=8.314472*J/K/mol MM=2.0158gm/mol V=0.755L
Z=Hydrogen compressability factor
R_h= R/MM=4.1246155*J/K/mol

n=(P*V)/(Z*R_h*T)
n=0.615 mol
mass=MM*n=1.241x10^-3kg

The Attempt at a Solution

However I want to know the actual gas volume in liters in the cylinder, therefore
Volume=Mass/Density
= 1.241x10^-3kg/0.08988g/L
=13.8L

The result is out with 1 liter in this case, and increase much more as the pressure approach 100 bar. What am I doing wrong ?

 

[nate808]

Thank you for sharing your experimental setup and calculations. It seems like you have a good understanding of the principles involved in your experiment. However, there are a few things that might be contributing to the discrepancy in your results.

Firstly, it is important to make sure that all of your units are consistent. In your equation for n, you have used pressure in kPa and volume in liters, but in your attempt at a solution, you have used mass in kg and density in g/L. It would be helpful to convert all of your units to either SI units or to the units used in your other equations.

Secondly, it is important to consider the compressibility factor (Z) in your calculations. This factor takes into account the deviation of real gases from ideal gas behavior, which can become significant at high pressures. It is possible that your value for Z is not accurate enough, leading to the discrepancy in your results. You may want to consider using a more precise value for Z or conducting further experiments to determine a more accurate value.

Lastly, it is important to ensure that your experimental setup and equipment are functioning properly. There may be sources of error in your setup that are contributing to the discrepancy in your results. It may be helpful to repeat the experiment multiple times to see if you consistently get the same result, and to compare your results with other similar experiments.

I hope this helps in your understanding of your results. Keep up the good work in your scientific endeavors.

 

[Blueshift5]

It appears that you have used the ideal gas law to calculate the number of moles of hydrogen in your cylinder and then used the density of hydrogen at 1 bar to calculate the volume. However, at a pressure of 10 bar, the density of hydrogen will be different due to the increased pressure causing the molecules to be closer together. This means that the density will not be 0.08988 g/L at 10 bar, resulting in a different volume calculation.

Additionally, the calculation of the compressibility factor (Z) for hydrogen is not a straightforward task and can vary depending on the temperature and pressure conditions. It is possible that your calculated value of Z is not accurate, leading to a discrepancy in your final volume calculation.

I would recommend consulting a gas properties table specific to hydrogen at 10 bar to accurately calculate the volume of gas in your cylinder. Additionally, it may be helpful to double check your experimental setup and data collection methods to ensure accurate measurements.