The measured volumetric flow rate of ethane at 10.0 atm absolute and 35^∘ C is 1.00 ×10^3 L / h.

step 1 You guys let's do problem 75. The first problem is we need to calculate the molar volume. For th

The measured volumetric flow rate of ethane at 10.0 atm...

Key Concepts

Compressibility Factor

The compressibility factor, denoted as z, is a dimensionless quantity that measures the deviation of a real gas from ideal behavior. A z value equal to 1 corresponds to an ideal gas, while deviations indicate the presence of intermolecular forces and non-ideal behavior. Calculating z is important for understanding how variables such as pressure and temperature influence the volume of a gas relative to the prediction of the ideal gas law.

Flow Rate Conversion for Real Gases

Flow rate conversion for real gases involves converting a measured volumetric flow rate into a molar flow rate and eventually into a mass flow rate while taking into account the non-ideal behavior of the gas. This process requires using corrected values for the molar volume, determined by equations of state such as the truncated virial equation, and the molecular weight of the gas. Understanding these conversion steps is crucial in applications where accurate monitoring and control of gas flow rates are necessary, especially under varying pressure and temperature conditions.

Truncated Virial Equation

The truncated virial equation is an equation of state that modifies the ideal gas law by including corrections for intermolecular interactions. It typically involves the inclusion of the second virial coefficient to account for deviations from ideal gas behavior, particularly at moderate pressures. This equation is useful for calculating real gas properties by approximating how pairs of molecules interact without resorting to a full virial expansion.

Second Virial Coefficient

The second virial coefficient quantifies the extent of pairwise interactions between gas molecules and is a measure of the deviation from ideal gas behavior. Its sign and magnitude indicate whether attractive or repulsive interactions dominate, and it is essential in the truncated virial equation for making corrections to the ideal gas law. This coefficient is particularly relevant in calculations that require a more accurate determination of molar volume and related properties under non-ideal conditions.

Transcript

00:01 You guys let's do problem 75.

00:04 The first problem is we need to calculate the molar volume.

00:09 For that we have the truncated viral equation of this state for non -ideal gas.

00:16 We can rearrange this equation of state for a specific volume.

00:21 This specific volume is equal to then rt divided by p, 1 plus bp divided by rt.

00:30 Now we need to calculate what is the what is the constant and the viral coefficient here b and everything else is given first of all let's get the critical temperature of ethan the critical temperature of ethan is 305 .4 kelvin and the critical pressure is 48 .2 atmosphere pressure for ethan now we can calculate the reduced temperature, tr.

01:08 Tr is as equal to the given temperature divided by the critical temperature.

01:14 Given temperature is 35 degrees celsius.

01:18 You need to convert it to kelvin skin divided by the critical temperature, 305 .4 kelvin.

01:25 So we can, the reduced temperature is 1 .009.

01:29 We can calculate the coefficient b0 is equal to 0 .083 minus 0 .422 divided by the critical divided by the reduced temperature to the power 1 .6 or 0 .083 minus 0 .422 divided by 1 .009 to the power 1 .6 which gives the coefficient b not as negative 0 .333 and another coefficient b1 is as equal to 0 .139 minus 0 .172 divided by t r to the power 4 .2 or 0 .139 minus 0 .172 divided by 1 .009 to the power 4 .2 or b1 is equal to negative 0 .0 to 66.

02:40 Therefore the viral coefficient is b is equal to r critical temperature divided by it pressure in the bracket b0 plus omega b1 eccentric factor omega let's calculate it 0 .082 1 liter mole inverse 1 is the gas constant critical temperature is 305 .4 kelvin critical pressure is 48 .2 atmospheric pressure b0 is 0 .0 is 0 .0 negative 0 .333, the eccentric factor for ethana 0 .098, and b1a 0 .0266.

03:44 And once we do this calculation, we will get the viral coefficient as negative 0 .1745 liter per mole.

03:54 Now we have this constant and we can then calculate what is the molar volume...

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