Question

We have air (21% O2 and 79% N2) at 23 bar and 30 C. 4. What is the ideal molar volume (m^3/kmol)? a. b. What is the Z factor? What is the real molar volume?

Answer 1

Answer:

The  ideal molar volume is  $\frac{V}{n} =V_z= 0.001095 \ m^3/mol$  

The  Z factor is  $Z = 0.09997$

The  real molar volume is $\frac{V_r}{n} = V_k= 0.0001095\ \frac{m^3}{mol}$

Explanation:

From the question we are told that

    The pressure is  $P = 23 \ bar = 23 *10^5 Pa$

      The temperature is  $T = 30 ^ oC = 303 \ K$

According to the ideal gas equation we have that

          $PV = nRT$

=>      $\frac{V}{n}=V_z= \frac{RT}{P}$

Where  $\frac{V}{n }$ is the molar volume  and  R is the gas constant with value

            $R = 8.314 \ m^3 \cdot Pa \cdot K^{-1}\cdot mol^{-1}$

substituting values

            $\frac{V}{n} =V_z= \frac{ 8.314 * 303}{23 *10^{5}}$

             $\frac{V}{n} =V_z= 0.001095 \ m^3/mol$            

The  compressibility factor of the gas is mathematically represented  as

            $Z = \frac{P * V_z}{RT}$

substituting values        

          $Z = \frac{23 *10^{5} * 0.001095}{8.314 * 303}$

          $Z = 0.09997$

Now the real molar volume is evaluated as

         $\frac{V_r}{n} = V_k= \frac{Z * RT }{P}$

substituting values

             $\frac{V_r}{n} = V_k= \frac{0.09997 * 8.314 * 303}{23 *10^{5}}$

             $\frac{V_r}{n} = V_k= 0.0001095\ \frac{m^3}{mol}$