Question

The absorption factor can be increased by:

• A. Increasing both gas and solvent flow rates
• B. Decreasing both gas and solvent flow rates
• C. Decreasing gas flow rate and increasing solvent flow rate
• D. Increasing gas flow rate and decreasing solvent flow rate

Hint:

Remember the formula for the absorption factor \( A = L/(mV) \). To increase \( A \), you want to increase the numerator (\( L \)) and/or decrease the denominator (\( V \)).

Answer 1

The Correct Option is C

Step 1: Understand the definition of the absorption factor.
The absorption factor \( A \) is a dimensionless group used in the design and analysis of gas absorption columns. It is defined as the ratio of the slope of the equilibrium curve to the slope of the operating line. For a dilute solution and assuming a linear equilibrium relationship \( y^ = mx \) (where \( y^ \) is the mole fraction of the solute in the gas in equilibrium with the liquid having a mole fraction \( x \), and \( m \) is the slope of the equilibrium curve), the absorption factor is given by: \[ A = \frac{L/V}{m} = \frac{L}{mV} \] where:
\( L \) is the molar flow rate of the liquid solvent.
\( V \) is the molar flow rate of the gas stream.
\( m \) is the slope of the equilibrium curve (\( dy^/dx \)).
A higher absorption factor generally indicates better absorption of the solute from the gas into the liquid solvent. Step 2: Analyze the effect of gas and solvent flow rates on the absorption factor.
From the formula \( A = \frac{L}{mV} \), we can see how changes in \( L \) (solvent flow rate) and \( V \) (gas flow rate) affect \( A \), assuming \( m \) (which depends on temperature and the solute-solvent system) remains constant. Increasing solvent flow rate (\( L \)): If \( L \) increases while \( V \) and \( m \) are constant, the absorption factor \( A \) increases proportionally.
Decreasing gas flow rate (\( V \)): If \( V \) decreases while \( L \) and \( m \) are constant, the absorption factor \( A \) increases inversely proportionally.
Step 3: Evaluate each option based on the relationship \( A = \frac{L}{mV} \).
Option 1 (Increasing both gas and solvent flow rates): If both \( L \) and \( V \) increase, the effect on \( A \) depends on the magnitude of the increase. If they increase by the same proportion, \( A \) remains constant. If \( V \) increases more than \( L \), \( A \) decreases, and if \( L \) increases more than \( V \), \( A \) increases. Therefore, this option is not always true. Option 2 (Decreasing both gas and solvent flow rates): If both \( L \) and \( V \) decrease, the effect on \( A \) again depends on the magnitude of the decrease. If they decrease by the same proportion, \( A \) remains constant. If \( V \) decreases more than \( L \), \( A \) increases, and if \( L \) decreases more than \( V \), \( A \) decreases. Therefore, this option is not always true. Option 3 (Decreasing gas flow rate and increasing solvent flow rate): If \( V \) decreases (denominator decreases) and \( L \) increases (numerator increases), the absorption factor \( A = \frac{L}{mV} \) will definitely increase. Option 4 (Increasing gas flow rate and decreasing solvent flow rate): If \( V \) increases (denominator increases) and \( L \) decreases (numerator decreases), the absorption factor \( A = \frac{L}{mV} \) will definitely decrease. Step 4: Select the option that leads to an increase in the absorption factor.
Decreasing the gas flow rate and increasing the solvent flow rate will increase the absorption factor.