Let's solve each part step by step as requested. --- ## 1. **Selectivity Calculation** **Given:** - Rate of desired product formation, \( r_D = 100 \) - Rate of undesired product formation, \( r_U = 20 \) **Formula:** \[ S_{D/U} = \frac{r_D}{r_U} \] **Calculation:** \[ S_{D/U} = \frac{100}{20} = 5 \] **Final Answer:** \[ \boxed{5} \] --- ## 2. **Space-Time (\(\tau\)) Calculation** **Given:** - Volume, \( V = 500 \) L - Flow rate, \( v_ = 100 \) L/min **Formula:** \[ \tau = \frac{V}{v_} \] **Calculation:** \[ \tau = \frac{500}{100} = 5 \text{ min} \] **Final Answer:** \[ \boxed{5~\text{min}} \] --- ## 3. **Half-Life (\( t_{1/2} \)) Calculation** **Given:** - Rate constant, \( k = .693 \) min\(^{-1}\) **Formula:** \[ t_{1/2} = \frac{\ln 2}{k} \] where \(\ln 2 \approx .693\). **Calculation:** \[ t_{1/2} = \frac{.693}{.693} = 1 \text{ min} \] **Final Answer:** \[ \boxed{1~\text{min}} \] --- ## 4. **Space Velocity (SV) Calculation** **Given:** - Volume, \( V = 10 \) L - Cross-section, \( A = 2 \) (since \( V = A \times L \)) - Flow rate, \( v_ \) (not specified in the image for this part, so use the general formula) ### **(a) Space Velocity (SV) as the Inverse of Space Time** **Formula:** \[ \text{Space Velocity (SV)} = \frac{1}{\tau} \] where \(\tau = \frac{V}{v_}\). So, \[ \text{SV} = \frac{v_}{V} \] If \( V = 10 \) L and \( v_ \) is known, plug in values; otherwise, leave in terms of variables. --- ### **Summary Table** | Calculation | Formula | Answer | |-----------------|------------------------------------|---------------| | Selectivity | \( S_{D/U} = \frac{r_D}{r_U} \) | \( 5 \) | | Space-Time | \( \tau = \frac{V}{v_} \) | \( 5~\text{min} \) | | Half-Life | \( t_{1/2} = \frac{.693}{k} \) | \( 1~\text{min} \) | | Space Velocity | \( \text{SV} = \frac{v_}{V} \) | Use values if known | --- **Let me know if you need further breakdown of the last part or clarification on any step!**