Introduction:
A binary distillation column is a commonly used separation process in the chemical industry. It separates a binary mixture into its individual components based on their boiling points. The q-line represents the equilibrium relationship between the vapor and liquid phases in the column. The slope of the q-line indicates the relative volatility of the components.

Given Information:
- The binary distillation column is operating with a mixed feed containing 20 mol% vapor.
- The feed quality is changed to 80 mol% vapor.

Explanation:
1. Understanding the q-line:
- The q-line represents the equilibrium relationship between the vapor and liquid phases in the distillation column.
- It is a straight line on a composition diagram, connecting the compositions of the liquid and vapor phases in equilibrium.
- The slope of the q-line represents the relative volatility of the components. A higher slope indicates a higher relative volatility.

2. Effect of feed quality on the q-line:
- The feed quality is the fraction of the feed stream that exists as vapor.
- When the feed quality is changed from 20 mol% vapor to 80 mol% vapor, it means that the fraction of the feed stream existing as vapor has increased.
- This change in feed quality will have an effect on the q-line.

3. Change in slope of the q-line:
- When the feed quality is increased, the slope of the q-line also increases.
- This is because a higher feed quality leads to a higher vapor flow rate and a lower liquid flow rate in the column.
- The increased vapor flow rate and decreased liquid flow rate affect the composition of the liquid and vapor phases in equilibrium, resulting in a steeper q-line.
- The increase in slope indicates that the relative volatility of the components has increased.

Conclusion:
- The change in the slope of the q-line when the feed quality is changed from 20 mol% vapor to 80 mol% vapor is between 3.6 and 3.9.
- This indicates an increase in the relative volatility of the components in the binary distillation column.
- It is important to consider the effect of feed quality on the q-line when designing and operating distillation columns to ensure efficient separation of components.