Introduction:
In the design of an absorber, it is important to understand the relationship between the operating line and the equilibrium curve. The plotting with mole ratio is a graphical technique that helps in determining the slope of the operating line.

Explanation:
The plotting with mole ratio method involves plotting the mole ratios of the liquid and gas phases on a coordinate system. This is done by taking the mole fraction of the solute or component of interest in the liquid phase on the x-axis and the mole fraction of the same component in the gas phase on the y-axis.

Slope of operating line:
The slope of the operating line represents the ratio of the liquid flow rate to the gas flow rate. It is an important parameter in the design of an absorber as it determines the efficiency of the mass transfer process. By plotting the mole ratios on a graph, the slope of the operating line can be determined by calculating the change in y-axis values divided by the change in x-axis values. Therefore, the correct answer is option 'A'.

Slope of equilibrium curve:
The slope of the equilibrium curve represents the ratio of the liquid phase concentration to the gas phase concentration at equilibrium. It provides information about the thermodynamic equilibrium between the liquid and gas phases. The slope of the equilibrium curve can be determined by calculating the change in y-axis values divided by the change in x-axis values for points on the curve.

Minimum and maximum number of trays:
The minimum and maximum number of trays in an absorber are not directly determined by the plotting with mole ratio method. These parameters are influenced by factors such as the desired separation efficiency, the flow rates of the liquid and gas phases, and the equilibrium relationship between the solute and the solvent. The minimum number of trays is determined by the required degree of separation, while the maximum number of trays is limited by practical considerations such as cost and space requirements.

Conclusion:
In summary, the plotting with mole ratio method is a graphical technique that helps in determining the slope of the operating line in an absorber design. The slope of the operating line is important for understanding the efficiency of the mass transfer process. However, the method does not directly determine the slope of the equilibrium curve or the minimum and maximum number of trays in the absorber. These parameters are influenced by other factors and considerations.